Advances in Computational Fluid Dynamics of Mechanical Processes in Food Engineering: Mixing, Extrusion, Drying, and Process Optimization

Abstract

Mechanical processes such as mixing, extrusion, and drying are key operations in food engineering, with a significant impact on product quality and process efficiency. The increasing complexity of food materials—due to non-Newtonian properties, multiphase structures, and thermal–mechanical interactions—requires advanced modeling approaches for process analysis and optimization. Computational Fluid Dynamics (CFD) has become a vital tool in this context. This review presents recent progress in the use of CFD for simulating key mechanical operations in food processing. Applications include the analysis of fluid flow, heat and mass transfer, and mechanical stresses, supporting improvements in mixing uniformity, energy efficiency during drying, and optimization of extrusion components (e.g., shaping dies). The potential for integrating CFD with complementary models for system-wide optimization is also discussed, including challenges related to scale-up and product consistency. Current limitations are outlined, and future research directions are proposed.

1. Introduction

1.1. Background and Motivation

Mechanical processes are fundamental to modern food manufacturing, playing a decisive role in transforming raw materials into structured, shelf-stable, and sensorially acceptable products. Unit operations such as mixing, extrusion, and drying govern key physical attributes of food—such as texture, porosity, moisture distribution, and structural integrity—while simultaneously influencing nutritional quality and sensory perception. These processes are also central to technological efficiency, enabling continuous production, process intensification, and waste minimization strategies [1,2]. However, food systems present unique modeling challenges due to their inherent complexity, which often includes non-Newtonian, viscoelastic, or multiphase behavior. Traditional design and optimization approaches—relying primarily on empirical correlations or pilot-scale experimentation—frequently prove inadequate when applied to novel formulations, high-value ingredients, or non-conventional equipment geometries. As a result, there is growing demand for predictive, flexible, and cost-effective modeling tools capable of supporting innovation in both product and process development [3,4].

Computational Fluid Dynamics (CFD) has emerged as a powerful and versatile tool in food engineering, offering detailed insights into fluid flow, heat and mass transfer, shear stress distribution, and material deformation. Although CFD has been extensively applied in the context of thermal processes—such as pasteurization, sterilization, and baking—its use in mechanical unit operations, including mixing and extrusion, represents a rapidly expanding area of research and industrial application [4,5]. Over the past two decades, a growing number of studies have demonstrated the value of CFD for virtual experimentation, process optimization, and scale-up, significantly reducing dependence on costly and time-consuming pilot trials. Furthermore, the integration of CFD with complementary numerical techniques—such as the Discrete Element Method (DEM) and the Finite Element Method (FEM)—has extended its applicability to systems involving complex particle–fluid interactions and deformable food matrices [5].

The aim of this review is to provide a comprehensive and structured overview of CFD applications in mechanical food processing, with a particular focus on three critical operations: mixing, extrusion, and drying. These unit operations were selected due to their technical complexity, their central role in food structure formation, and the increasing volume of CFD-based research dedicated to their simulation and optimization.

This review paper aims to provide a comprehensive and up-to-date synthesis of advancements in CFD and mechanical process modeling applied to food engineering, with a specific focus on mixing, extrusion, and drying operations. The literature search was systematically conducted across major scientific databases, including, but not limited to, Scopus, Web of Science, and Google Scholar.

To ensure a broad yet relevant scope, the search strategy employed a combination of keywords and phrases, such as:

• “CFD food engineering”
• “food processing simulation”
• “mixing modeling food”
• “extrusion simulation food”
• “drying CFD food”
• “food process optimization”
• “rheology food modeling”
• “multiphase food flow”

Emphasis was placed on retrieving peer-reviewed journal articles, review papers, and highly cited conference proceedings published primarily within the last 5–10 years (2014–2024), to capture the most recent advancements. However, foundational and seminal works published earlier were also included where they provided essential context or historical perspective.

The selection process involved an initial screening of titles and abstracts to assess relevance to the stated scope of the review. Full-text articles were then retrieved and thoroughly evaluated for their contribution to the understanding and application of CFD and mechanical models in the specified food engineering operations. Particular attention was paid to studies presenting novel methodologies, significant improvements in predictive capabilities, and practical implications for process design and optimization.

The gathered information was then critically analyzed, synthesized, and organized into thematic sections to highlight key findings, identify emerging trends, discuss challenges, and propose future research directions in the field. This systematic approach ensures the comprehensiveness and reliability of the insights presented in this review.

1.2. Importance of Mechanical Processes in Food Engineering

Mechanical processes are fundamental in food engineering, transforming raw ingredients into structured, stable, and sensory-acceptable products by influencing their physical form, microstructure, and functional characteristics, thereby impacting production efficiency, nutrition, and organoleptic properties.

Key mechanical unit operations include:

• Mixing and Homogenization: Ensuring uniform ingredient distribution, texture control, and product stability (e.g., emulsions, doughs) [6].
• Extrusion: Combining thermal and mechanical energy to create texturized products like cereals, snacks, pasta, and meat analogues through continuous processing, shaping, and even encapsulation [7].
• Size Reduction and Shaping: Operations like cutting, grinding, and forming that impact product uniformity and subsequent processing [8].
• Mechanical Drying Assistance: Systems (e.g., fluid-bed, vibratory) that use airflow and mechanical agitation to enhance mass and heat transfer, reduce drying times, and prevent agglomeration [9].

These operations enable process intensification, increasing productivity, reducing energy consumption, and minimizing waste. For example, twin-screw extrusion allows in situ mixing, cooking, and shaping in a single unit. Mechanically induced structuring is crucial for novel food textures, such as fibrous plant-based meat analogues or aerated products like mousses [10]. Furthermore, mechanical processes affect food safety and shelf-life by controlling moisture content, water activity, and structural integrity. Their complex nature, involving interactions of mechanical forces, thermal effects, and material properties, necessitates advanced modeling tools like CFD for design, scale-up, and real-time control [11].

2. Overview of Mechanical Processes in the Food Industry

2.1. Classification of Mechanical Unit Operations

Mechanical unit operations in food engineering encompass a broad range of processes that involve the application of mechanical forces to transform raw or intermediate food materials into products with desired properties. These operations are integral to the structure formation, compositional uniformity, and functionality of food products, and are typically classified based on the type of mechanical action applied and the intended processing goal. Below is an overview of the main categories:

(a)

Size Reduction and Comminution

This group includes mechanical operations that decrease the particle size of solids or droplets to improve processability or modify texture. Subtypes include: cutting, slicing, grinding, and milling (e.g., in vegetable or meat processing), emulsification (e.g., in sauces or dairy systems), pulping and refining (e.g., in fruit/vegetable purees). These operations often involve high energy input and require control to avoid overheating or structural damage to sensitive ingredients [12].

(b)

Mixing and Homogenization

These processes involve the mechanical agitation of multiple components to achieve a uniform composition or distribution. They can be further classified as: solid–solid mixing (e.g., blending powders or granular ingredients), liquid–liquid mixing (e.g., emulsification), solid–liquid mixing (e.g., batter or dough preparation), gas–liquid or gas–solid mixing (e.g., aeration of foams or whipped products). Key mechanisms include convective transport, diffusion, and shear-induced deformation. Equipment examples: ribbon blenders, planetary mixers, high-shear homogenizers [13].

(c)

Shaping and Forming

Mechanical shaping processes confer the final geometry to food products and often influence their internal structure. Examples include: extrusion—combining mechanical and thermal energy to texturize and shape, moulding, sheeting, and stamping—common in bakery and confectionery, encapsulation and pelletizing—for controlled release or convenience [14].

(d)

Mechanical Drying Assistance

Mechanical forces are often used to enhance drying kinetics by improving mass and heat transfer or preventing agglomeration. These include: fluidized bed drying—where gas flow suspends and agitates particles, vibratory drying—where mechanical vibrations promote uniform drying and prevent sticking, spouted beds or mechanically stirred dryers—improving contact between food particles and hot air [15].

(e)

Mechanical Separation

This group involves the use of mechanical energy to separate components based on size, density, or phase. Major types include: centrifugation—separation of immiscible liquids or clarification, sieving and screening—classification of powders and particles, membrane-assisted mechanical filtration (e.g., tangential flow filters with dynamic agitation). Although typically considered physical separation techniques, these operations rely on carefully controlled mechanical parameters to be effective [16].

(f)

Transport and Conveyance

Mechanical handling systems are essential for moving raw materials and products throughout processing lines. Although not directly transforming product properties, these operations affect residence time, mechanical stress, and product integrity. Systems include: screw conveyors, belt conveyors, and pneumatic transport systems, often modeled with CFD for pressure drop and flow optimization [17].

2.2. Relevance to Product Quality, Safety, and Process Efficiency

Mechanical processes in food engineering are not only fundamental to the transformation of raw ingredients into consumable products but also play a pivotal role in ensuring product quality, microbiological and physical safety, and process efficiency. The ability to precisely control these operations directly affects the consistency, functionality, and overall consumer acceptability of the final product, while also determining resource utilization and environmental impact [18].

(a)

Product Quality and Functional Attributes

Mechanical operations such as mixing, extrusion, and shaping have a profound influence on the structural and rheological characteristics of food products. These attributes include:

• Texture and mouthfeel—determined by the degree of mixing, shear history, or expansion during extrusion.
• Homogeneity and stability—influenced by mixing intensity and residence time; insufficient mixing can lead to ingredient separation, while overmixing may cause structural breakdown.
• Microstructure formation—such as air incorporation in whipped products or matrix development in extruded snacks and plant-based meat analogues.

Mechanical forces affect protein denaturation, starch gelatinization, and fat crystallization—all of which contribute to the sensory properties and shelf-life of the product.

(b)

Food Safety and Process Hygiene

While mechanical operations are primarily physical in nature, they also contribute to food safety through:

• Reduction of microbial load—in some cases, such as extrusion, the combination of mechanical and thermal energy may reduce microbial populations.
• Prevention of contamination—through proper equipment design that avoids dead zones and facilitates cleaning.
• Uniform distribution of preservatives or critical ingredients, which supports consistent antimicrobial efficacy.

Poorly designed mechanical systems can create risk-prone areas where residues accumulate or where heat- and shear-sensitive nutrients degrade, leading to potential safety and quality issues [19,20,21].

(c)

Process Efficiency and Resource Optimization

From an industrial perspective, mechanical operations are among the most energy-intensive stages of food processing. CFD-assisted design and optimization can help:

• Reduce energy and water usage by improving mixing or drying uniformity,
• Minimize material losses by preventing product buildup or segregation,
• Enhance throughput and equipment utilization through better flow dynamics and reduced downtime.

For example, CFD can identify areas of flow stagnation or recirculation that increase processing time or energy demand. In extrusion, optimizing screw configuration and die geometry via CFD can improve throughput without sacrificing product quality.

(d)

Process Scalability and Reproducibility

A key challenge in food engineering is scaling up from laboratory or pilot scale to industrial production while maintaining product attributes. Mechanical processes are particularly sensitive to scale-dependent factors, such as flow regime changes, shear gradients, and heat generation.

CFD modeling allows for virtual scaling, where process parameters and geometry can be adapted to predict performance at larger scales. This improves reproducibility and reduces the risk of product failure during scale-up.

3. Fundamentals of CFD in the Context of Mechanical Processes

3.1. Governing Equations

CFD offers a robust mathematical and numerical framework for simulating fluid flow, heat transfer, and mass transport in food processing systems. At the heart of CFD lie the Navier–Stokes equations, which express the fundamental conservation principles of mass and momentum. However, the inherent complexity of food matrices and their transformation during mechanical processes often necessitates the integration of additional submodels, including those for turbulence, multiphase flow, and non-Newtonian rheology, to accurately capture real process behavior [22].

The continuity equation, which governs mass conservation, is expressed for incompressible fluids as:

$${\displaystyle \frac{\partial \rho }{\partial t}}+\nabla ·\left(\rho u\right)=0$$

For systems with constant density ρ, this simplifies to:

$$\nabla ·u=0$$

where $\rho$—fluid density [kg/m³], $u$—velocity vector [m/s], $t$—time [s]. The conservation of momentum is described by the incompressible Navier–Stokes equation:

$$\rho \left({\displaystyle \frac{\partial u}{\partial t}}+u\cdot \nabla u\right)=-\nabla p+\nabla \cdot \tau +\rho g$$

where $p$—pressure [Pa], $\tau$—stress tensor [Pa], $g$—gravitational acceleration vector [m/s²]. For Newtonian fluids, the stress tensor is defined as:

$$\tau =\mu (\nabla u+{\nabla u}^T)$$

with $\mu$—dynamic viscosity [Pa·s], ${\nabla u}^T$—transpose of the velocity gradient tensor. In non-Newtonian food systems, viscosity is often a function of shear rate, temperature, or time, requiring the use of rheological models such as the power-law or Herschel–Bulkley formulations to describe flow resistance under process-specific conditions.

When thermal effects are important—such as in extrusion, pasteurization, or high-shear mixing—the energy conservation equation is incorporated:

$$\rho c_p\left({\displaystyle \frac{\partial u}{\partial t}}+u\cdot \nabla T\right)=\nabla \cdot (k\nabla T)+\Phi$$

where

$c_p$—specific heat capacity at constant pressure [J/(kg·K)]

$T$—temperature [K]

$k$—thermal conductivity [W/(m·K)]

$\Phi$—viscous dissipation term [W/m³].

Turbulence, a key feature in many mechanical food operations—including high-speed mixing, extrusion preconditioning, and pneumatic transport—is generally modeled using approximation methods due to the computational expense of Direct Numerical Simulation (DNS). The most widely used approach is Reynolds-Averaged Navier–Stokes (RANS), which introduces time-averaged equations and requires turbulence closure models. The k–ε model, known for its robustness and computational efficiency, is widely applied under the assumption of isotropic turbulence. The k–ω model is a two-equation turbulence model that solves transport equations for turbulent kinetic energy (k) and specific dissipation rate (ω). It provides improved accuracy in predicting near-wall flows and boundary layer behavior, making it suitable for confined or wall-bounded geometries commonly encountered in food processing equipment. For greater fidelity, especially in capturing transient or large-scale eddies, Large Eddy Simulation (LES) resolves the larger turbulent structures while modeling the smaller scales, at the cost of higher computational demand. Detached Eddy Simulation (DES) offers a hybrid approach that combines RANS and LES, providing a balance between resolution and cost for geometrically complex systems like twin-screw extruders or baffled tanks. The choice of turbulence model depends on the flow regime, domain complexity, and mesh resolution. It is important to note that RANS models, although computationally efficient, may exhibit limited accuracy in food systems characterized by strong phase separation, such as emulsions or aerated structures, or those with complex non-Newtonian rheology. RANS models assume isotropic turbulence and often fail to capture transient, anisotropic eddies or flow instabilities critical to phase distribution and microstructure formation. In contrast, LES offers higher fidelity by resolving large-scale turbulent structures and accommodating localized flow features. However, LES requires fine mesh resolution and significantly greater computational resources, which can be prohibitive for large-scale or multiphase food processes. Therefore, the choice between RANS and LES should balance accuracy needs with practical constraints, especially when modeling shear-sensitive or structurally evolving food materials [23]. Multiphase flow modeling is often essential in food processing, where systems commonly involve coexisting solid, liquid, and gas phases. The EE (Euler–Euler) approach treats each phase as a continuous, interpenetrating medium, making it suitable for dense suspensions such as doughs, batters, or gas–solid fluidized beds. The EL (Euler–Lagrange) model, in contrast, tracks discrete particles or droplets within a continuous fluid phase and is especially effective for simulating mixing, emulsification, or spray processes. The Volume of Fluid (VOF) method is used to capture sharp interfaces between immiscible fluids—such as oil–water systems or foam generation—making it valuable in modeling surface evolution and interfacial dynamics [23]. Each multiphase modeling strategy requires the accurate specification of interphase forces, including drag, lift, and virtual mass, along with closure relationships to describe momentum, heat, and mass transfer between phases. These parameters are often derived empirically and must be validated against experimental data for each specific food system to ensure model fidelity.

3.2. Boundary Conditions, Mesh Generation, Solver Types

Accurate CFD simulations of mechanical processes in food engineering critically rely on precise definitions of boundary conditions, mesh topology, and numerical solver settings, all of which dictate numerical stability, convergence, and physical fidelity [24,25].

Boundary conditions are crucial for replicating operational environments, with typical applications including velocity inlets and pressure outlets for continuous flows, no-slip conditions at solid surfaces for viscous effects, and defined wall temperatures or heat transfer coefficients for thermal considerations [26]. Symmetry and periodic conditions can reduce computational load for repetitive geometries, while moving wall or dynamic mesh techniques are essential for systems with mechanical motion. Mesh generation, a pivotal aspect, involves choosing between structured meshes for simple domains and unstructured meshes for complex geometries like extrusion screws or baffled chambers, with fine resolution near walls being vital for capturing boundary layer phenomena in non-Newtonian materials. Dynamic meshing strategies such as sliding or overset meshes are employed for moving components, and mesh independence studies are routinely conducted to ensure solution accuracy [27]. The selection of numerical solvers is equally vital; pressure-based solvers are commonly used for incompressible food systems, while density-based solvers are reserved for compressible flows. Solver strategies can be segregated for weakly coupled systems or coupled for strong interdependencies, with transient solvers necessary for unsteady dynamics.

The accuracy and reliability of CFD simulations critically depend on mesh quality, which influences convergence behavior, computational efficiency, and the fidelity of predicted physical fields (e.g., velocity, temperature, and shear stress). Poor mesh resolution, especially in regions with high gradients or complex geometries, can lead to numerical diffusion, under-resolved boundary layers, or even divergence [28,29]. Different types of meshes are employed based on the geometry and nature of the simulation. Structured meshes offer high accuracy and efficiency for simple, orthogonal domains due to their regular topology. However, they are less suited for complex geometries typical in food processing equipment. Unstructured meshes, composed of tetrahedral, hexahedral, or polyhedral elements, provide greater flexibility for irregular domains but may require additional refinement and careful mesh quality control. Hybrid meshes, which combine structured and unstructured regions, are increasingly used to balance accuracy and computational cost [30]. For mechanical food processes involving moving parts—such as rotating impellers or screw elements—dynamic meshing techniques (e.g., sliding mesh or overset mesh) are essential to capture time-dependent interactions. Mesh refinement is particularly important near walls and interfaces, where boundary layers, shear gradients, or phase interfaces are present. Mesh independence studies are recommended to confirm that simulation results do not significantly change with finer mesh resolution [31].

Finally, spatial and temporal discretization schemes, along with numerical parameters like under-relaxation factors and convergence criteria, must be carefully tuned to maintain solver robustness, and rigorous experimental validation is paramount for establishing predictive reliability and model credibility [25].

3.3. CFD Models for Non-Newtonian and Viscoelastic Food Materials

Many food materials exhibit complex rheological behaviors that deviate significantly from the assumptions of Newtonian fluid dynamics. Products such as doughs, batters, purees, emulsions, and protein gels often demonstrate shear-thinning, viscoplastic, thixotropic, or viscoelastic properties. Accurate modeling of these behaviors is essential for realistic CFD simulations of food processing operations, including mixing, shaping, extrusion, and transport. Proper incorporation of non-Newtonian rheology into CFD models ensures reliable predictions of pressure drop, shear rate distribution, residence time, energy input, and temperature profiles. Failing to account for these behaviors can lead to incorrect process design and suboptimal product quality [32]. Food systems are typically classified into several categories of non-Newtonian behavior. Shear-thinning or pseudoplastic behavior, where apparent viscosity decreases with increasing shear rate, is common in sauces, dairy emulsions, fruit pulps, and starch-based formulations. Conversely, shear-thickening or dilatant behavior, characterized by an increase in viscosity with shear rate, is less common but can occur in concentrated starch slurries. Yield stress fluids—such as ketchup, mayonnaise, and chocolate—require a minimum stress threshold to initiate flow. Thixotropic materials, including certain gels and pastes, exhibit a time-dependent decrease in viscosity under constant shear. Finally, viscoelastic materials display both elastic and viscous responses, as seen in protein gels, gluten networks, and high-protein extrudates [33].

To accurately simulate these behaviors, CFD platforms must incorporate appropriate rheological models. One of the most widely used formulations is the power-law model:

$${\mu }_{app}=K\cdot {{\dot{\gamma }}^{n-1}}^{\dot{}}$$

where μ_app is the apparent viscosity, $K$ is the consistency index, $\dot{\gamma }$ is the shear rate, and $n$ is the flow behavior index. Although computationally efficient and suitable for shear-thinning fluids, this model lacks a yield stress component and becomes inaccurate at very low shear rates [34].

For materials that exhibit both shear-thinning and yield stress behavior, the Herschel–Bulkley model is preferred:

$$\tau ={\tau }_y+K\cdot {\dot{\gamma }}^n$$

Here, $\tau$ is the shear stress and ${\tau }_y$ is the yield stress. This model is appropriate for viscoplastic food systems such as tomato paste, meat emulsions, and chocolate. A simpler alternative is the Bingham plastic model:

$$\tau ={\tau }_y+{\mu }_p\cdot \dot{\gamma }$$

which assumes linear behavior beyond the yield stress and is often used to approximate the flow of materials that behave as solids until a threshold is exceeded where $\tau$—shear stress [Pa], ${\tau }_y$—yield stress [Pa], i.e., the minimum stress required to initiate flow, ${\mu }_p$—plastic viscosity [Pa·s], representing the slope of the stress–shear rate curve beyond yield $\dot{\gamma }$—shear rate [1/s], the rate of deformation of the fluid. Additional models such as the Casson model, commonly used for chocolate, and the Carreau–Yasuda and Cross models, which capture shear-thinning behavior across a broad range of shear rates, are also implemented in commercial CFD software like ANSYS Fluent, COMSOL Multiphysics, and OpenFOAM. The selection of a rheological model should be informed by experimental data obtained via rotational rheometry under conditions relevant to the process being modeled [33,35,36]. In systems where elasticity plays a significant role, such as during dough kneading, extrusion of gelatinous materials, or structuring of plant-based meat analogues, viscoelastic models are necessary to capture the material response accurately. The Maxwell model is used to describe linear viscoelastic fluids with stress relaxation characteristics, while the Kelvin–Voigt model accounts for time-dependent strain and instantaneous elastic recovery. More advanced models, such as Oldroyd-B and Giesekus formulations, are used in CFD simulations to predict time-dependent viscoelastic flow, particularly under complex flow fields in extrusion dies or shearing zones. These models require the inclusion of additional stress transport equations, making simulations more sensitive to numerical parameters such as mesh quality and time-step size, and significantly increasing computational costs. As a result, viscoelastic models are typically reserved for systems where texture development is critically dependent on elastic properties [37,38]. The selection of an appropriate rheological model for CFD applications in food engineering must balance several considerations. The accuracy of experimental data—particularly under realistic shear rates and temperature conditions—is essential for model calibration. The nature of the process also dictates model choice: shear-thinning models may be sufficient for high-shear processes such as extrusion, while yield-stress models are necessary for low-shear applications involving pasty or gel-like materials. Viscoelastic models are recommended only when elasticity plays a key role in the process outcome. Numerical stability is another important factor, as viscoplastic and viscoelastic models can cause convergence issues. Additionally, more complex models demand finer meshes, smaller time steps, and longer computational runtimes [39].

A practical example of viscoelastic model validation can be found in the CFD simulation of gluten-rich dough mixing. In this application, experimental data from oscillatory shear rheometry—used to characterize the dough’s storage (G′) and loss (G″) moduli—served as the basis for calibrating a generalized Maxwell model. The model was then applied in CFD to simulate flow and stress fields in a spiral mixer. Simulated velocity profiles and shear zones were compared with particle tracking velocimetry (PTV) measurements and torque data from pilot-scale trials, demonstrating good agreement and confirming the predictive capabilities of the viscoelastic model under realistic processing conditions [40].

3.4. Coupling with Other Simulation Tools (DEM, FEM, etc.)

While CFD is a powerful tool for simulating fluid dynamics, heat and mass transfer, and hydrodynamic forces, its predictive capabilities can be substantially enhanced through coupling with complementary numerical methods.

In food engineering, integration with approaches such as the DEM, FEM, population balance modeling, and data-driven algorithms allows for the simulation of multiphysics phenomena involving complex interactions among solid particles, fluids, deformable materials, and mechanical components. These hybrid modeling strategies are increasingly employed in the study and optimization of unit operations including mixing, extrusion, shaping, agglomeration, and drying [41]. Coupling CFD with DEM has proven particularly effective for systems involving particulate materials and fluid flow. DEM is a particle-based method that tracks the motion, collision, and contact forces of individual particles, while CFD models the surrounding fluid as a continuum. In the coupled CFD–DEM framework, the fluid phase is typically solved using an Eulerian approach, whereas the particle phase is described in a Lagrangian framework. Momentum exchange between the two phases is handled through interphase force models, including drag and pressure gradient terms. Applications in food processing include modeling mixing efficiency in solid–solid blenders, simulating fluidization behavior in drying chambers or spouted beds, and analyzing particle residence time and heat transfer in spray dryers. Despite its accuracy, CFD–DEM coupling is computationally demanding, especially when simulating large particle populations. Industrial-scale simulations often require the use of parallel computing and coarse-graining techniques to reduce the computational burden [9,42].

The FEM, on the other hand, is well suited for modeling the mechanical response of soft or deformable food materials. FEM allows detailed simulation of stress–strain behavior, material deformation, and structural integrity during processing. Coupling CFD with FEM enables the simulation of fluid–structure interactions (FSI), where deformation of food matrices influences flow fields and vice versa. Such coupling is critical in modeling phenomena like die swell during extrusion, shrinkage and collapse during convective or vacuum drying, and the deformation of gels or flexible molds during shaping. These coupled problems can be approached using monolithic solvers that simultaneously solve governing equations for both fluid and solid domains or through partitioned methods that exchange boundary data between CFD and FEM solvers. Tools such as COMSOL Multiphysics and Abaqus are commonly used alongside CFD platforms to perform these analyses [43,44]. Beyond DEM and FEM, other hybrid modeling strategies are gaining importance in food engineering. Coupling CFD with PBM (Population Balance Model) enables tracking of particle or droplet size distributions, coalescence, and breakage phenomena, which are essential in emulsification, crystallization, and agglomeration processes. CFD coupled with chemical kinetics allows for the simulation of simultaneous transport and transformation phenomena such as Maillard reactions, starch gelatinization, and protein denaturation during extrusion or thermal treatment. More recently, machine learning (ML) models have been trained on CFD-generated data to rapidly predict process outcomes and optimize operational parameters, significantly reducing computational requirements. Additionally, integration of CFD models with sensor data in real-time environments has facilitated the development of digital twin systems for predictive monitoring and control, aligning food manufacturing with Industry 4.0 paradigms [5,45].

Despite the growing utility of coupled simulations, several challenges remain. These include high computational demands, particularly in fully coupled or transient simulations, as well as the difficulty of ensuring compatibility between different solvers or software platforms. Hybrid modeling also increases the complexity of model validation, requiring extensive experimental data to confirm the accuracy of results across multiple domains. Nevertheless, the development of open-source platforms such as OpenFOAM for CFD and LIGGGHTS for DEM has increased accessibility and flexibility. Future directions in this area will likely include modular co-simulation environments, improved data exchange protocols, and integration with edge computing and AI technologies. These advances are expected to enhance the role of multiphysics modeling in smart food manufacturing and precision process control.

4. CFD Simulation of Mixing Processes

4.1. Types of Mixers and Their Working Principles

Mixing is a fundamental mechanical operation in food processing, serving to homogenize ingredients, disperse particulates, form emulsions or foams, and induce targeted microstructural transformations. The effectiveness of mixing depends not only on the operational parameters but also on the type of mixer and the rheological characteristics of the food material. The diversity of materials handled in the food industry—ranging from powders and slurries to viscous doughs and multiphase emulsions—has led to the development of a wide array of mixing technologies, each adapted to specific process requirements and physical states of the ingredients [44].

Mixers are commonly classified based on the phase composition of the processed material and the dominant mixing mechanism they employ. In solid–solid systems, ribbon blenders and paddle mixers are widely used. Ribbon blenders feature a horizontal trough with helical ribbons that rotate to create counter-current flows, whereas paddle mixers use flat or curved blades to move material in multiple directions. Both designs rely primarily on convective mixing and are well suited for fragile, dusty, or hygroscopic powders [46,47]. For high-viscosity and viscoelastic systems such as doughs and batters, planetary and spiral mixers are preferred. Planetary mixers utilize an agitator that rotates on its axis while orbiting around a central shaft, ensuring effective mixing throughout the bowl. Spiral mixers, characterized by a rotating spiral agitator and stationary bowl, are optimized for gluten development and hydration uniformity in bread doughs. These systems are widely adopted in bakery operations. High-shear mixers, including rotor–stator systems, are applied in processes requiring emulsification, dispersion, and droplet size reduction. The rotor rotates rapidly within a stationary stator, generating intense shear and turbulence that disrupt droplet structures and facilitate mixing of immiscible phases. These systems are common in the production of sauces, dairy emulsions, and mayonnaise [48]. In continuous operations, static mixers play a vital role. These devices contain stationary internal elements that divide and recombine flow streams, inducing mixing through flow redirection rather than mechanical agitation. Static mixers are energy-efficient and well suited for blending miscible liquids or introducing additives into flowing systems [49]. Tumbling mixers, such as V-blenders and double-cone mixers, operate by rotating a container filled with the material. Mixing is achieved by gravitational motion, making them ideal for gentle handling of delicate or abrasive solids. Although mixing rates are relatively low, these devices are advantageous in pharmaceutical and nutritional powder processing where minimal shear is desirable. Extruder-mixers, including single- and twin-screw configurations, integrate transport, mixing, and thermal processing in a continuous format. The geometry of the screw—defined by pitch, length, and mixing element design—determines the level of shear and residence time, which are critical parameters in thermomechanical applications such as snack production or plant-based meat extrusion. Finally, fluid and pneumatic mixers rely on gas flow (typically air or steam) to agitate solid or liquid systems. These are found in fluidized beds and bubble column reactors, where mixing is induced by the motion of gas bubbles through the material. Such systems are prevalent in drying and coating processes for snacks and cereals. The mechanisms underlying mixing can be broadly categorized as convective, diffusive, shear-induced, or turbulence-driven. Convective mixing involves the bulk movement of material from one location to another and dominates in systems such as ribbon and paddle mixers. Diffusive mixing arises from random particle motion and is particularly relevant in dry powder blending. Shear-induced mixing results from velocity gradients and is responsible for droplet breakup or structural modification, especially in rotor–stator and extrusion systems. Turbulent mixing, characterized by eddy formation and energy cascades, enhances mass and heat transfer in high-Reynolds-number flows. Flow patterns within mixers—ranging from laminar to turbulent—are determined by the Reynolds number, geometry of the mixing vessel, and material properties such as viscosity and density. Understanding these patterns is critical for accurate prediction of mixing efficiency, energy input, and thermal behaviour [50].

Mixer selection in food applications must consider material rheology, shear sensitivity, sanitation requirements, and operational mode. High-viscosity or yield-stress materials require high-torque mixing systems, whereas low-viscosity liquids benefit from high-speed agitation. Shear-sensitive materials, such as probiotics or enzymatic systems, demand gentle handling to avoid degradation. In hygiene-critical processes, such as infant formula or dairy production, mixers must support Clean-in-Place (CIP) procedures or be easily disassembled for thorough sanitation. Furthermore, batch mixers offer flexibility and control for small-scale or variable production, while continuous mixers provide greater throughput and consistency for large-scale operations [51]. A comprehensive understanding of mixing technologies and their underlying principles is essential for appropriate equipment selection and process design. When combined with CFD-based modeling of flow fields, shear zones, and residence time distributions (RTD), this knowledge enables the optimization of mixing performance and supports the development of high-quality, consistent food products.

4.2. CFD Modeling of Laminar and Turbulent Mixing

CFD provides a powerful framework for analyzing mixing processes in food engineering, enabling detailed visualization and quantification of flow characteristics such as velocity fields, shear zones, vorticity, and RTDs. Whether operating in laminar, transitional, or turbulent regimes, CFD delivers insights into mixing performance that are often inaccessible through experimental methods, particularly when working with opaque, heterogeneous, or shear-sensitive food systems.

Understanding flow behavior across different regimes is essential for designing efficient mixers, optimizing energy use, and ensuring consistent product quality [52]. In laminar mixing, flow is characterized by the dominance of viscous forces and an absence of turbulent fluctuations, typically occurring at Reynolds numbers below approximately 2000. This regime is common in high-viscosity food systems such as doughs, batters, emulsions, and pastes. Mixing in such systems is governed primarily by convective transport driven by impeller or screw rotation, shear-induced deformation of fluid layers, and limited molecular diffusion across interfaces. CFD models in the laminar regime can directly solve the Navier–Stokes equations without incorporating turbulence models, offering both computational efficiency and accuracy. For non-Newtonian fluids, shear-dependent viscosity models—such as the power-law or Herschel–Bulkley models—are implemented to accurately reflect the fluid’s rheological behaviour [53]. CFD simulations under laminar conditions provide key outputs including detailed velocity and shear rate distributions, which are particularly important for evaluating structural transformations in protein-rich or viscoelastic systems. Additional metrics such as mixing indices and the intensity of segregation help quantify spatial homogeneity, while RTD analysis supports process monitoring and control, especially in continuous systems. Optimization efforts in laminar mixing often focus on refining impeller geometry, adjusting rotation speeds, and improving baffle placement to reduce dead zones and enhance fluid circulation [54]. Turbulent mixing, by contrast, occurs at Reynolds numbers typically above 4000, where inertial forces dominate and the flow becomes chaotic and time-dependent. This regime is encountered in low-viscosity systems, including slurries, thin emulsions, and liquid–liquid dispersions processed in high-speed mixers such as rotor–stator devices or impeller-based reactors. Turbulence enhances mixing through the rapid generation and dissipation of eddies, which stretch and fold fluid elements, resulting in high shear rates and efficient macro- and micro-scale blending. These conditions are favorable for droplet breakup, solid dispersion, and rapid emulsification [55]. Due to the inherent complexity and computational cost of resolving turbulent flows, DNS is rarely feasible for industrial-scale systems. Instead, CFD relies on turbulence models to approximate the effects of turbulent fluctuations. The RANS models are the most widely used, with variants such as the k–ε model providing robust performance for high-Reynolds-number flows, and the k–ω model offering improved accuracy near walls and in confined geometries. The Reynolds Stress Model (RSM) allows for anisotropic turbulence modeling in swirling or complex flows. For more detailed resolution of transient mixing dynamics, LES is employed to capture large-scale turbulent structures while modeling the smaller eddies [56]. CFD simulations of turbulent mixing yield quantitative maps of turbulent kinetic energy (TKE), energy dissipation rates, and mixing time scales, all of which are essential for process optimization and scale-up. In multiphase systems, simulations also predict droplet or bubble size distributions and their evolution during mixing, supporting the design of emulsification or aeration processes. These outputs inform decisions on impeller type, rotational speed, fill level, and baffle configuration to achieve the desired mixing performance while minimizing energy consumption [57].

In practice, CFD modeling of laminar and turbulent mixing has been successfully applied across a range of food engineering applications, including the design and scale-up of vessels for sauces, creams, and batters; emulsification in high-shear devices; foam generation during whipping; and continuous powder–liquid mixing in inline homogenizers (Table 1). CFD has been used to optimize the mixing of high-viscosity doughs containing gluten and fiber, where conventional empirical approaches fail to capture the complex viscoelastic behavior. In industrial-scale planetary mixers, CFD simulations allow prediction of gluten network development and uniformity of hydration [58].

Optimization strategies typically involve iterative evaluation of geometry and process parameters. Increasingly, CFD results are integrated with statistical methods such as DoE (Design of Experiments) or machine learning models to identify key process drivers and improve robustness. Such hybrid approaches support faster development cycles, improved product consistency, and greater operational efficiency in both pilot- and industrial-scale mixing systems. This is exemplified in Figure 1, which shows CFD-predicted velocity fields and flow patterns in a stirred tank equipped with different baffle configurations, illustrating the impact of geometry on mixing intensity and vortex formation.

Figure 1. Velocity contour and flow field in a stirred tank equipped with sine baffles: (a) standard configuration; (b) modified impeller-baffle setup. Source: Zhou et al. (2022) [59] [Reproduced under CC BY 4.0 license from Appl. Sci. MDPI].

Figure 1. Velocity contour and flow field in a stirred tank equipped with sine baffles: (a) standard configuration; (b) modified impeller-baffle setup. Source: Zhou et al. (2022) [59] [Reproduced under CC BY 4.0 license from Appl. Sci. MDPI].

Table 1. Summary of mixer types, dominant mixing mechanisms, and applicable CFD modeling approaches.

Mixer Type	Mixing Mechanism	Typical Food Systems	CFD Modeling Approach	References
Ribbon blender	Convective	Powders, spices	RANS, steady-state, single-phase	[60]
Paddle mixer	Convective + shear	Granules, fragile solids	RANS, Eulerian, DEM coupling (optional)	[61]
Spiral/planetary mixer	Shear-induced, viscoelastic deformation	Doughs, batters	Laminar CFD, non-Newtonian, viscoelastic	[62]
Rotor–stator mixer	High shear, turbulence	Emulsions, sauces	Transient RANS or LES, VOF (for multiphase)	[63]
Static mixer	Flow redirection, laminar or turbulent	Liquids, miscible additives	Laminar or turbulent CFD, passive scalar	[64]
V-blender/double-cone	Gravitational, diffusive	Nutraceutical powders	Not typically modeled (quasi-static)	[65]
Twin-screw extruder mixer	Shear, distributive and dispersive mixing	Meat analogues, cereal doughs	Transient, moving mesh, non-Newtonian CFD	[66]
Fluidized bed mixer	Pneumatic agitation, collisions	Powders, granules (during drying)	Euler–Euler or CFD–DEM	[67]

Table 1. Summary of mixer types, dominant mixing mechanisms, and applicable CFD modeling approaches.

Mixer Type	Mixing Mechanism	Typical Food Systems	CFD Modeling Approach	References
Ribbon blender	Convective	Powders, spices	RANS, steady-state, single-phase	[60]
Paddle mixer	Convective + shear	Granules, fragile solids	RANS, Eulerian, DEM coupling (optional)	[61]
Spiral/planetary mixer	Shear-induced, viscoelastic deformation	Doughs, batters	Laminar CFD, non-Newtonian, viscoelastic	[62]
Rotor–stator mixer	High shear, turbulence	Emulsions, sauces	Transient RANS or LES, VOF (for multiphase)	[63]
Static mixer	Flow redirection, laminar or turbulent	Liquids, miscible additives	Laminar or turbulent CFD, passive scalar	[64]
V-blender/double-cone	Gravitational, diffusive	Nutraceutical powders	Not typically modeled (quasi-static)	[65]
Twin-screw extruder mixer	Shear, distributive and dispersive mixing	Meat analogues, cereal doughs	Transient, moving mesh, non-Newtonian CFD	[66]
Fluidized bed mixer	Pneumatic agitation, collisions	Powders, granules (during drying)	Euler–Euler or CFD–DEM	[67]

4.3. RTD and Mixing Indices

Assessment of mixing performance in food processing systems requires more than qualitative flow visualization or velocity field interpretation. Quantitative indicators such as RTD and mixing indices offer deeper insight into the uniformity of mixing, the time materials spend in equipment, and the consistency of the final product. CFD-based computation of these parameters is particularly valuable in food systems where experimental access is limited by factors such as opacity, stickiness, or compositional heterogeneity [68]. RTD characterizes the spread of time that fluid elements or particles spend within a processing unit. In food applications, RTD is critical for evaluating mixing uniformity, detecting dead zones and short-circuiting, and ensuring the reproducibility of continuous or semi-continuous operations, including extrusion and dough mixing. It also informs predictions of product quality in processes involving time-sensitive transformations such as enzymatic reactions, starch gelatinization, or protein denaturation. RTD is typically computed in CFD by introducing a passive scalar tracer and solving its transport equation, allowing the tracer’s outlet concentration profile to be tracked over time. Alternatively, particle-tracking methods may be used, where a population of massless particles is injected into the flow and their trajectories are recorded to extract residence time data [69]. From RTD simulations, several key descriptors can be derived. The mean residence time, denoted as tˉ, provides an average time fluid elements spend in the system. The variance of residence time reflects the degree of flow dispersion. The exit age distribution function, E(t), and the cumulative distribution function, F(t), describe the probability distribution of residence times and allow classification of the flow regime—ranging from ideal plug flow to well-mixed flow or intermediate cases involving back-mixing or channeling [70]. Mixing indices serve as quantitative measures of homogeneity and are especially important in processes requiring uniform ingredient distribution, phase dispersion, or texture development. One commonly used metric is the Coefficient of Variation (CoV), defined as:

$$CoV={\displaystyle \frac{\sigma }{\mu }}$$

where σ is the standard deviation and μ is the mean concentration of a given component in the mixing domain. Lower values of CoV indicate more homogeneous mixing. Another index is the Intensity of Segregation, I, calculated as:

$$I={\displaystyle \frac{{\sigma }^2-{\sigma }_{\infty }^2}{{\sigma }_0^2-{\sigma }_{\infty }^2}}$$

where σ₀ is the initial standard deviation, and σ∞ is the variance associated with perfectly mixed conditions. Additional indices such as the Mixing Efficiency Index (MEI) or the Scale of Segregation are used to evaluate the temporal or spatial progression of mixing in both batch and continuous systems [71]. CFD simulations enable the spatial and temporal mapping of these indices throughout the mixing equipment, allowing engineers to identify poorly mixed zones, optimal shear regions, and dynamic changes in non-steady-state operations. These insights are essential for improving mixing performance, especially when physical testing is constrained or impractical [72]. In industrial practice, CFD-based analysis of RTD and mixing indices has been applied to optimize screw configurations in continuous mixers and extruders, redesign impeller geometries and baffles to reduce ingredient segregation, and ensure uniform distribution of critical additives such as enzymes, salts, or micronutrients. For instance, in continuous dough mixing, variability in residence time due to inadequate screw design can result in non-uniform gluten development. In emulsification processes, uneven mixing may promote droplet coalescence, leading to phase separation and reduced product stability. Advanced simulations increasingly integrate RTD with reaction kinetics or rheological evolution models to predict coupled physical–chemical transformations, thereby supporting formulation and equipment decisions [73]. Despite their utility, CFD-based predictions of RTD and mixing quality must be validated with experimental data to ensure credibility. Common validation methods include tracer studies using chemical markers, flow visualization via MRI (Magnetic Resonance Imaging) or positron emission tomography (PET), and post-process statistical analysis of concentration distributions in batch mixing systems. Moreover, achieving reliable results requires ensuring mesh independence, proper solver settings, and realistic boundary conditions tailored to the specific system under investigation (

Table 2. Application of CFD Methods in Mechanical Food Processes.

Process	Dominant Physical Phenomena	CFD Modeling Approaches	Example Industrial Applications	Applications in Food Industry	References
Mixing	Laminar or turbulent flow Rotational motion, shearing, recirculation Dispersing multiple phases	Navier–Stokes (RANS, LES) Turbulence models: k-ε, k-ω, RSM Non-Newtonian fluid models (Power-law, Herschel–Bulkley) RTD & mixing indices CFD–DEM coupling	Emulsion homogenization Dough or batter mixing Inline blending in beverage and dairy industries	Quality control in sauces, batters, emulsions; Uniform ingredient distribution; Viscosity optimization	[75,76]
Extrusion	Thermo-mechanical coupling Shear-induced structuring Phase transitions (e.g., vaporization, expansion)	Coupled thermal–fluid simulations Non-Newtonian models (Herschel–Bulkley, viscoelastic) VOF for expansion CFD + reaction kinetics CFD–FEM for deformation	Expanded snacks, breakfast cereals Plant-based meat extrusion Optimization of die and screw configuration	Texturization of meat analogs; Control of porosity and expansion; Nutrient delivery modulation	[34,77]
Mechanically Aided Drying	Gas–solid interactions Heat and mass transfer Fluidization, vibration	Multiphase CFD (EE or EL) Evaporation and moisture transport models Turbulence: k-ε, LES CFD–DEM for particle motion	Fluidized bed and vibratory drying Powder drying (milk, coffee, flavors) Granule/agglomerate stabilization	Moisture reduction in powders; Shelf-life extension; Prevention of caking or collapse	[78,79]
Homogenization & Emulsification	High shear, cavitation Droplet breakup and dispersion Two-phase mixing	Rotor–stator CFD geometries Shear rate and energy dissipation modeling EL (for droplets) VOF for immiscible interface tracking	Mayonnaise and sauce emulsification Dairy product homogenization Emulsion stabilization processes	Stable emulsion formation; Reduced fat content products; Improved mouthfeel and rheology	[55,80]
Foaming/Aeration	Gas incorporation Bubble formation and stabilization Surface tension effects	EL or VOF (for bubbles) Surface tension and bubble coalescence models Turbulence: LES, RANS	Aerated desserts and whipped toppings Foam-based dairy and confectionery products	Structure control in mousses and whipped products; Sensory texture improvement; Gas volume consistency	[81,82]
Coating/ Agglomeration	Droplet–particle interaction Growth, coalescence, consolidation Moisture and heat transfer	CFD–PBM EL (droplet tracking) DEM for particle interactions Adhesion and wetting models	Instantized powders Flavor/encapsulation coating Agglomerated granules	Controlled release (flavors, nutrients); Improved solubility and dispersibility; Functional food coatings	[83,84]
Mechanical Conveying	Multiphase flow (solid–gas) Pressure drop and friction Shear-induced degradation or segregation	CFD–DEM coupling (e.g., screw conveyors) RANS for air–solid interactions Wall shear and slip analysis	Pneumatic transport systems Screw and belt conveyors Optimizing feed uniformity and throughput	Bulk material handling; Reducing breakage and segregation; Consistent throughput	[85]
Mechanically Mixed Reactors	Solid–liquid or gas–liquid mixing Oxygen or substrate transport Heat and shear interactions affecting biochemical reactions	Newtonian/non-Newtonian CFD models Mass transfer and oxygen solubility modeling Optionally coupled with kinetic or enzymatic models	Yogurt, kefir, or enzyme reactors Bioreactor design and scale-up	Fermentation optimization; Enzyme reaction control; Flavor and texture consistency in cultured products	[86]
Mechanical Cooling	Forced convection Air or fluid flow around products Heat removal efficiency	CFD with conjugate heat transfer Airflow turbulence models (k-ε, k-ω) Thermal gradient visualization	Cooling of bars, baked goods, or chocolate Design of tunnel coolers and refrigerated conveyors	Post-baking cooling; Chocolate tempering; Crystallization control	[87,88]
High-Shear Inline Processing	Extreme velocity gradients Energy dissipation Short residence time with rapid mixing/shearing	CFD for shear rate, turbulence intensity Inline geometry modeling RTD analysis	Inline emulsification Functional ingredient dispersion Continuous thermal/mechanical treatment	Rapid emulsification of dairy/fat mixtures; Inline processing of functional drinks; Minimization of microbial growth time window	[80]

) [74].

5. CFD in Extrusion Processes

5.1. Extrusion Mechanisms in Food Processing

Extrusion is a high-intensity thermomechanical process that transforms raw food materials into structured, texturized, and shelf-stable products by forcing them through a shaped die under precisely controlled conditions of heat, pressure, and shear. It integrates several unit operations—mixing, cooking, shaping, and expansion—into a single continuous system, making it one of the most versatile technologies in modern food processing. Common applications include the production of breakfast cereals, snacks, pasta, pet food, and increasingly, plant-based meat analogues. Understanding the underlying mechanisms of extrusion is essential for accurate process control, effective product design, and reliable computational modeling. These mechanisms arise from complex interactions between material properties, screw configuration, process parameters, and equipment geometry (Table 2) [34].

The extrusion process can be conceptually divided into several sequential zones. In the feeding and conveying zone, raw materials, typically in powder or granular form, are introduced into the extruder via a hopper. Here, the rotating screw transports the material forward, often resulting in compaction and increased bulk density, though no significant thermal transformations occur at this stage. In the compression and melting zone, the channel depth of the screw decreases, leading to increased pressure and shear. Mechanical energy is converted into heat, inducing partial melting or plasticization of the food matrix. Water within the system serves both as a lubricant and a medium for heat transfer, and under pressure, superheated steam may form [89].

As the material advances, it enters the mixing and homogenization zone, where shear elements or kneading blocks enhance both dispersive and distributive mixing, ensuring uniform temperature distribution and consistency. In twin-screw extruders, especially with co-rotating intermeshing screws, intense mixing is achieved through controlled residence time and precise flow management. Further along the barrel, thermomechanical energy initiates a series of physicochemical transformations—such as starch gelatinization, protein denaturation, lipid melting, and Maillard or enzymatic reactions—which are critical to the development of product texture, nutritional quality, and flavour [52].

In the final pressure build-up and shaping zone, the material is compressed against the die, creating the high-pressure conditions necessary for flow through the restricted orifice. Upon exiting the die, a sudden pressure drop triggers flash evaporation of water, causing the product to expand and acquire a porous structure. The extrudate is then shaped and cut to the desired length using rotating knives located at the die face. Subsequent cooling stabilizes the structure, preventing collapse or deformation and locking in the final texture [90].

Mechanical and thermal interactions within the extruder are highly coupled and non-linear. Shear forces generated by screw rotation promote mixing, reduce apparent viscosity, and contribute to internal heating via viscous dissipation. Friction between the material, screw, and barrel further elevates the temperature. External barrel heaters are used to establish and control temperature profiles, especially in low-moisture formulations. The rate and efficiency of heat and mass transfer are determined by the material’s viscosity, thermal conductivity, and specific heat capacity. Many food materials exhibit shear-thinning or viscoelastic behavior, adding additional complexity to the control and modeling of extrusion dynamics [91].

Screw design has a profound influence on process performance. Key parameters include screw diameter, pitch, and channel depth, as well as the configuration and sequence of conveying, mixing, and reverse elements. The screw speed and the length-to-diameter (L/D) ratio also affect energy input and residence time. Likewise, die geometry governs pressure drop, product expansion, and final shape. Small die openings typically result in higher pressures and greater expansion, while specialized geometries—such as annular or slit dies—can be used to produce layered or fibrous structures, as in the case of meat analogues. Multi-orifice dies enable co-extrusion or encapsulation of functional ingredients. The precise coordination of screw and die design is essential to achieve the desired structural, textural, and functional properties of the extrudate [92,93].

Extrusion accommodates a wide range of product types with distinct structural and functional objectives. Expanded snacks and breakfast cereals rely on steam-induced expansion and starch matrix setting to develop light, crispy textures. Pasta and noodles are produced via low-temperature, high-pressure extrusion, yielding dense, non-expanded products. In plant-based meat analogues, high-moisture or low-moisture extrusion techniques are applied to generate fibrous structures that mimic muscle tissue. Extrusion is also used to encapsulate bioactive compounds and flavors within biopolymer matrices, thereby protecting sensitive ingredients and enabling controlled release [94].

Despite its versatility, extrusion remains a challenging process to model due to its inherent complexity. The process is multiphase, involving solid–liquid–gas interactions; it features time- and temperature-dependent rheology, moving boundaries caused by rotating screws and deformable materials, and simultaneous chemical and physical transformations. These factors pose significant computational and experimental challenges, especially when aiming to simulate extrusion behavior under industrial conditions. Nevertheless, understanding the mechanisms of extrusion is foundational for advancing digital process modeling and simulation in food engineering [95,96].

5.2. Multiphase and Thermal Aspects in CFD Models

Food extrusion processes are inherently multiphase and thermomechanically complex, involving simultaneous interactions between solids, liquids, gases, and superheated vapors under dynamically changing and often non-isothermal conditions. Capturing this complexity in CFD simulations requires the integration of advanced multiphase flow models and robust thermal analysis that reflect the real behavior of heterogeneous food matrices. Key modeling considerations include the treatment of phase interactions, energy dissipation, moisture transport, and strong nonlinearities associated with material properties and transformations.

During extrusion, food systems typically consist of heterogeneous mixtures comprising starch, proteins, lipids, fibers, and water. These components interact through various phase phenomena, including solid–liquid dispersion, vaporization at the die exit, and bubble formation during sudden pressure drops. Modeling such systems necessitates appropriate multiphase CFD frameworks. The EE approach treats all phases as interpenetrating continua and is effective for dense mixtures or slurries. It is particularly suitable for predicting bulk pressure buildup and phase distribution along the screw channel. In contrast, the EL model tracks discrete particles or droplets within a continuous phase, making it appropriate for localized simulations of entrained air, vapor bubbles, or solid inclusions. The VOF method is employed when accurate tracking of sharp phase interfaces is essential, such as in the case of vapor–melt boundaries or product swelling at the die exit. Each of these modeling strategies requires appropriate interphase momentum exchange terms, including drag, lift, and virtual mass forces, as well as rheological descriptions tailored to the specific material phases involved.

Thermal effects are central to extrusion, as the process is highly non-isothermal and governed by both externally applied heat and internally generated thermal energy. Heat is supplied by barrel heaters and augmented by frictional forces and viscous dissipation within the screw channel. CFD models must solve the energy conservation equation in conjunction with mass and momentum balances. The generalized form of the energy equation used in CFD for extrusion processes is:

$$\rho C_p\left({\displaystyle \frac{\partial T}{\partial t}}+u\cdot \nabla T\right)=\nabla \cdot (k\nabla T)+\Phi$$

where ρ is the material density, Cₚ is the specific heat capacity, k is the thermal conductivity, and Φ is the viscous dissipation term. The inclusion of viscous heating is essential in high-shear zones, where mechanical energy is rapidly converted into heat, altering local temperature profiles. Since thermal properties of food materials are highly dependent on temperature and moisture content, variable-property models or empirical correlations are often needed to ensure accurate simulation.

A defining feature of extrusion is the phase change of water from liquid to vapor, particularly during the depressurization that occurs at the die exit. This transition drives product expansion and contributes to the formation of the porous structure characteristic of many extruded foods. Accurately modeling this phenomenon requires the incorporation of latent heat effects, evaporation kinetics, and coupled heat and mass transfer processes. Advanced CFD models implement phase-change source terms within the energy equation and simulate moisture transport through diffusion–convection equations. These models are capable of predicting critical process outcomes such as die pressure, expansion ratio, and residual moisture content, all of which influence product texture, density, and shelf stability.

Another important aspect of extrusion modeling is the rheological complexity of food materials, which typically exhibit non-Newtonian, temperature-dependent, and often viscoelastic behavior. Most food matrices demonstrate shear-thinning characteristics, while protein-rich or fiber-containing formulations may also exhibit yield stress and viscoelasticity. CFD simulations incorporate rheological models such as the Herschel–Bulkley or Carreau–Yasuda equations, which are calibrated against experimental data over a wide range of shear rates and temperatures. In multiphase systems, each phase may require an independent rheological description, and effective bulk viscosity is often estimated as a function of phase volume fractions and interaction dynamics.

Despite their advantages, multiphase and thermal CFD models present significant computational and experimental challenges. High-resolution meshes are required near screw elements and die regions to resolve steep gradients in velocity, temperature, and phase distribution. Thermal and rheological phenomena must be tightly coupled to maintain numerical stability, and validation is complicated by limited access to in-process data on internal pressure, temperature, and moisture. Often, only indirect validation is possible, for example by comparing predicted and observed expansion ratios, or final product moisture content. Fully coupled multiphase–thermal simulations are computationally demanding and may require model simplifications for practical use in industrial settings.

Nevertheless, the predictive capabilities afforded by such simulations are increasingly valuable in food engineering. They support the design of advanced screw and die geometries, optimize process parameters for targeted structural and sensory outcomes, and accelerate product development through digital prototyping. Their relevance is particularly pronounced in the growing fields of plant-based foods, high-protein snacks, and functional extrudates, where precise control of phase and thermal dynamics is essential for product quality and consumer acceptance.

5.3. Prediction of Pressure, Temperature, and Shear Profiles

Accurate prediction of pressure, temperature, and shear stress profiles along the extrusion barrel and die is essential for understanding the thermomechanical environment that shapes the final structure and properties of extruded food products. These physical parameters govern critical aspects of the process, including material flow, energy input, product expansion, moisture reduction, and textural development. CFD provides a robust and non-invasive means to simulate and visualize these fields with high spatial and temporal resolution, supporting process design, control, and optimization [74].

Pressure profiles along the extrusion screw are particularly important, as they determine the extent of material compaction, melting, and the force required to push the mass through the die. In CFD simulations, pressure gradients are obtained from the momentum conservation equations and are influenced by the screw geometry and configuration (including compression zones and kneading elements), the viscosity and flow resistance of the processed matrix, and the backpressure created by the die. Typically, pressure is low in the feeding zone, gradually increases through the compression and melting sections, and reaches a maximum at the die entry—often in the range of 5 to 20 MPa, depending on the product type and moisture content. CFD allows for virtual testing of different screw designs and die geometries, enabling optimization of pressure buildup and prevention of issues such as overpressurization, incomplete melting, or throughput fluctuations [57].

Temperature distribution within the extruder also plays a pivotal role, as many physicochemical changes—such as starch gelatinization, protein denaturation, and moisture vaporization—are thermally activated. CFD solves the energy balance equation to simulate temperature fields, accounting for external barrel heating, viscous and frictional heat generation, thermal conduction through the matrix, and latent heat associated with phase transitions. These simulations provide temperature maps across both axial and radial sections of the barrel, which help identify hot spots that may degrade nutrients or induce color changes, and cold zones where incomplete cooking or phase transitions can occur. Accurate modeling of thermal gradients is particularly relevant for maintaining product homogeneity and ensuring efficient expansion. CFD-based temperature profiles also support thermal validation and safety assessments, such as estimating lethality in pasteurized extrudates [97].

Shear stress and shear rate distributions are equally critical in extrusion processes, as mechanical deformation influences microstructural alignment, mixing efficiency, and energy dissipation. Shear stress (τ) is computed in CFD from local velocity gradients and the apparent viscosity of the food matrix using the following relationship:

$$\tau =\mu ({\gamma }^{\dot{}})\cdot {\gamma }^{\dot{}}$$

where μ(γ^̇) represents the shear-rate-dependent viscosity and γ^̇ denotes the local shear rate. This relationship is especially important for modeling non-Newtonian materials such as doughs, meat analogues, or protein-rich formulations, which exhibit shear-thinning, viscoplastic, or viscoelastic behavior. CFD simulations allow identification of high-shear regions—typically near barrel walls, screw surfaces, or narrow die channels—where energy input is concentrated. These zones play a key role in dispersive and distributive mixing, as well as in the alignment of fibrous structures in plant-based extrudates. However, excessive shear may lead to overprocessing or mechanical degradation of sensitive compounds, underscoring the importance of accurate shear modeling for texture control [98]. Figure 2 shows how nozzle diameter affects the shear rate distribution in syringe-based extrusion of rice paste, highlighting the influence of die geometry on flow behavior and material deformation during food 3D printing.

The practical value of simulating pressure, temperature, and shear profiles is well documented across industrial applications. CFD-based predictions support process optimization by enabling fine-tuning of screw speed, feed rate, moisture content, and barrel temperature to achieve desired structural and functional properties. They inform equipment design by guiding the selection and configuration of screw elements, die dimensions, and heating zones for consistent performance. Scale-up from laboratory to industrial scale—traditionally a trial-and-error task—benefits from CFD’s ability to replicate flow, thermal, and stress behavior across different geometries and operating conditions. Furthermore, simulations assist in troubleshooting by revealing processing anomalies, such as recirculation zones, localized overheating, or pressure instabilities, which may otherwise go undetected [100].

Although CFD provides powerful insights, accurate prediction of these key profiles depends on several factors. Reliable rheological and thermophysical property data—measured under relevant shear and temperature conditions—are critical for defining model parameters. Mesh quality, numerical schemes, and solver settings must be carefully selected to resolve sharp gradients and complex boundary layers. Experimental validation using thermocouple data, pressure sensors, or torque measurements remains essential to ensure the credibility of simulation outputs. Advances in real-time CFD integration, machine learning-assisted modeling, and digital twin development are likely to further enhance the role of pressure, temperature, and shear simulations in intelligent extrusion process control [101,102].

5.4. Coupling CFD with Reaction Kinetics and Product Texture Modelling

Food extrusion is a complex process that combines mechanical, thermal, and chemical transformations. Alongside mixing and shaping, extrusion induces temperature- and shear-dependent reactions that significantly affect the final product’s structure, nutritional quality, and sensory properties. To achieve predictive capability and process understanding, CFD can be coupled with reaction kinetics and texture formation models. This integrated approach enables the simulation of structure–process–property relationships and supports the design of extrusion conditions that deliver targeted product attributes, such as expansion, texture, and nutrient retention [73].

Among the key reactions occurring during extrusion are starch gelatinization, dextrinization, protein denaturation and aggregation, lipid melting, Maillard browning, and thermal degradation of sensitive compounds such as enzymes and vitamins. These transformations can be described using classical Arrhenius-type kinetics, where the temperature-dependent rate constant k(T) is given by:

$$k(T)=A\cdot exp\left(-{\displaystyle \frac{E_a}{RT}}\right)$$

where A is the pre-exponential factor, Eₐ is the activation energy, R is the universal gas constant, and T is the absolute temperature, typically obtained from CFD simulation outputs. The extent of reaction or conversion, denoted as α, can then be modeled using a general rate equation:

$${\displaystyle \frac{d\alpha }{dt}}=k(T)\cdot f(\alpha )$$

In this formulation, f(α) reflects the reaction mechanism or kinetics model, which may be first-order, autocatalytic, or diffusion-controlled. When coupled with CFD-derived profiles of temperature, shear rate, and residence time, these equations allow prediction of starch gelatinization levels (relevant to expansion and digestibility), protein unfolding and network formation (affecting texture), color and flavor development via Maillard reactions, and nutrient losses due to thermal degradation [98,103].

For example, Zhou and Langrish (2024) developed a coupled CFD–kinetics model to simulate the Maillard reaction during spray drying of dairy-based feed [104]. The model integrated local temperature and moisture profiles with first-order reaction kinetics and included both deterministic and stochastic modeling frameworks. Their predictions of browning intensity across the drying chamber correlated well with experimental Lab* color measurements, confirming the model’s capacity to forecast spatial non-uniformities in product appearance. This work exemplifies how CFD models, when coupled with thermal reaction kinetics, can be used not only for process optimization but also for predicting quality attributes like browning [104]. In an industrial baking context, Therdthai et al. (2004) developed a coupled 3D CFD–kinetic model to simulate starch gelatinization during the continuous baking of sandwich bread in a travelling-tray oven [105]. The model integrated simulated crumb temperature profiles with a first-order kinetic equation, allowing for time- and position-resolved predictions of gelatinization extent. Validation with experimental tray-scale variation confirmed the model’s predictive capability for baking progression and identified heat distribution asymmetries as key drivers of structural inhomogeneity. The model was also applied to test modified operating conditions, successfully predicting complete baking while reducing energy usage [105].

Texture formation in high-moisture extrusion of plant-based meat analogues, such as soy or pea protein systems, strongly depends on shear gradients and thermal transitions within the die. CFD has been coupled with viscoplastic and thermal models to simulate fiber alignment and anisotropic structure development, mimicking the fibrous texture of real meat. Studies by Emin et al. 2021 demonstrated how screw speed and die channel geometry influence shear-induced structuring, providing valuable guidelines for designing fibrous analogues with targeted mechanical properties [77,106]. Key mechanisms include shear- and extensional-flow-induced molecular alignment, thermal softening and subsequent setting of biopolymer matrices, and water evaporation leading to expansion and porous structure development. To simulate these effects, CFD can be integrated with viscoelastic and thermomechanical models describing the deformation behavior of complex biopolymer systems. Additionally, porosity evolution and bubble nucleation models are employed to predict structure formation during flash evaporation, while crust formation models may be used to describe setting phenomena at the die exit, particularly in high-temperature or high-shear regimes. A practical example is the modeling of fiber alignment in plant-based meat analogues, where the combined analysis of velocity gradients and shear stress fields within the die enables prediction of anisotropy and structural orientation that directly influence consumer perception and sensory acceptance [2].

The coupling of CFD with kinetic and texture models can be implemented through two main strategies. The most common is sequential coupling, in which CFD simulations are first performed to obtain temperature, pressure, shear, and residence time data. These outputs are then used as inputs for standalone kinetic or structural models implemented in platforms such as MATLAB, COMSOL, or via custom scripts. Alternatively, a fully coupled modeling approach involves solving the governing equations for fluid flow, heat and mass transfer, and reaction kinetics simultaneously within a unified numerical framework. Although more accurate and detailed, this method is computationally demanding and requires robust solver capabilities. Some commercial packages, such as COMSOL Multiphysics and ANSYS Fluent with user-defined functions (UDFs), support such multiphysics coupling, while others rely on co-simulation strategies or modular integration [78].

Integrated CFD–kinetic–texture models have been successfully applied to optimize die and screw configurations, predict expansion, crispness, and porosity in extruded snacks, control the degree of protein denaturation in high-protein products, and design plant-based analogues with defined fiber orientation and mechanical behavior. These models also facilitate identification of thermal hotspots that may compromise nutrient stability, supporting targeted process adjustments to minimize degradation. In industrial contexts, such tools are increasingly incorporated into digital twin systems, supporting real-time virtual prototyping and reducing the dependency on costly physical trials [107]. In the production of plant-based meat analogues via high-moisture extrusion, CFD simulations—when coupled with rheological and thermal data—enable prediction of fibrous alignment within soy or pea protein matrices, thus allowing texture tuning and consumer acceptability optimization [108,109].

Despite their potential, coupled simulations face several challenges. Accurate parameter estimation—such as activation energies, pre-exponential factors, or viscoelastic moduli—requires experimental measurements under process-relevant conditions. Computational cost remains a barrier, especially for three-dimensional, transient, or multiphase simulations. Furthermore, the validation of predicted conversion rates, structural features, or textural attributes demands reliable in situ measurements, which may require advanced techniques such as near-infrared spectroscopy (NIR), MRI, or mechanical texture analysis [110].

6. CFD Analysis of Drying as a Mechanically Aided Process

6.1. Fluid-Bed Drying and Spray Drying as Coupled Heat-Mass Transfer and Mechanical Systems

Drying is a fundamental unit operation in food engineering, essential for improving product shelf life, microbiological stability, and handling characteristics. Among the most widely used drying methods are fluid-bed drying and spray drying, which integrate thermal and mechanical phenomena within inherently multiphase systems. The application of CFD provides valuable insights into these processes by enabling detailed analysis of airflow behavior, particle or droplet motion, temperature and moisture distributions, and mechanical agitation—variables that are often challenging to measure directly (Table 2) [74].

CFD simulations of spray drying processes for dairy emulsions, such as infant formula or milk protein concentrates, enable prediction of droplet trajectories, temperature gradients, and zones susceptible to wall deposition. Langrish et al. (2020) applied Lagrangian–Eulerian modeling to a lab-scale spray dryer and identified how airflow asymmetries caused incomplete drying and powder loss [111]. These insights support chamber design modifications that improve hygienic performance and powder yield in industrial dairy powder production [111].

Fluid-bed drying is based on suspending food particles in an upward stream of hot air, where the drag force exerted by the gas counterbalances the gravitational force. This creates fluid-like behavior of the solid phase, promoting efficient heat and mass transfer. Mechanical effects, such as vibration or pulsating airflow, are commonly employed to improve particle mobility and prevent agglomeration. Fluid-bed drying is widely applied in the processing of powders, pellets, and coated particles. CFD models typically use EL or EE frameworks to simulate gas–solid interactions, enabling prediction of particle velocities, residence times, temperature profiles, moisture reduction, and zones susceptible to agglomeration. Coupling CFD with the DEM allows for detailed representation of inter-particle collisions and granular bed behavior, especially important in high-throughput or vibration-assisted systems [112].

Spray drying, on the other hand, involves the transformation of liquid feeds into fine droplets, which are then rapidly dried in a hot gas environment. This process is characterized by strong coupling between heat and mass transfer, droplet dynamics, and chamber airflow. It is widely used in the production of dairy powders, flavorings, instant beverages, and encapsulated bioactives. CFD simulations of spray drying focus on droplet atomization, trajectory prediction via Lagrangian particle tracking, and modeling of evaporation kinetics as a function of local temperature, humidity, and vapor pressure. Advanced simulations may also account for phenomena such as droplet shrinkage, crust formation, internal moisture diffusion, and wall deposition, which are critical for ensuring product quality, maximizing yield, and maintaining hygienic operation [113]. Spray drying of dairy emulsions, such as infant formula or coffee creamers, benefits from CFD modeling to ensure uniform droplet drying and minimize wall deposition—critical factors for product safety and consistency [106,114].

A key aspect of both drying methods is the integration of mechanical factors with heat and mass transfer. In fluid-bed systems, mechanical agitation enhances mixing and drying uniformity, and CFD–DEM coupling is often employed to describe particle–particle interactions. In spray dryers, atomizers introduce swirling or turbulent velocity fields that significantly influence droplet dispersion and drying trajectories. Accurate modeling requires simultaneous resolution of Navier–Stokes equations, species transport equations for water vapor, energy equations for temperature fields, and motion equations for dispersed phases [115].

CFD-based modeling has been successfully applied to optimize industrial drying processes. In fluid-bed systems, simulations have helped improve airflow uniformity, reduce coating damage in agglomerated powders, and enhance thermal efficiency. In spray drying, CFD supports the design of chamber geometries that minimize wall fouling and improve powder recovery, as well as the selection of atomization parameters for better droplet control. These applications contribute to energy savings, improved product consistency, and more effective scale-up from laboratory to industrial systems [116].

Despite significant progress, several challenges remain in the CFD analysis of drying operations. High computational demands, especially when coupling with DEM or modeling individual droplet behavior in spray systems, limit practical implementation. Additionally, thermo-physical property data for complex food matrices are often lacking, and experimental validation of internal process variables remains difficult due to opacity and heterogeneity. Future developments are expected to focus on integrating CFD with real-time process control, using surrogate models enhanced by machine learning, developing multiscale frameworks linking droplet or particle microstructure with macroscopic behavior, and implementing digital twins for predictive maintenance and optimization [102].

6.2. CFD Modeling of Particle-Fluid Interactions

Particle–fluid interactions are central to numerous food processing operations, particularly those involving drying and mechanical transport, such as fluidized and spouted beds, spray drying, suspension mixing, and pneumatic conveying. These interactions critically influence heat and mass transfer efficiency, particle residence time, product uniformity, and final structural integrity. CFD provides a powerful framework for analyzing such multiphase systems, enabling detailed insights into flow behavior, particle dynamics, and coupled transport phenomena [117].

In food processing, particle–fluid systems exhibit diverse configurations. These include solid particles suspended in gas flows, as in fluidized beds; liquid droplets dispersed in air streams, as encountered in spray drying; gas–solid transport in pneumatic conveying; and solid–liquid suspensions such as starch or fiber dispersions in hydration tanks. The behavior of these systems is governed by a combination of particle characteristics (including size, shape, and density), fluid properties (such as viscosity, temperature, and velocity), and interfacial forces (e.g., drag, lift, and virtual mass effects). In dense particulate systems, particle–particle collisions and contact mechanics further complicate the flow regime and influence energy dissipation and mixing efficiency [112].

CFD offers several modeling strategies for particle–fluid interactions, selected based on the system’s concentration, scale, and flow regime. In the EE or two-fluid model, both the fluid and particulate phases are treated as interpenetrating continua. This approach is particularly suited to dense flows, such as those in fluidized or spouted beds, and relies on momentum exchange terms and drag force correlations, including those proposed by Gidaspow or Wen–Yu, to describe interphase interactions [118].

The EL model adopts a different strategy, treating the fluid as a continuum while tracking individual particles using Newton’s second law of motion:

$$m_p{\displaystyle \frac{{dv}_p}{dt}}=\sum F$$

where m_p is the particle mass, v_p is its velocity, and ∑F represents the sum of forces acting on the particle, including drag, buoyancy, gravity, and lift. This method is ideal for dilute systems and allows for detailed analysis of particle trajectories, deposition zones, and drying behavior—particularly relevant in spray drying and powder dispersion modelling [113].

In systems with intense particle–particle interactions—such as cohesive powders, vibrating beds, or granulation processes—CFD can be coupled with the DEM. DEM accounts for contact forces, friction, restitution, and cohesion during collisions, providing insight into mechanical stress distribution, agglomeration dynamics, and powder flowability [42].

Heat and mass transfer processes are tightly coupled with particle–fluid dynamics and are crucial for predicting product behavior during drying and transport. CFD models typically incorporate convective heat transfer using Nusselt number correlations, surface evaporation models for droplets or wet particles, and—in the case of porous or larger particles—intraparticle heat and moisture diffusion. In spray drying, models may also account for crust formation, which alters evaporation dynamics and affects particle morphology and product quality [119].

Practical applications of CFD in this context include predicting moisture front progression during fluidized grain drying, simulating droplet drying paths and wall deposition in spray dryers, and evaluating agglomeration risks under varying humidity and temperature conditions. Such models support optimization of process parameters, including air velocity, particle size distribution, inlet temperature, and chamber geometry [39].

CFD modeling of particle–fluid systems has been successfully employed across various food sectors. Notable applications include optimizing fluidized bed dryers for dairy powders, coffee, and spices; improving airflow and droplet dispersion in spray drying of emulsions and encapsulates; minimizing energy use and particle breakage in pneumatic conveying lines; and enhancing powder rehydration through controlled porosity development in agglomerated particles. These efforts contribute to more energy-efficient, uniform, and scalable processes [120].

Despite these advances, CFD modeling of particle–fluid interactions remains computationally intensive, especially in simulations using CFD–DEM coupling or large-scale Lagrangian tracking. Additional challenges include the limited availability of accurate thermophysical properties for food materials (e.g., thermal conductivity, cohesion parameters) and the difficulty of model validation due to the optical opacity and heterogeneity of food systems [41].

Future developments are expected to include hybrid modeling approaches that integrate CFD with machine learning algorithms or PBM to better capture agglomeration, droplet size evolution, and breakup. Emerging experimental techniques such as Particle Tracking Velocimetry (PTV), X-ray tomography, and MRI will support more robust model validation. Furthermore, the integration of CFD with real-time sensor data into digital twin frameworks may enable predictive and adaptive control of particle–fluid processes in next-generation food manufacturing environments [121].

CFD-based modeling of particle–fluid interactions thus plays a vital role in advancing the understanding and optimization of drying, mixing, and transport operations in food engineering. Its continued evolution—alongside developments in materials characterization, computing, and automation—will facilitate the design of efficient, high-performance, and quality-focused food processes [122].

6.3. Optimization of Drying Chamber Geometry and Air Flow

The geometric configuration of a drying chamber and the internal airflow patterns play a critical role in determining the efficiency, uniformity, and quality of food drying processes such as spray drying, fluidized bed drying, and spouted bed drying. Poor design may result in flow recirculation, wall deposition, non-uniform temperature distribution, particle agglomeration, and thermal degradation of the product. CFD has become an essential tool for analyzing and optimizing these systems, allowing detailed visualization of airflow, temperature, moisture gradients, and particle trajectories [123]. Figure 3 illustrates transient airflow behavior and mesh deformation in a spray drying chamber at different time steps, providing insight into the dynamic fluid–structure interaction and the importance of mesh resolution in unsteady CFD simulations.

• Role of Geometry in Drying Performance

Drying chamber geometry directly influences RTD, contact efficiency between drying air and product, and powder recovery. Key design goals include minimizing dead zones and flow separation, promoting uniform residence times, and preventing product fouling or wall deposition. Geometric parameters such as chamber height-to-diameter ratio, air inlet positioning, plenum and distributor plate design, cone angle, and exhaust duct orientation all contribute to drying performance. Even small geometric modifications can significantly alter airflow behavior and, consequently, product quality and energy consumption [124].

• CFD-Based Analysis of Airflow Dynamics

CFD simulations solve the Navier–Stokes equations coupled with turbulence models (e.g., k–ε, RANS, or LES) to provide a high-resolution picture of airflow dynamics within the chamber. These simulations offer insights into velocity fields, streamlines, TKE, and the formation of vortices or stagnation zones. In spray dryers, for instance, airflow may be axial, tangential (swirling), or radial; CFD helps determine the configuration that ensures optimal droplet dispersion, evaporation kinetics, and powder collection [123].

In fluidized bed systems, CFD is used to evaluate the uniformity of airflow through perforated distributor plates. Simulations help ensure balanced pressure drop, prevent channeling or slugging, and promote homogeneous suspension and mixing of particles. The analysis may also consider the effects of plenum shape and inlet geometry on air distribution and energy efficiency [125].

• Optimization Strategies Using CFD

Geometry optimization through CFD involves refining chamber contours, adjusting inlet nozzle orientation, and tuning plenum and exhaust designs to achieve desirable flow patterns. Specific strategies include:

• Reducing recirculation and energy losses through smoother transitions and optimized chamber tapers,
• Improving dispersion by selecting appropriate inlet angles and nozzle sizes,
• Enhancing drying uniformity with balanced airflow from distributor plates,
• Minimizing powder loss or fouling through optimized exhaust duct design.

Multi-objective optimization frameworks are often employed to balance competing goals, such as reducing energy consumption, minimizing residence time variance, and maximizing product quality. CFD results are frequently combined with DoE and response surface methodology to explore the design space efficiently and determine optimal process windows [73,83].

7. Process Optimization Through CFD Simulations

7.1. DoE and CFD

The integration of CFD with DoE methodologies offers a powerful framework for systematic and efficient process optimization in food engineering. While CFD provides detailed insights into transport phenomena—such as flow behavior, heat transfer, and mass diffusion—DoE enables the structured exploration of input variables and their interactions, facilitating the identification of optimal process conditions with a limited number of simulations [126].

By combining CFD and DoE, engineers can leverage high-resolution simulation data to build predictive models that reduce development time and cost while improving process understanding. This synergy is particularly valuable in applications involving nonlinear, multiparametric systems, where conventional trial-and-error approaches are inefficient or impractical [127].

In the context of CFD, DoE is used to efficiently explore the design space, quantify the impact of process parameters, and construct surrogate models or response surfaces that approximate CFD outputs. Typical experimental designs applied include full and fractional factorial designs, central composite and Box–Behnken designs for response surface methodology, Latin hypercube sampling (LHS) for meta-modeling, and Taguchi methods for robustness analysis [128].

A standard CFD–DoE workflow begins with defining the optimization objectives (e.g., maximizing drying uniformity, minimizing energy consumption) and selecting key input parameters such as air velocity, temperature, nozzle geometry, or screw speed. Based on these factors, a design matrix is generated using DoE software platforms. CFD simulations are then performed for each design point, and the resulting data are analyzed using statistical tools such as analysis of variance (ANOVA) and regression modeling. The final step involves building predictive models and validating the identified optimum through high-fidelity simulation or experimental trials. This approach allows for multidimensional optimization while avoiding the computational burden of exhaustive parametric sweeps [129].

Applications of the CFD–DoE approach in food process engineering are diverse. In spray drying, it has been used to optimize inlet air temperature, feed rate, and droplet size to enhance powder quality and minimize wall deposition. In extrusion cooking, CFD–DoE models support the balance between energy efficiency and product texture by analyzing the effects of screw speed and barrel temperature. In mixing processes, this method helps identify the ideal impeller geometry and rotational speed for achieving uniform ingredient distribution in minimal time. In fluid-bed drying, it has been used to tune distributor plate configurations and airflow rates for energy-efficient operation without compromising product quality [130].

An illustrative example is the optimization of spray drying for probiotic powders, where CFD–DoE analysis revealed strong interaction effects between inlet temperature and feed rate on final moisture content and bacterial viability. Using a central composite design, a response surface model was developed with a prediction error below 5%, later validated in pilot-scale experiments [131].

The advantages of integrating DoE with CFD include a substantial reduction in the number of simulations or trials, improved understanding of parameter interactions, and the ability to construct predictive tools for control and scale-up. This integration also supports multi-objective optimization strategies, balancing factors such as quality, efficiency, and environmental impact [132].

Nonetheless, limitations exist. The accuracy of outcomes depends on the quality and resolution of CFD simulations, and computational cost can escalate with high model complexity or numerous factors. Additionally, response surfaces may struggle to capture highly nonlinear or discontinuous behaviors. These issues can be mitigated through adaptive sampling, hybrid DoE–AI strategies, or combining coarse and fine modeling approaches [133].

Looking forward, advances in CFD–DoE integration are expected to focus on automation, cloud-based computing, and real-time feedback loops. Automated optimization workflows that link CFD solvers with statistical tools and machine learning algorithms will enable broader adoption in industry. Integration with real-time sensor data and digital twin architectures will further enhance the capability of CFD-driven models to support agile, efficient, and data-informed food process development [134].

7.2. Sensitivity Analysis and Parameter Estimation

In computational modeling of food processes, sensitivity analysis (SA) and parameter estimation (PE) are essential tools for understanding the influence of uncertain input variables and for calibrating models to experimental or industrial data. Their integration with CFD enhances model robustness, reduces uncertainty, and improves predictive reliability across applications such as process optimization, scale-up, and real-time control. These techniques are especially important in food systems, where thermophysical and rheological properties—such as viscosity, diffusivity, or heat transfer coefficients—are often variable and difficult to measure directly, and where multiple coupled phenomena such as phase change or biochemical reactions occur [135].

• SA: Scope and Methods

SA quantifies how variations in input parameters influence model outputs. In CFD applications, this can help prioritize critical inputs, guide model simplification, and improve experimental planning. Two main categories of SA are commonly used:

• Local SA, which evaluates small perturbations of individual parameters using partial derivatives or finite difference methods. It is best suited for smooth, deterministic models but is limited in nonlinear or interactive systems.
• Global SA, which assesses variability across the entire parameter space using statistical techniques such as:

  ○

  Morris screening (qualitative ranking),

  ○

  Sobol’ indices (variance-based decomposition),

  ○

  Fourier amplitude sensitivity testing (FAST),

  ○

  LHS with regression or surrogate modeling.

• Global SA is particularly useful in complex CFD scenarios such as extrusion, spray drying, or fluidized bed systems, where nonlinear interactions between inputs are common [136].

• PE in CFD Models

PE involves identifying unknown model parameters by minimizing the difference between simulated and observed outcomes. In CFD-based food process models, PE is used to calibrate:

• Rheological laws (e.g., power-law, Herschel–Bulkley),
• Kinetic expressions (e.g., reaction rate constants, activation energy),
• Transport coefficients (e.g., diffusivity, evaporation rates),
• Boundary conditions (e.g., convective heat transfer coefficients).

PE problems are often formulated as optimization tasks, where the goal is to minimize an objective function, typically the sum of squared errors between experimental and simulated data:

$$minimize\sum _{i=1}^n{\left(y_i^{exp}-y_i^{sim}\left(\theta \right)\right)}^2$$

Here, θ represents the parameter set to be estimated. Estimation methods include gradient-based algorithms (e.g., Levenberg–Marquardt), metaheuristics (e.g., genetic algorithms, particle swarm optimization), and Bayesian approaches such as Markov Chain Monte Carlo (MCMC), which also provide uncertainty bounds [137,138].

• Integrated SA–PE Workflows

Combining SA with PE enhances computational efficiency and model reliability. SA helps prioritize parameters for estimation and reduce problem dimensionality, while PE refines parameter values based on experimental alignment. This integrated approach improves model validation and uncertainty quantification [139].

For instance, in spray drying of probiotic formulations, SA identified inlet air temperature and droplet size as key variables affecting survival and moisture content, which were subsequently estimated from drying curves. In extrusion modeling, calibrated shear-thinning parameters (flow index, consistency) allowed accurate prediction of pressure and expansion across varying moisture levels [140].

• Challenges and Best Practices

Despite their value, SA and PE in CFD face notable challenges:

• High computational cost: Repeated simulations across parameter sets are resource-intensive; surrogate models (e.g., Kriging, neural networks) can help alleviate this burden.
• Identifiability issues: Multiple parameter combinations may yield similar outputs, requiring regularization and sensitivity-based filtering.
• Uncertain or noisy experimental data: In-process measurements (e.g., local temperature, velocity) are often difficult to obtain with sufficient accuracy.

Best practices include mesh and time-step independence verification, constraining parameters using literature data or physical measurements, and applying cross-validation to assess generalizability [141].

• Future Directions

Ongoing developments in this field aim to make SA and PE more efficient and accessible. Promising trends include:

• Real-time PE using sensor data within digital twin environments,
• Integrated uncertainty quantification and risk-informed design,
• ML-assisted surrogate modeling for rapid SA/PE in large-scale CFD problems,
• Open-source workflows combining solvers (e.g., OpenFOAM) with libraries such as SALib or UQLab.

Overall, SA and PE are foundational for advancing predictive, calibrated, and data-driven CFD modeling in food engineering [142].

7.3. Limitations and Challenges in CFD of Food Processes

Despite its powerful capabilities, the application of CFD in food engineering remains limited by several key factors. One critical issue is the lack of accurate thermophysical data for complex food matrices. Many food materials exhibit composition-dependent properties (e.g., thermal conductivity, specific heat, effective diffusivity), which vary with moisture content, temperature, and structural state. These variables are often poorly characterized, making it difficult to build reliable simulation models [143]. In unit operations such as extrusion and drying, energy and momentum equations are typically well-established, but mass transfer processes—particularly water transport—remain insufficiently addressed. Advanced CFD models must incorporate moisture sorption isotherms, non-Fickian diffusion, and evaporation kinetics, which are rarely available for real foods [144]. Moreover, phase transitions, such as the glass transition (Tg), significantly affect mass transfer, structural integrity, and product texture. However, CFD rarely includes Tg-related behavior, even though it is crucial for predicting drying-induced changes in crispness, stickiness, or collapse. In spray drying, for instance, exceeding Tg leads to wall deposition, while in extrusion, transitions around Tg influence melt viscosity and final texture [145,146]. Finally, CFD struggles to predict sensory attributes, such as crispness, chewiness, or moisture perception, due to the lack of quantitative texture–structure–process models. While indirect correlations exist (e.g., between porosity and crunchiness), direct modeling of sensory outcomes remains a challenge [147,148,149,150]. Addressing these limitations will require improved food-specific property databases, better coupling between CFD and experimental data (e.g., via in-line NIR or MRI), and integration with multiphysics models capturing chemical, mechanical, and sensory phenomena.

7.4. Coupling CFD with AI/ML for Optimization

The integration of CFD with Artificial Intelligence (AI) and ML offers significant potential for advancing food process optimization. While CFD provides detailed, physics-based insights into transport phenomena, it remains computationally demanding—especially for high-resolution models, SA, or multi-objective optimization. By coupling CFD with AI/ML, it becomes possible to approximate simulation outputs rapidly, explore large design spaces, and enable real-time decision-making and control [151].

AI-driven surrogate models—trained on CFD or experimental data—can predict key outcomes such as temperature profiles, shear stress, or product attributes with high speed and acceptable accuracy. These models reduce computational time from hours to seconds and are particularly valuable for tasks like uncertainty quantification, parameter sweeps, and adaptive control. Among the most commonly applied ML techniques are Artificial Neural Networks (ANNs), Support Vector Machines (SVMs), Gaussian Process Regression (GPR), Random Forests, and deep learning architectures such as autoencoders. These tools are trained using datasets generated either offline (via CFD) or online (via sensors), or through hybrid physics-informed approaches [152].

The typical CFD–ML workflow includes data generation through simulations or experiments, feature selection and preprocessing, model training and validation, and deployment for optimization or control. Active learning loops, in which additional CFD runs are iteratively used to refine the surrogate model, further improve accuracy and robustness [153].

Practical applications of CFD–ML coupling in food engineering include spray drying (e.g., predicting wall deposition and droplet behavior), extrusion (e.g., forecasting expansion or texture based on process conditions), and mixing or fermentation (e.g., optimizing impeller design and oxygen transfer rates). Deep learning models have also been used to predict spatial temperature and moisture gradients in drying equipment, enabling faster and more precise system optimization [154].

Key advantages of CFD–ML integration include drastically reduced simulation time, improved scalability for high-dimensional problems, and the ability to perform real-time control. However, challenges remain: model performance depends heavily on the quality and representativeness of the training data, black-box models may lack physical interpretability, and extrapolation beyond the training domain is often unreliable. Emerging solutions include physics-informed neural networks (PINNs), which embed physical laws into the learning process, and hybrid frameworks combining CFD, ML, and kinetic models [155].

Looking ahead, adaptive systems that update surrogate models in real time using live process data, coupled with explainable AI and automated ML pipelines (AutoML), are expected to become central to intelligent food manufacturing. The integration of CFD with AI/ML not only enhances computational efficiency but also paves the way for flexible, responsive, and sustainable production systems aligned with Industry 4.0 paradigms [156].

7.5. Reduction of Energy Consumption and Improvement of Product Quality

In modern food manufacturing, the concurrent pursuit of energy efficiency and superior product quality is paramount, with CFD serving as a pivotal technology to achieve these objectives. CFD provides profound insights into thermal distribution, flow dynamics, and physical interactions within processing systems, enabling optimization of equipment and conditions to minimize energy consumption while enhancing product attributes such as texture, moisture, and nutritional value [157]. Energy-intensive operations like drying, extrusion, and mixing particularly benefit from CFD, which helps identify thermal inefficiencies, redesign pathways to reduce energy loss, and optimize process parameters. For instance, in spray drying, CFD minimizes wall deposition and recirculation, while in extrusion, it helps configure screws and dies for minimal torque and thermal input. Beyond energy savings, CFD significantly contributes to product quality by modeling moisture profiles for uniform dehydration, ensuring adequate thermal processing without nutrient loss, and analyzing shear fields and RTD to design desired textures. It also aids in preserving color, flavor, and functional compounds by preventing localized overheating. Critically, CFD facilitates multi-objective optimization, allowing engineers to balance energy use and product quality through surrogate modeling techniques and integration with real-time control systems. Industrial case studies, such as CFD-based redesign of spray dryers for infant formula or optimization of pasteurization tunnels, have consistently demonstrated significant energy reductions (10–30%) alongside measurable improvements in product consistency. Future advancements will likely involve the integration of CFD with real-time sensor data, AI-driven predictive control, and digital twin platforms, alongside the incorporation of environmental metrics, to foster more sustainable food production [157].

8. Current Challenges and Future Perspectives

8.1. Model Validation and Scalability

Despite the growing use of CFD in food process engineering, key challenges remain in model validation, generalization, and scalability. Accurate simulations rely not only on the strength of numerical solvers but also on reliable input data, realistic boundary conditions, and robust validation methods across different scales and equipment types. Bridging the gap between laboratory-scale modeling and industrial-scale implementation remains a crucial objective for both researchers and practitioners [57].

Model validation in food systems is inherently difficult due to the complexity of the materials and the limited accessibility of internal process variables. Many food matrices are opaque, sticky, or thermally sensitive, making direct measurement of velocity fields, temperature gradients, or concentrations infeasible. Moreover, thermophysical and rheological properties—such as viscosity, diffusivity, or thermal conductivity—are often poorly characterized and highly variable. When multiphysics interactions such as reaction kinetics or phase transitions are included, the number of uncertain parameters increases further. Practical boundary and initial conditions also tend to be non-uniform, with heterogeneities in moisture content, particle size, or composition that deviate from idealized simulation assumptions [74].

Due to these constraints, model validation often relies on indirect or surrogate metrics. Common approaches include comparing simulation outputs with product temperature profiles, RTDs, drying curves, or quality attributes such as porosity, expansion ratio, or texture. However, spatially resolved, quantitative validation—particularly for velocity or shear fields—is typically limited to laboratory or pilot-scale systems with specialized instrumentation [107].

Scalability poses another challenge. As models are scaled from lab to industrial conditions, geometric complexity increases, flow regimes shift (e.g., from laminar to turbulent), and process dynamics become more nonlinear. In large-scale equipment, control systems, mechanical wear, and operator interventions further complicate predictions. High-resolution 3D simulations of industrial systems are often computationally expensive, limiting their use for design iterations or real-time control. Moreover, scaling laws based on dimensionless numbers such as Reynolds or Nusselt may not apply consistently in non-Newtonian or multiphase systems [73].

To improve both validation and scalability, several strategies are being pursued. Hybrid modeling approaches that combine CFD with experimental calibration, empirical correlations, or machine learning can reduce reliance on fully resolved physics. Modular validation, in which subsystems (e.g., mixing, heating, drying) are tested independently before being integrated, helps isolate uncertainties. SA and Bayesian inference techniques can be used to quantify parameter uncertainty and evaluate model robustness under varying conditions. DoE provides a systematic framework for validation across a broad operational space, while non-invasive imaging techniques such as MRI, PIV (Particle Image Velocimetry), or X-ray CT allow for more detailed measurements in research settings [158].

Emerging digital twin platforms offer a promising solution for industrial-scale validation, enabling CFD models to be continuously updated using real-time process data. Looking ahead, further improvements are expected through the development of standardized property databases, automated meshing tools, and cloud-based GPU-accelerated simulation environments. Advances in physics-informed machine learning (PIML) could also support real-time model correction and adaptive control [120].

Ultimately, overcoming the current limitations in model validation and scalability will be essential for mainstream adoption of CFD in food engineering. When fully integrated, validated models will enable predictive quality control, efficient scale-up, and more sustainable, data-driven manufacturing practices [74].

8.2. Integration with Real-Time Process Control

The transition toward Industry 4.0 is transforming food manufacturing through automation, interconnectivity, and data-driven decision-making. Central to this transformation is the concept of the digital twin—a dynamic, virtual representation of a physical process that continuously mirrors and responds to real-world operations. When combined with computational models and real-time data streams, digital twins enable predictive, adaptive, and autonomous control strategies [159].

In food engineering, digital twins integrate high-fidelity physics-based models (e.g., CFD), sensor inputs (temperature, moisture, torque), machine learning algorithms for anomaly detection and surrogate modeling, and control logic for process optimization. CFD plays a pivotal role by simulating heat and mass transfer, fluid flow, and complex multiphase interactions that are otherwise difficult to observe directly. It also enables the creation of virtual sensors and boundary condition estimators, providing deeper insight into internal process dynamics [160].

Applications of CFD-enhanced digital twins in food processing include spray drying systems (to monitor droplet trajectories and prevent fouling), extrusion (to estimate pressure and specific mechanical energy), mixing (to control residence time and shear distribution), and thermal treatments (to ensure uniform pasteurization under varying loads). These simulations can be synchronized with sensor feedback in real time, enabling operators to perform what-if analyses, anticipate system deviations, and fine-tune process parameters dynamically [161].

Implementing such systems requires a robust digital infrastructure. This includes IoT-enabled devices, edge computing for local data processing, cloud integration for storage and analytics, and interoperable communication protocols (such as OPC UA or MQTT) that facilitate data exchange between simulation environments and control platforms like SCADA or MES [120].

The industrial benefits are considerable: improved product consistency, reduced energy usage, early detection of faults, enhanced responsiveness to raw material variability, and accelerated scale-up using validated virtual prototypes. These capabilities embody the core principles of Industry 4.0, including interoperability, transparency, and cyber-physical system integration [159].

Nevertheless, challenges remain. Traditional CFD models are often too computationally intensive for real-time deployment, necessitating the use of surrogate models or reduced-order approaches. Maintaining model accuracy over time requires continuous recalibration to reflect equipment wear or fouling. Standardized protocols for simulation-control integration are still under development, and cybersecurity must be rigorously addressed [162].

Future advancements are expected to focus on hybrid modeling approaches that combine physics-based and AI-driven components, self-updating digital twins, and integrated sustainability tracking (e.g., CO₂ footprint, energy intensity). As food manufacturing continues its digital evolution, the integration of CFD with real-time control offers a powerful framework for smarter, more flexible, and sustainable processing systems.

9. Conclusions

CFD is becoming a central tool in the analysis and optimization of mechanical food processes. This review has outlined the main advances and challenges associated with its application in mixing, extrusion, and drying systems, emphasizing its predictive capability and contribution to process understanding.

CFD provides detailed insights into flow behavior, temperature gradients, and shear distribution, allowing for improved design and control of food processing equipment. Its ability to simulate non-Newtonian and multiphase systems is particularly relevant in extrusion and drying, where material complexity is high. Coupling CFD with other modeling tools such as the DEM, FEM, and reaction kinetics further extends its applicability to realistic, multiphysics scenarios.

Industrial case studies demonstrate that CFD can significantly enhance product quality, reduce energy consumption, and support faster scale-up. However, successful implementation requires accurate characterization of material properties, appropriate model selection, and experimental validation using techniques such as PIV, MRI, or thermal imaging.

Looking forward, CFD is expected to play an increasingly strategic role in digital food manufacturing. Its integration into digital twins, smart control systems, and AI-driven optimization workflows aligns with the goals of Industry 4.0 and sustainable food production. By fostering interdisciplinary collaboration and improving access to validated models and datasets, CFD can drive innovation in the design of efficient, resilient, and consumer-focused food processes.