Rheological Modeling in Recycled Polyolefin Systems: A Systematic Review of Model Classification, Applicability, and Limitations for Eco-Composite Design

Abstract

The application of rheological modeling in polyolefin-based systems has gained increasing attention in the context of sustainable materials and circular economy strategies. In particular, the use of recycled polyolefins reinforced with lignocellulosic fillers presents significant opportunities, but also introduces challenges associated with structural heterogeneity, degradation, and variability in processing behavior. Despite rheology’s central role in linking structure, processing, and properties, its use as a predictive tool in recycled systems remains insufficiently systematized. This work presents a systematic review conducted according to PRISMA guidelines to analyze the use of rheological models in polyolefin-based systems, with particular emphasis on their applicability to recycled materials and composite formulations. We analyze 50 studies using a structured data extraction protocol. The results show that rheological modeling approaches can be organized into a hierarchical framework ranging from indirect flow parameters and generalized Newtonian fluid models to viscoelastic, structural, multiscale, and hybrid approaches. However, these approaches are not evenly distributed across system types. Advanced models are predominantly applied to compositionally controlled systems, whereas recycled and post-consumer polyolefins are mainly addressed using simplified models or experimental characterization. The analysis further indicates that rheology is primarily used for data fitting and process simulation, with limited application as a predictive tool for material formulation. Quantitative trends reported in the literature indicate that filler incorporation typically increases viscosity by approximately 20–200%, depending on filler content, dispersion quality, and interfacial interactions. However, variability in experimental conditions and material heterogeneity significantly limits cross-study comparability. From a mechanistic perspective, the main limitation lies not in the availability of rheological models but in their adaptability to heterogeneous systems characterized by variable composition, degradation, and limited experimental accessibility. This review identifies a gap between the development of rheological models and their application in recycled polyolefin systems. Future progress on eco-composite design will require further development of integrative approaches that balance physical insight, predictive capability, and experimental feasibility. In this context, rheology should be repositioned from a post-characterization technique to a central tool for the design and optimization of sustainable polymer composites. From an applied perspective, these findings support the use of rheological parameters as practical indicators for guiding formulation strategies and optimizing processing conditions in recycled polyolefin-based materials.

1. Introduction

The increasing interest in circular economy strategies has driven the development of approaches aimed at the recycling and valorization of thermoplastic polymers [1,2,3]. Development has particularly focused on polyolefins such as polyethylene (PE) and polypropylene (PP) due to their high production volumes and widespread presence in post-consumer waste streams [4,5,6,7,8,9,10,11,12]. In this context, the incorporation of lignocellulosic materials as reinforcement in thermoplastic composites has emerged as a promising alternative that can improve mechanical performance while reducing environmental impact [13,14,15,16,17,18,19].

However, both the processing and performance of recycled polyolefin-based systems present significant challenges associated with inherent structural and compositional variability. Factors such as thermo-oxidative degradation, broad molecular weight distributions, the presence of contaminants, and phase heterogeneity directly affect melt behavior; in turn, these aspects influence key processing phenomena such as flow stability, dispersion of reinforcement, and ultimately the final properties of the material [20,21,22].

Thermoplastic polymers are processed in the molten state, where they can be shaped into functional parts through operations such as extrusion and injection molding. Under these conditions, the flow behavior of polymer melts becomes a critical factor governing processability and final material performance. Rheology provides a fundamental framework for characterizing how materials respond to applied stress and deformation through parameters such as viscosity and viscoelastic properties [23,24,25].

These rheological characteristics are strongly influenced by intrinsic factors including molecular weight, molecular architecture, crystallinity, and the presence of fillers or reinforcing phases. As a result, they directly affect key processing phenomena such as mixing efficiency, flow stability, and dispersion of reinforcement. Therefore, a comprehensive understanding of melt rheology together with the ability to describe it through appropriate constitutive models is essential for optimizing processing conditions, predicting material behavior, and designing polymer systems with consistent and tailored properties [26,27,28].

Rheological models expressed as constitutive equations relating stress and deformation play a central role in representing and predicting the flow behavior of polymer melts under different processing conditions [29,30,31]. In this context, rheology is not only a characterization tool but also a fundamental framework for understanding and potentially predicting the relationship between structure, processing, and properties in polymer systems [32,33]. However, a significant portion of the literature on polyolefin-based composites, particularly those involving recycled materials, has traditionally emphasized mechanical and thermal performance, while the systematic use of rheological modeling as a tool for formulation and design remains comparatively less explored.

Rheological modeling approaches reported in the literature span a wide range of formulations that describe the flow behavior of polymer melts, from empirical descriptions to advanced constitutive models [23,31,34]. A summary of commonly used rheological models, including their constitutive equations and key parameters, is provided in

Table 1. Rheological models, governing equations, and parameters.

Model	Governing Equation	Parameters and Variables
Newtonian	$\tau =\eta \dot{\gamma }$	$\tau$: shear stress; $\eta$: viscosity; $\dot{\gamma }$: shear rate
Power Law (Ostwald–de Waele)	$\tau =K{\dot{\gamma }}^n$	K: consistency index; n: flow behavior index
Bingham Plastic	$\tau ={\tau }_0+{\mu }_p\dot{\gamma }$	${\tau }_0$: yield stress; ${\mu }_p$: plastic viscosity
Herschel–Bulkley	$\tau ={\tau }_0+K{\dot{\gamma }}^n$	${\tau }_0$: yield stress; K: consistency; n: flow index
Cross Model	$\eta \left(\dot{\gamma }\right)={\eta }_{\infty }+{\displaystyle \frac{{\eta }_0-{\eta }_{\infty }}{1+{\left(k\dot{\gamma }\right)}^m}}$	${\eta }_0$: zero-shear viscosity; ${\eta }_{\infty }$: infinite-shear viscosity; $k,m$: constants
Carreau Model	$\eta \left(\dot{\gamma }\right)={\eta }_{\infty }+({\eta }_0-{\eta }_{\infty }){\left[1+{\left(\lambda \dot{\gamma }\right)}^2\right]}^{{\displaystyle \frac{n-1}{2}}}$	${\eta }_0$: zero-shear viscosity; $\lambda$: time constant; n: index
Carreau–Yasuda	$\eta \left(\dot{\gamma }\right)={\eta }_{\infty }+({\eta }_0-{\eta }_{\infty }){\left[1+{\left(\lambda \dot{\gamma }\right)}^a\right]}^{{\displaystyle \frac{n-1}{a}}}$	${\eta }_0,{\eta }_{\infty }$: viscosities; $\lambda$: time constant; $a,n$: parameters
Ellis Model	$\eta \left(\tau \right)={\displaystyle \frac{{\eta }_0}{1+{\left({\displaystyle \frac{\tau }{{\tau }_{1/2}}}\right)}^{\alpha -1}}}$	${\eta }_0$: zero-shear viscosity; ${\tau }_{1/2}$: reference stress; $\alpha$: index
Maxwell Model	$\tau +\lambda {\displaystyle \frac{d\tau }{dt}}=\eta {\displaystyle \frac{d\gamma }{dt}}$	$\lambda$: relaxation time; $\eta$: viscosity
Kelvin–Voigt	$\tau =E\gamma +\eta {\displaystyle \frac{d\gamma }{dt}}$	E: elastic modulus; $\eta$: viscosity
Oldroyd-B	$\tau +{\lambda }_1\stackrel{▿}{\tau }=\eta \left(\dot{\gamma }+{\lambda }_2\stackrel{▿}{\dot{\gamma }}\right)$	${\lambda }_1,{\lambda }_2$: relaxation times; $\eta$: viscosity
Giesekus	$\tau +\lambda \stackrel{▿}{\tau }+{\displaystyle \frac{\alpha \lambda }{\eta }}\tau ·\tau =\eta \dot{\gamma }$	$\lambda$: relaxation time; $\alpha$: mobility factor
Phan–Thien–Tanner (PTT)	f(tr$\tau )+\lambda {\tau }^{▿}={\eta }_0\dot{\gamma }$	$\lambda$: relaxation time; f: stress function
Rolie-Poly	Tube-based constitutive equation	Parameters related to reptation, stretch, and relaxation

.

Rheological models have predominantly been developed and validated for systems with controlled composition, which raises important questions regarding their transferability to more complex materials such as post-consumer recycled polyolefins. This situation raises a fundamental question: to what extent are existing rheological models applicable to recycled systems, and how can they be used to support the formulation of eco-composites based on polyolefins?

Unlike previous reviews that have focused primarily on wood–plastic composites or mechanical performance, the present work specifically addresses rheological modeling as a tool for formulation. This includes not only the identification of models used in the literature but also their classification, level of complexity, application context, and limitations when applied to recycled systems.

It is important to note that during the review process the number of studies explicitly addressing post-consumer polyolefins was found to be limited. Rather than interpreting this as a lack of research, this observation suggests that the application of rheological modeling in such systems has not yet been systematically explored or consistently reported. For this reason, studies based on virgin polymers or systems with controlled composition were also considered, providing a comparative framework to evaluate the potential transferability of modeling approaches.

Despite the extensive use of rheological models in polymer science, their application as predictive tools in heterogeneous recycled systems remains fragmented. Existing studies tend to treat rheology as either a post-characterization technique or a fitting tool rather than as a central variable for formulation and design. This gap is particularly critical in post-consumer polyolefins, where composition is often unknown and highly variable. Within this context, the objective of this work is to analyze the use of rheological models as predictive tools in the formulation of polyolefin-based systems, with particular emphasis on their applicability to recycled materials. To this end, the following research questions (RQ) are addressed:

• RQ1: What types of rheological models are most commonly applied in polyolefin-based systems?
• RQ2: How have these models been used to support material formulation and processing?
• RQ3: What are the main challenges and opportunities associated with their application to recycled polyolefin systems?

By addressing these questions, this work aims not only to synthesize the related literature but also to identify patterns, limitations, and opportunities that may contribute to the development of more robust and transferable approaches for the design of recycled polymer composites, thereby enhancing the revalorization of waste polymer streams.

2. Methodology

A systematic literature review was conducted following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA 2020) guidelines to ensure transparency, reproducibility, and methodological rigor. The objective of this review was to identify, classify, and analyze the use of rheological models in polyolefin-based systems, particularly polyethylene (PE) and polypropylene (PP), with emphasis on their applicability to recycled materials and lignocellulosic fiber-reinforced composites. The study selection process followed the PRISMA framework and consisted of four stages: identification, screening, eligibility, and inclusion. The study selection process is summarized in a PRISMA flow diagram (Figure 1), which illustrates the stages of identification, screening, eligibility, and inclusion of studies. The diagram integrates both the initial database search (Scopus) and a complementary manual search, enhancing its transparency and reproducibility.

2.1. Identification Phase

During our analysis of the SCOPUS dataset, we observed that the number of studies explicitly addressing post-consumer polyolefins was limited. Rather than interpreting this as a lack of research activity, this observation was understood as a limitation associated with database indexing and keyword sensitivity, particularly in relation to heterogeneous recycled systems. To address this limitation and enhance the review’s representativeness, we ran a complementary search strategy on Google Scholar, which offers broader indexing coverage including open-access journals and institutional repositories. This search kept the study’s original thematic focus on the application of rheological models in polyolefin-based systems relevant to recycling and composite materials.

2.1.1. Records Identified in SCOPUS

The initial search was performed using the Scopus database, selected for its extensive coverage of peer-reviewed scientific literature and advanced filtering capabilities.

A structured search strategy was developed based on combinations of keywords related to polymer type (polyolefins, polyethylene, polypropylene), system characteristics (recycling, composites, post-consumer materials), and rheological behavior (rheology, rheological modeling, constitutive models, melt flow behavior, melt flow index). Boolean operators (AND/OR) were consistently applied to combine keyword groups.

The search strategy was developed through a progressive refinement process, starting from broad rheology-related queries and incorporating additional terms related to composite formulation, natural fibers, and mechanical properties. The evolution of search queries and their corresponding results is summarized in the Supplementary Materials, which also provide the complete search strings to ensure transparency and reproducibility.

The main search string applied in Scopus was:

(“polyolefins” OR “polyethylene” OR “polypropylene”) AND (“rheology” OR “rheological modeling” OR “constitutive models”) AND (“recycling” OR “composites” OR “post-consumer”)

To improve relevance, filters were applied to restrict the results to the following:

• Publication period: 2015–2025,
• Document types: Research articles and review papers,
• Subject areas: Engineering, materials science, chemistry, environmental science, and chemical engineering,
• Language: English.

2.1.2. Additional Records Identified in Google Scholar

Equivalent keyword combinations to those used in Scopus were applied iteratively in Google Scholar, incorporating both general terms and specific model names to refine the results. Priority was given to studies published in peer-reviewed indexed journals whenever possible. At the same time, open-access sources were also considered when they made relevant contributions to rheological modeling in polyolefin-based systems.

The base search equation used was:

Polyolefins AND Composites AND Recycling AND Rheology

To refine the results, additional searches were conducted using exact phrases and specific rheological models, including:

“rheological models”, “Bingham”, “Carreau–Yasuda”, “Cross–WLF”, “Herschel–Bulkley”, “Power law”, “Giesekus”, “K-BKZ”, “Phan–Thien–Tanner”, and “Computational models”.

Further restrictions were applied by requiring the presence of at least one of the following terms: “polyethylene” or “polypropylene”. Only studies involving thermoplastic systems and including explicit rheological characterization or modeling were considered.

2.2. Screening Phase

During the screening stage, titles and abstracts were reviewed to assess their relevance to the scope of this study. Records that did not address rheological characterization, polymer processing, or recycling of polyolefins were excluded.

In the eligibility stage, full-text articles were evaluated to determine their compliance with the inclusion criteria, with particular emphasis on the explicit use of rheological models or rheological parameters in the molten state.

2.3. Eligibility Phase

2.3.1. Inclusion and Exclusion Criteria

To ensure the scientific relevance and consistency of the selected studies, explicit inclusion and exclusion criteria were defined and applied throughout the evaluation process.

Inclusion criteria:

• Peer-reviewed journal articles (original research or review).
• Studies involving polyolefins (PE, PP, or their blends).
• Explicit rheological characterization or application of rheological models in the molten state.
• Systems involving recycling, composites, or related processing contexts.
• Studies incorporating natural fibers or lignocellulosic reinforcement.
• Publications in English within the period 2015–2025.

Exclusion criteria:

• Studies lacking rheological characterization or modeling (except those using MFI as a flow indicator).
• Studies focused exclusively on thermal, mechanical, or morphological characterization without rheological context.
• Non-thermoplastic polymer systems.
• Non-peer-reviewed documents, including conference papers, theses, patents, and technical reports.

2.3.2. Final Study Selection

The studies selected from SCOPUS consisted of 21 studies, which were included in the initial corpus for qualitative analysis [35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55]. The complementary search in Google Scholar resulted in the identification of 29 additional studies, which were evaluated using the same inclusion and exclusion criteria [56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84]. After this process, a total of 50 studies (21 from the initial Scopus search and 29 from the complementary search) were included in the final qualitative synthesis. A summary of this literature corpus is shown in

Table 2. Screening dataset, Part A: Bibliographic and material-system descriptors ($n=50$).

ID	Title	Year	Polymer Matrix	Reinforcement/Filler	Material System	Material Condition
1	A comparative study of kraft pulp fibres and the corresponding fibrillated materials	2023	PE (LDPE, HDPE)	Kraft pulp fibers/CNF	PE biocomposites with cellulosic reinforcement	Virgin
2	Anisotropic permeability and non-Newtonian flow in melt impregnation	2025	PP	Glass fiber	PP + glass fiber composite	Virgin
3	Challenges in the mechanical recycling and upcycling of mixed PCR	2024	Mixed polyolefins	None	Mixed post-consumer plastics review	Recycled
4	Characterization, processing, and modeling of industrial recycled polyolefins	2024	rPP	None	Industrial recycled polyolefins	Recycled
5	Computer-Aided Design of the Composition of Extrudable Polymer–Polymer UHMWPE Composites	2019	UHMWPE	PP + HDPE-g-SMA	Polymer–polymer UHMWPE composites	Virgin
6	Effect of the addition of cellulose filaments on the relaxation behavior of thermoplastics	2021	PS, PP	Cellulose filaments	Thermoplastic composites with cellulose filaments	Virgin
7	Effect of the melt flow index of an HDPE matrix on the properties of composites with wood particles	2020	HDPE	Wood particles	HDPE + wood particle composites	Virgin
8	Effects of lignocellulosic fillers from waste thyme on melt flow behavior	2019	Bio-HDPE	Industrial thyme waste	Bio-HDPE lignocellulosic composite	Virgin
9	Evaluation of the Mechanical, Thermal and Rheological Properties of Hop, Hemp and Wood Fiber Plastic Composites	2023	HDPE	Hop bines/hemp/wood fibers	WPC systems with natural fibers	Virgin
10	In situ experimental investigation of fiber orientation kinetics and rheology of polymer composites	2025	PE	Short glass fibers	Short-fiber reinforced PE	Virgin
11	Interfacial properties of polyethylene/PLA blends	2024	LDPE	PLA dispersed phase	LDPE/PLA blends with PE-g-MAH	Virgin
12	Linear viscoelasticity of PP/PS/MWCNT composites	2022	PP/PS blend	MWCNT	PP/PS/MWCNT composite	Virgin
13	Manufacture and rheological behavior of all recycled PET/PP microfibrillar blends	2023	rPP	rPET microfibrils	Recycled rPET/rPP microfibrillar blend	Recycled
14	Mechanical and rheological properties of recycled HDPE and ronier palm fiber biocomposites	2022	rHDPE	Palm leaf fiber	rHDPE natural fiber composite	Recycled
15	Modeling linear and nonlinear rheology of industrial incompatible polymer blends	2024	PP	POE dispersed phase	Incompatible PP/POE blends	Virgin
16	Rheological Basics for Modeling of Extrusion Process of Wood Polymer Composites	2021	PP	Wood flour	PP-based wood–plastic composites	Virgin
17	Rheology, Mechanical Properties, and Thermal Stability of Maleated Polyethylene Filled with Nanoclays	2015	MAPE	Nanoclay	MAPE nanoclay composites	Virgin
18	Rheology for Modeling of Extrusion of Wood Plastic Composites	2022	PP/HDPE	Wood flour	WPC extrusion review	Virgin
19	Tailored recycled composites: Enhancing the performance of injection moulded post-consumer polypropylene composites	2025	rPP/homoPP	Glass fiber	Recycled PP reinforced composites	Recycled
20	Testing the PTT Rheological Model for Extrusion of Virgin and Composite Materials in View of Enhanced Conductivity and Mechanical Recycling Potential	2021	PP	Graphite	Filled PP composites	Virgin
21	The Effect of Fibers’ Length Distribution and Concentration on Rheological and Mechanical Properties of Glass Fiber–Reinforced Polypropylene Composite	2022	PP	Glass fiber	Short-fiber reinforced PP	Virgin
22	A Network-Theory-Based Comparative Study of Melt-Conveying Models in Single-Screw Extrusion: A. Isothermal Flow	2018	Polyolefins	None	Melt conveying in extrusion	Virgin
23	An Upcycling Strategy for Polyethylene Terephthalate Fibers: All-Polymer Composites with Enhanced Mechanical Properties	2024	HDPE	rPET fibers	rPET-fiber reinforced HDPE	Recycled
24	Analysis of process parameters related to the single screw extrusion of recycled polypropylene blends by using design of experiments	—	PP/rPP	None	Recycled PP blends under extrusion	Recycled
25	Characterisation of Nanoclay and Spelt Husk Microfiller-Modified Polypropylene Composites	2022	PP	Husk + nanoclay	PP lignocellulosic/nanoclay composite	Virgin
26	Correlating processing variables to material properties in recycled polypropylene: A data-driven approach	2025	PP	None	Recycled PP under controlled reprocessing	Recycled
27	Data-Driven Modelling of Polyethylene Recycling under High-Temperature Extrusion	2022	PE	None	Recycled PE under high-temperature extrusion	Recycled
28	Determination of Viscosity Curve and PVT Properties for Wood-Polymer Composite	2018	PP	Wood fibers	WPC processing rheology	Virgin
29	Effect of Elasticity on Heat and Mass Transfer of Highly Viscous Non-Newtonian Fluids Flow in Circular Pipes	2025	POE	None	Highly viscous polyolefin elastomer melt	Virgin
30	Effect of Recycling on the Mechanical, Thermal and Rheological Properties of Polypropylene/Carbon Nanotube Composites	2022	PP	MWCNT	PP/MWCNT nanocomposite under recycling cycles	Recycled
31	Exploring New Applications of Municipal Solid Waste	2025	Mixed polymers (PE/PP/PS/PET)	Mixed waste fibers/inorganics	MSW-based composites	Recycled
32	Formulating calcium carbonate masterbatches	2022	LLDPE	CaCO3	CaCO3 masterbatch	Virgin
33	Fundamentals of Global Modeling for Polymer Extrusion	2019	General polymers	None	Global modeling of extrusion	Virgin
34	Green Recycling for Polypropylene Components by Material Extrusion	2024	PP	None	Recycled PP for material extrusion (MEX)	Recycled
35	Influence of Spinning Temperature and Filler Content on the Properties of Melt-Spun Soy Flour/Polypropylene Fibers	2019	PP	Soy flour	Soy flour/PP fibers	Virgin
36	In-line rheometry of polypropylene based Wood Polymer Composites	2015	PP	Wood fibers	PP-based WPC	Virgin
37	Investigating Non-Newtonian Flow Characteristics of Polypropylene: A Computational Fluid Dynamics Study Utilizing COMSOL Multiphysics	2024	PP	None	PP melt through extrusion die	Virgin
38	Investigation of Fiber Orientations and Weld Lines of Short Fiber–Reinforced Injection-Molded Components	2024	PP, PA66, PPS	Glass fibers	Short-fiber reinforced injection-molded polymers	Virgin
39	Lab-scale processing of waste airbags for the development of fibre-reinforced geopolymer composite	2025	Geopolymer matrix	Waste airbag polyamide fibers	Fiber-reinforced geopolymer	Recycled fibers
40	Morphology, Rheology and Crystallization in Relation to the Viscosity Ratio of Polystyrene/Polypropylene Polymer Blends	2020	PS	PP dispersed phase	PS/PP blends	Virgin
41	Multiscale viscoplastic modeling of recycled glass fiber-reinforced thermoplastic composite	2022	PA66	Glass fibers	Recycled glass-fiber reinforced thermoplastic composite	Recycled
42	Processing Behavior Evolution of Recycled Polypropylene: An Integrated Experimental and Computer-Aided Engineering Simulation Study	2024	PP	None	Recycled PP through multiple extrusion cycles	Recycled
43	Reprocessing Possibilities of Poly(3-hydroxybutyrate-co-3-hydroxyvalerate)–Hemp Fiber Composites Regarding the Material and Product Quality	2024	PHBV	Hemp fiber	PHBV/hemp biocomposite under reprocessing	Reprocessed
44	Rheological Properties of Wood–Plastic Composites by 3D Numerical Simulations: Different Components	2021	HDPE	Wood fiber	WPC with varying wood content	Virgin
45	Simulation of the Melt Conveying Zone of a Single-Screw Extruder for Mixed Polymer Materials Using an Isothermal Analytical Flat Plate Model	2025	PP/PA12 blends	None	Mixed polymer materials in single-screw extrusion	Mixed/recycled-like
46	Simulation and modeling of macro and micro components produced by powder injection molding: A review	2020	Binder systems	Powders	Powder injection molding feedstocks	Composite
47	Structure–Property Relationships in Polyethylene-Based Composites Filled with Biochar Derived from Waste Coffee Grounds	2019	PE	Biochar from coffee grounds	PE + biochar composite	Virgin
48	Structure-rheology Properties of Polyethylenes with Varying Macromolecular Architectures	2023	LDPE/LLDPE	None	Polyethylenes with varying architecture	Virgin
49	Study on the Melt Rheological Characterization of Micro-Tube Gas-Assisted Extrusion Based on the Cross-Scale Viscoelastic Model	2024	Polymer melt	Gas-assisted layers (not reinforcement)	Micro-tube gas-assisted extrusion	Virgin
50	Synergy of Fiber Surface Chemistry and Flow: Multi-Phase Transcrystallization in Fiber-Reinforced Thermoplastics	2022	iPP	Glass fibers/aramid fibers	Fiber-reinforced thermoplastics	Virgin

and

Table 3. Screening dataset, Part B: modeling approach, analytical purpose, and interpretation fields ($n=50$). Study ID links each row to Part A.

ID	Model Type	Modeling Level	Approach Type	Purpose	Relation to Formulation	Key Insight	Justification
1	Micromechanical (non-rheological)	Level 1	Experimental	Formulation/ processability context	Indirect	Pulp fibers outperformed CNF; limited melt-flow relevance	Contains flow-related parameter and formulation relevance
2	Herschel–Bulkley + Navier–Stokes	Level 3	Constitutive/ computational	Processing	Indirect	Model predicted impregnation flow with low error	Explicit rheological model validated experimentally
3	Cox–Merz/Mark–Houwink (theoretical use)	Level 1	Review/empirical	Characterization	Indirect	Rheology is central to understanding recyclability and degradation	Strong rheological characterization framework
4	Power-law (process-oriented)	Level 2	Empirical/ computational	Processing	Indirect	Materials with similar MFI may behave very differently during processing	Uses rheological variables and process modeling
5	DOE/response surface	Level 1	Computational/ optimization	Formulation	Direct	MFI incorporated as a design variable for formulation optimization	Computational modeling uses rheological parameter explicitly
6	Modified Carreau–Yasuda + percolation	Level 3	Constitutive/ structural	Structure–property	Indirect	Yield stress and relaxation behavior revealed percolation	Explicit model with strong rheological interpretation
7	—	Level 1	Experimental	Formulation	Direct	Lower MFI matrix improved dispersion and final properties	Uses MFI to guide formulation behavior
8	Cross–WLF	Level 2	Constitutive/ simulation	Processing	Direct	Filler increased viscosity and affected injection processability	Explicit rheological model used in processing simulation
9	—	Level 1	Experimental	Characterization	Direct	Fiber type and size affected viscosity and processability	Relevant rheological characterization
10	Jeffery/Folgar–Tucker	Level 4	Structural/ computational	Modeling	Indirect	Fiber orientation kinetics govern rheological response under shear	Structural model connecting flow and orientation
11	Palierne	Level 4	Structural/ constitutive	Formulation/ interface analysis	Direct	Compatibilizer reduced interfacial tension and improved blend morphology	Explicit structural rheological model
12	YZZ (modified)	Level 4	Structural	Structure–property	Indirect	Model linked rheology with domain size and co-continuity	Advanced structural rheological model
13	Cross with yield stress	Level 3	Constitutive	Structure–property/ formulation	Direct	Microfibrillation strongly altered rheological response and formulation behavior	Recycled system with explicit rheological model
14	Einstein-type/correlational	Level 1	Experimental	Characterization	Direct	Fiber addition increased moduli and altered viscoelastic behavior	Clear rheological characterization despite limited modeling
15	Rolie-Double-Poly	Level 3	Multiscale/constitutive	Predictive modeling	Indirect	Model predicted linear and nonlinear rheology from molecular structure	Advanced constitutive model
16	Power-law + Klein + Navier slip	Level 2	Process rheology	Processing	Indirect	Rheological properties directly controlled extrusion behavior	Explicit flow models for WPC processing
17	Cross	Level 2	Constitutive	Structure–rheology	Indirect	Percolation-like filler effects modified viscoelastic response	Explicit rheological model
18	Ostwald–de Waele/Navier/ Bingham	Level 2	Review/process modeling	Processing	Indirect	Slip and yield stress are critical in WPC extrusion	Relevant rheological modeling review
19	DOE/RSM	Level 1	Statistical/empirical	Optimization	Direct	Processing variables and rheological indicators guide composite optimization	Uses rheological variables in predictive optimization
20	Phan–Thien–Tanner (PTT)	Level 3	Constitutive	Processing simulation	Indirect	PTT captured viscoelastic flow behavior at low filler contents	Advanced viscoelastic model
21	Herschel–Bulkley	Level 4	Structural/ constitutive	Structure–flow analysis	Direct	Fiber length distribution affected rheological parameters and flow	Model links structure and rheology
22	Power-law/Carreau–Yasuda	Level 2	Process modeling	Processing	Indirect	Non-Newtonian rheology governs melt conveying in extrusion	Strong theoretical rheology for extrusion
23	Carreau–Yasuda	Level 3	Structural/ constitutive	Structure–flow	Indirect	Elongational flow induced fibrillation and changed rheological response	Explicit rheological model in recycled composite
24	DOE/RSM	Level 1	Statistical/ empirical	Processing optimization	Indirect	Viscosity-related variables controlled torque and extrusion pressure	Reology implicit but relevant to processing
25	—	Level 1	Experimental	Characterization	Indirect	Nanoclay and husk modified melt viscosity only moderately	Rheological characterization relevant to formulation
26	Mark–Houwink + ML (SVM/ANN/RSM)	Level 5	Hybrid/data-driven	Prediction/process optimization	Direct	ML correlated residence time, viscosity, and molecular weight	Data-driven rheological prediction
27	Carreau–Yasuda + Cox–Merz + ML	Level 5	Hybrid/ constitutive/ML	Prediction	Indirect	Inverse rheology enabled prediction of molecular weight degradation	Strong integration of rheology and ML
28	Power-law (implicit)	Level 2	Experimental/ simulation	Processing	Indirect	Injection-based method improved viscosity estimation for WPCs	Relevant rheological curve determination
29	Cross + Wagner	Level 3	Constitutive/CFD	Processing	Indirect	Elasticity strongly affected pressure drop and residence-time distribution	Advanced constitutive modeling
30	Carreau–Yasuda + Cox–Merz	Level 3	Experimental/ constitutive	Characterization	Indirect	Recycling altered zero-shear viscosity but preserved useful performance	Strong rheological modeling in recycled nanocomposite
31	—	Level 1	Experimental	Feasibility/ characterization	Indirect	Heterogeneous MSW composites showed rheological behavior comparable to WPCs	Highly relevant to unknown-composition systems
32	Modified Carreau–Yasuda	Level 2	Formulation/ constitutive	Formulation	Direct	Additives controlled viscosity and facilitated masterbatch design	Explicit rheological model for formulation
33	Global model	Level 2	Theoretical/ simulation	Processing	Indirect	Extrusion requires coupled modeling of solids, melting, and melt flow	Provides processing framework
34	—	Level 1	Experimental	Processing/ printability	Indirect	Recycled PP showed comparable printability to virgin filament under controlled conditions	Rheology used to define processing window
35	—	Level 1	Experimental	Processing	Indirect	Filler loading and temperature strongly affected melt-spinning processability	Clear rheological processing relevance
36	Cox–Merz/shift factor (supporting)	Level 2	Experimental/ in-line	Processing	Indirect	In-line rheometry captured real-process behavior better than off-line methods	Highly relevant for process-representative rheology
37	Carreau–Yasuda	Level 2	Computational/CFD	Processing	Indirect	Shear thinning explained velocity and pressure distributions in the die	Explicit rheological model in CFD
38	Power-law/Modified Cross–WLF	Level 4	CAE/structural	Processing simulation	Indirect	Gate position dominated weld lines and fiber orientation	Rheology embedded in processing simulation
39	Bingham	Level 1	Experimental	Formulation/ processing	Indirect	Fiber addition caused exponential rise in yield stress	Comparative rheological context involving recycled polymer fibers
40	Carreau–Yasuda fit/viscosity ratio framework	Level 4	Experimental/ structural	Structure–rheology	Indirect	Viscosity ratio governed droplet-to-fibril morphology transition	Key structure–rheology study
41	Viscoplastic constitutive model	Level 4	Multiscale/FE	Structure–property	Indirect	Microstructure controlled the viscoplastic mechanical response of recycled composite	Links microstructure and constitutive behavior
42	—	Level 1	Experimental + CAE	Processing behavior	Indirect	Repeated extrusion caused progressive viscosity reduction while retaining processability	Directly relevant to simulated aging/recycling
43	—	Level 1	Experimental	Recyclability/ processing	Indirect	Repeated processing caused limited changes in viscosity and product quality	Useful comparative recyclability study
44	Power-law	Level 2	Experimental/CFD	Processing	Indirect	Higher wood content increased pseudoplasticity and shear thinning	Explicit model plus simulation
45	Bird–Carreau–Yasuda + mixing rules	Level 5	Analytical/ experimental	Prediction of extrusion behavior	Direct	Mixing rules predicted effective viscosity of polymer mixtures with low error	Highly relevant to unknown-composition systems
46	Cross–WLF/Carreau–Yasuda/Herschel–Bulkley	Level 2	Review/ modeling	Process simulation	Indirect	Accurate simulation depends on reliable rheological inputs	Supports role of rheology in process simulation
47	—	Level 4	Experimental/ structural	Structure–property	Direct	Filler slowed chain dynamics and improved thermo-oxidative stability	Highly relevant to coffee-derived reinforcement systems
48	TTS/structural rheology	Level 4	Experimental/ structural	Structure–rheology	Indirect	Long-chain branching dominated rheological response and strain hardening	Core structure–rheology reference
49	DCPP cross-scale viscoelastic model	Level 5	Simulation + experiment	Cross-scale processing analysis	Indirect	Scale-dependent viscoelasticity significantly affected extrusion behavior	Advanced multiscale rheological modeling
50	FEM-supported transcrystallization framework	Level 4	Experimental + modeling	Morphology development	Indirect	Morphology resulted from synergy between flow and interface chemistry	Connects flow, interface, and morphology

. The PRISMA flow diagram (Figure 1) includes both the initial database search and the complementary manual search in order to improve transparency while addressing the under-representation of post-consumer polyolefin systems in indexed databases.

2.4. Inclusion Phase (Data Analysis)

The corpus considered for the literature review consisted of fifty studies. A structured data extraction protocol was developed and applied to all selected studies to ensure consistency and comparability.

For each study, the following information was systematically recorded:

• Polymer system (virgin, recycled, or composite)
• Type of reinforcement (if applicable)
• Rheological model(s) used (primary and secondary)
• Rheological variables considered (e.g., viscosity, storage modulus, loss modulus)
• Application of the model (fitting, predictive, process-related, or structural)
• Level of model complexity.

Based on this information, rheological models were classified into a hierarchical framework ranging from indirect flow parameters to generalized Newtonian models, viscoelastic constitutive models, structural approaches, and hybrid or data-driven methods. This classification enabled a structured comparative analysis of modeling approaches and their applicability to polyolefin-based systems, particularly in the context of recycled materials.

The extracted information was organized and synthesized to support both a structured comparative analysis and a comprehensive overview of the reviewed studies. A summarized representation of the main modeling approaches and their applications is presented in the tables. The complete dataset, including detailed information such as material systems, rheological data types, model parameters, and modeling approaches, is provided in Table 2 and Table 3 for all 50 studies, providing support for the classification and comparative discussion developed in the Section 3 and Section 4. The inclusion of studies based on virgin or compositionally controlled systems is intended to establish a comparative framework for evaluating the transferability of rheological modeling approaches to heterogeneous recycled systems.

3. Results and Findings

The selection process following the PRISMA methodology yielded 50 scientific articles that met the established inclusion criteria. Of these, 21 corresponded to the original dataset of the review, while 29 were incorporated through a complementary search aimed at expanding thematic coverage and strengthening the analysis. This section presents the main concepts and structure of the literature included in the review.

The analyzed studies primarily involve polyolefin-based systems (PE and PP), including both virgin and recycled materials. These systems encompass a wide range of configurations, including polymer blends, lignocellulosic fiber-reinforced composites, materials containing mineral fillers or nanoparticles, and highly heterogeneous systems such as municipal solid waste streams. Overall, a predominance of studies focus on non-recycled or compositionally controlled systems, whereas research explicitly addressing post-consumer polyolefins represents a smaller proportion of the analyzed corpus [48,65,68]. Due to the number of studies included in the analysis, representative references are provided throughout this section to illustrate the identified trends and modeling approaches. A complete description of all analyzed studies is available in Table 2 (Part A) and Table 3 (Part B), which show summaries of the literature corpus included in this review. Part A includes bibliographic information (title and year published) and material system descriptors for the 50 papers. Only sixteen documents report on rheological models of recycled materials. The other works focus on virgin materials, meaning that the models do not need to account for the heterogeneity challenges that many recycled polymer streams present. Part B of the table presents the modeling approach, analytical purpose, and interpretation fields for the studies included in the review.

3.1. Classification of Identified Rheological Models

Based on our systematic analysis, the rheological models reported in the literature can be organized into a hierarchical structure of five levels, defined according to their complexity, physical basis, and typical application level. A summary of the levels is presented in

Table 4. Summary of rheological modeling approaches applied to thermoplastic systems, complexity, typical applications, and required variables.

Modeling Level	Model Type	Model Examples	Typical Systems	Main Variables	Application Context	Typical Application
Level 1	Indirect flow parameters	MFI/MFR, Torque	Recycled polymers, heterogeneous systems	Melt flow index, torque	Processability assessment, screening	Screening
Level 2	Generalized Newtonian Fluid (GNF)	Power-law, Cross, Carreau–Yasuda	Virgin polymers, simple blends, recycled systems	Viscosity, shear rate, flow index	Rheological curve fitting, basic process modeling	Descriptive
Level 3	Viscoelastic constitutive models	PTT, Giesekus, Rolie-Double-Poly	Virgin polymers, controlled composites	Storage and loss modulus, relaxation time	Advanced flow simulation, time-dependent behavior	Predictive
Level 4	Structural/ microstructural models	Suspension models, fiber orientation models	Fiber-reinforced composites, multiphase systems	Viscosity, structural parameters	Structure–property relationships, dispersion analysis	Predictive/ Structural
Level 5	Advanced/ hybrid approaches	Multiscale models, ML-assisted models, mixing rules	Complex blends, recycled systems, eco-composites	Effective viscosity, multiscale parameters	Predictive	Predictive/ Integrative

.

Level 1: Indirect rheological parameters.

This level includes the use of indirect flow parameters such as melt flow index (MFI/MFR) or torque measurements, which describe general trends in material behavior without relying on explicit constitutive formulations [53,58].

Level 2: Generalized Newtonian fluid (GNF) models.

This category includes models such as power law, Cross, and Carreau–Yasuda which describe non-Newtonian behavior through algebraic relationships between shear stress and shear rate [50,51,55,78].

Level 3: Viscoelastic constitutive models.

This level includes models such as Phan–Thien–Tanner (PTT), Giesekus, and Rolie-Double-Poly which incorporate memory effects and relaxation mechanisms, enabling the description of time-dependent and history-dependent behavior [49,54,61].

Level 4: Structural and multiscale models.

These approaches are often used to establish structure–property relationships, relating rheological behavior to aspects of material microstructure such as phase distribution, fiber orientation, and interfacial interactions [45,46,55].

Level 5: Advanced and hybrid approaches.

This level includes multiscale frameworks and hybrid approaches combining physics-based modeling with data-driven techniques, enabling integrative and predictive descriptions of complex systems [60,61,75,80].

3.2. Modeling Approaches Reported in the Review Corpus

To provide a structured overview of the modeling approaches identified in the reviewed studies, Table 4 summarizes the main categories identified in this review and their relevance for the analysis, including processing and formulation of polymer systems and recycled polyolefins. The main rheological models are organized by classification, typical systems, application context, and associated rheological variables. This synthesis enables a direct comparison between modeling levels and highlights their distribution across different types of polyolefin-based systems.

Such classification reveals the coexistence of approaches with different levels of complexity and application scope, which are not uniformly distributed across the analyzed systems [48,54,75].

This hierarchical classification reveals that model selection is not arbitrary but rather strongly dependent on system complexity; simpler models (Levels 1–2) are predominantly used in recycled systems, whereas advanced models (Levels 3–5) are mainly applied to compositionally controlled materials.

3.3. Relationship Between System Type and Modeling Level

The comparative analysis of the reviewed studies reveals a clear relationship between the complexity of the polymer system and the level of rheological modeling employed. In systems based on virgin polymers or compositionally controlled blends, there is a higher prevalence of models at the medium and high levels (Levels 3–5), including constitutive and multiscale approaches [54,71,83].

In contrast, systems involving recycled polyolefins, particularly those of post-consumer origin or with undefined composition, are predominantly analyzed using approaches at the lower and medium levels (Levels 1–2), based on experimental characterization or simplified GNF models [48,65,68].

Finally, rheological modeling is limited or absent in highly heterogeneous systems such as municipal solid waste streams, being largely restricted to experimental assessments of processability [43,65].

This distribution suggests a critical limitation: the models with higher predictive capability are rarely applied to the systems that would benefit most from them, namely, heterogeneous recycled polyolefins.

3.4. Types of Rheological Modeling Usage

The identified models fulfill different roles within the analyzed studies, which can be grouped into four main categories:

• Experimental data fitting: Models used to describe rheological curves obtained from experimental measurements [64].
• Predictive modeling: Models applied to anticipate material behavior under different conditions [61].
• Process analysis: Integration of rheological models into simulations of extrusion, injection molding, or other processing operations [58,71].
• Structural interpretation: Use of rheology to infer microstructural features such as dispersion, interfacial interactions, or phase distribution [45,55].

Overall, rheological models are primarily used for data fitting and process simulation, while their use as predictive tools for formulation remains limited [45,55,61].

3.5. Rheological Variables Considered

The rheological variables reported in the analyzed studies include viscosity, viscoelastic moduli, yield stress, relaxation time, flow index, and zero-shear viscosity [50,54,74].

The selection of variables depends on the type of model employed and the objectives of each study, with greater diversity observed in works that apply constitutive or structural modeling approaches [45,55].

Among the rheological models identified, the Carreau–Yasuda model was selected for detailed parameter-level comparison due to its relatively frequent use across the analyzed studies. As shown in

Table 5. Comparative summary of Carreau–Yasuda parameters in representative polyolefin systems.

Study	System	T (°C)	${\mathit{\eta }}_0\left(\mathit{Pas}\right)$	$\mathit{\lambda }\left(\mathit{s}\right)$	n	a	Key Observation
[53]	Representative system	~200	~3.1 × 103	~0.52	~0.53	~0.46	Typical CY behavior in polyolefin system
[56]	HDPE	200	~3.2 × 105	9.18	0.2	0.57	High entanglement, strong shear-thinning
[61]	Recycled PE	190	~2.5 × 106	0.33	0.058	0.25	Degradation modifies rheological response
[74]	PS (base)	—	3150	0.517	0.534	0.457	Reference condition
[74]	PP55 (high filler)	—	389	0.114	0.67	0.933	Filler reduces ${\eta }_0$ and alters flow behavior

, the model parameters exhibit significant variation depending on polymer type, degradation state, and filler content.

Beyond their role as model inputs, these variables also reflect the underlying physical behavior of polymer systems under flow. In particular, shear viscosity provides a direct representation of how molecular structure, filler content, and interfacial interactions influence processability, which may assist in designing formulas for eco-polymers.

Figure 2 illustrates representative rheological trends commonly observed in filled polyolefin systems. The curves illustrate representative trends reported in the literature, including increased viscosity with filler loading and modifications in flow behavior associated with improved dispersion and interfacial interactions. Both axes are presented on a logarithmic scale. Viscosity decreases with increasing shear rate, reflecting typical shear-thinning behavior. The incorporation of fillers generally leads to an increase in viscosity across the entire shear rate range, which is associated with restricted chain mobility and enhanced particle–matrix interactions. At higher filler loadings, this effect becomes more pronounced and may be related to the formation of particle networks or agglomerated structures. These trends are consistently reported across the reviewed studies and form the basis for the interpretation and modeling of rheological behavior in both virgin and recycled systems.

3.6. Evidence of Fragmentation in Modeling Approaches

Analysis of the reviewed corpus reveals a heterogeneous distribution in the use of rheological models, with no single dominant approach across the literature [43,54,75]. While some studies employ advanced models with high descriptive capability [54,75], others rely solely on experimental analysis or limited empirical correlations without formal modeling [43,70].

This variability is strongly associated with the type of system under analysis, particularly in terms of compositional control and structural complexity.

Across the reviewed studies, the addition of fillers generally leads to a significant increase in viscosity, typically ranging from approximately 20% to over 200% depending on filler content, dispersion quality, and interfacial interactions. This variability reflects the complex interplay between microstructure and flow behavior in both virgin and recycled systems.

A key limitation identified across the analyzed studies is the lack of standardization in rheological testing conditions. Variations in temperature, shear rate or frequency range, and measurement geometry significantly affect the reported values of viscosity and viscoelastic parameters, limiting direct comparison between studies.

Despite these limitations, consistent qualitative trends can be identified, particularly regarding the influence of filler content and structural heterogeneity on rheological response. In experimental conditions, the results indicate that rheological modeling in polymer systems spans a wide range of approaches, from empirical descriptions to advanced multiscale formulations. However, this diversity is not evenly distributed across system types. In particular, the application of rheological models to recycled polyolefins—especially post-consumer streams—remains comparatively limited relative to studies based on virgin or compositionally controlled systems [48,54,65,68,83]. This asymmetry provides a clear basis for our subsequent discussion of the applicability, limitations, and future opportunities of rheological modeling in recycled polymer systems.

4. Discussion

Our analysis of the results presented in Section 3 allows for classification of rheological models used in the literature along with a deeper understanding of how these models are applied in material formulation and the factors limiting their use in recycled polyolefin systems. In this sense, the discussion is structured around three main axes: model typology (RQ1), applications in formulation and processing (RQ2), and challenges and opportunities (RQ3), all of which directly emerge from the patterns identified in the results.

4.1. Rheological Model Typology and Distribution (RQ1)

As shown in Section 3.2, the identified rheological models can be organized into a hierarchical framework ranging from indirect flow parameters to advanced multiscale approaches. This classification reflects not only differences in mathematical complexity but also distinct ways of representing the behavior of polymer melts.

To facilitate a structured comparison of rheological modeling approaches,

Table 6. Representative rheological models, governing equations, and applicability in polyolefin systems.

Model	Governing Equation	Key Parameters	Physical Interpretation	Applicability in Polyolefins
Power-law (Ostwald–de Waele)	$\tau =K{\dot{\gamma }}^n$	K: consistency; n: flow index	Empirical description of shear-thinning	Simple flow characterization; limited predictive capability
Cross	$\eta ={\eta }_{\infty }+{\displaystyle \frac{{\eta }_0-{\eta }_{inf}}{1+(k{\dot{\gamma )}}^m}}$	${\eta }_0,{\eta }_{\infty },k,m$	Transition from Newtonian plateau to shear-thinning	Processing simulations; extrusion/injection modeling
Carreau–Yasuda	$\eta =\eta \infty +({\eta }_0-\eta \infty ){[1+\left(\lambda {\dot{\gamma )}}^a\right)]}^{{\displaystyle \frac{n-1}{a}}}$	${\eta }_0,{\eta }_{\infty },\lambda ,n,a$	Captures full viscosity curve and shear-thinning behavior	Most versatile model for polyolefin melts
Herschel–Bulkley	$\tau ={\tau }_0+K{\dot{\gamma }}^n$	${\tau }_0$, K, n	Incorporates yield stress + shear-thinning	Filled systems; particle-reinforced composites
Phan–Thien–Tanner (PTT)	Constitutive viscoelastic equation	$\lambda ,ϵ,\xi$	Nonlinear viscoelastic behavior	Advanced simulations; viscoelastic flow
Oldroyd-B	Constitutive viscoelastic equation	${\lambda }_1,{\lambda }_2$	Ideal viscoelastic fluid behavior	Theoretical reference; limited practical use

summarizes representative models along with their governing equations, key parameters, and typical applicability in polyolefin systems. This comparison highlights the tradeoff between model simplicity and physical representativeness, particularly when applied to heterogeneous recycled materials.

As shown in Table 6, simpler models such as the Power law and Cross equations provide practical descriptions of flow behavior but lack structural sensitivity. In contrast, the Carreau–Yasuda model offers a more comprehensive representation of viscosity across shear regimes, while viscoelastic constitutive models introduce additional complexity that is often difficult to apply in heterogeneous recycled systems.

Generalized Newtonian fluid (GNF) models (power-law, Cross, Carreau–Yasuda), as summarized in Table 4, represent the most widely used group in the literature for describing the non-Newtonian behavior of polyolefins [50,51,55,78]. Their simplicity and relatively low parameter requirements make them suitable for engineering applications, particularly in process simulations [34,85,86].

In contrast, viscoelastic constitutive models such as Phan–Thien–Tanner (PTT) and Rolie-Double-Poly enable the description of time-dependent and history-dependent phenomena [30,85,86,87], and are mainly used in studies focused on fundamental material behavior or advanced simulations [49,54,61]. In this context, the Carreau–Yasuda model (Table 5) represents an intermediate approach that balances descriptive capability and practical applicability, making it particularly suitable for analyzing polyolefin systems with varying levels of complexity.

Additionally, structural and multiscale models establish links between rheological response and material microstructure [34,85,86], including effects related to phase distribution, fiber orientation, and interfacial interactions [45,46,55]. This comparison highlights that different modeling approaches capture distinct aspects of material behavior, ranging from purely empirical descriptions of flow to models that incorporate structural and microstructural information.

However, as evidenced in Section 3.3, these modeling levels are not uniformly distributed across the analyzed systems but are instead strongly dependent on the type of material. While higher-complexity models are predominantly applied to compositionally controlled systems [54,71,83], recycled systems are typically addressed using simplified models or direct experimental characterization [48,65,68]. This pattern indicates that the literature does not follow a linear evolution toward increasingly sophisticated models, instead exhibiting a coexistence of approaches operating in parallel and conditioned by material complexity. This coexistence suggests that model selection is not driven solely by theoretical suitability but also by practical constraints such as data availability and system heterogeneity. As a result, the most advanced rheological models are seldom applied to recycled polyolefin systems, where their potential predictive value would be most relevant.

4.2. Application of Rheological Modeling in Formulation and Processing (RQ2)

The results indicate that rheological modeling fulfills multiple roles within the analyzed studies (Section 3.4), with the most common being experimental data fitting and process analysis. In the first case, models are primarily used to describe experimentally obtained rheological curves, without necessarily aiming at broader predictive capabilities [74]. In the second, they are integrated into simulations of extrusion or injection molding processes to estimate operational variables such as pressure, temperature, and flow distribution [68,81]. In contrast, the use of rheological modeling as a tool for material formulation remains limited, although rheological parameters such as viscosity, $\left(G^{\prime }\right)$, and $\left(G^{″}\right)$ are frequently used to infer aspects such as filler dispersion or matrix–filler interactions [31,38]. In this context, specific rheological parameters can be directly associated with material performance; for instance, an increase in the low-frequency storage modulus $\left(G^{\prime }\right)$ is often linked to the formation of filler networks and correlates with improved stiffness and tensile modulus. Similarly, changes in zero-shear viscosity $\left({\eta }_0\right)$ are commonly associated with molecular weight variations and can influence processability and mechanical behavior [21,23,26,56]. In recycled systems, this limitation becomes even more evident. As shown in Section 3.3, studies involving post-consumer polyolefins predominantly rely on empirical or simplified approaches [41,75,78], which restricts the possibility of establishing generalizable relationships between composition, rheology, and performance. In this context, the increase in viscosity with filler loading can also be interpreted from a structural standpoint in terms of rheological percolation. At critical filler concentrations, the formation of interconnected particle networks leads to a transition in flow behavior, often reflected by a marked increase in low-frequency moduli and the emergence of yield-like responses. Although this phenomenon is well documented in composite systems, its identification in lignocellulosic and recycled polyolefin systems remains challenging due to the variability in particle size, dispersion, and interfacial interactions. As a result, although rheological models are applied in different contexts, their effectiveness varies significantly depending on the system characteristics. In compositionally controlled systems, these models are commonly used to predict material behavior and optimize processing conditions with relatively high accuracy. However, in recycled polyolefin systems their application is often limited to describing general flow trends such as viscosity reduction due to thermomechanical degradation. In addition, the variability in rheological testing conditions across studies, such as differences in temperature, shear rate or frequency range, and measurement geometry, further complicates the comparison and generalization of results, particularly in heterogeneous recycled systems. For example, generalized Newtonian models have been successfully used to capture shear-thinning behavior and to adjust processing parameters in recycled polypropylene systems; nevertheless, these approaches do not account for key structural factors such as changes in molecular weight distribution, the presence of contaminants, or variations in filler dispersion, all of which are inherent to post-consumer materials. As a result, the use of rheological models in recycled systems remains predominantly descriptive rather than predictive, highlighting a gap between model capability and practical application in formulation and design.

Nevertheless, recent studies suggest emerging advances in this direction, particularly through hybrid approaches that combine physics-based modeling with data-driven techniques [71,86] as well as through the use of effective rheological properties to represent complex mixtures [88]. These developments indicate a potential transition toward more predictive tools, although their application remains at an early stage.

4.3. Challenges and Opportunities in Recycled Systems (RQ3)

Based on the patterns identified in the results, several factors can be identified as limiting the application of rheological modeling in recycled polyolefins [55,58,59,60].

First, the structural and compositional complexity of these materials represents a fundamental challenge. As shown in Section 3.3, the presence of polymer blends, degradation effects, and contaminants introduces variability that complicates the application of models originally developed for ideal systems [48,65].

Second, experimental limitations affect the acquisition of reliable rheological data, particularly in systems with high filler content or strong heterogeneity, where modeling is often replaced by direct characterization approaches [43,69,70].

A third factor is the mismatch between modeling levels and application needs. The results (Section 3.2 and Section 3.6) indicate that advanced models are not applied in the systems where they would be most useful, with simpler approaches dominating for recycled materials [48,54,75].

More sophisticated models typically rely on parameters that are difficult to measure experimentally, such as relaxation spectra or interfacial properties, which limits their practical implementation [45,46]. These challenges are not independent but rather intrinsically interconnected, as they all contribute to the variability of rheological response. In heterogeneous recycled systems, rheological behavior reflects the combined effects of molecular degradation, compositional variability, and interfacial interactions, making it difficult to isolate individual contributions through conventional modeling approaches. Despite these challenges, the results also highlight relevant opportunities, including:

• Development of hybrid approaches combining physical modeling and machine learning techniques [60,61].
• Use of effective properties and mixing rules to represent complex systems [27].
• Implementation of advanced experimental techniques such as in-line rheometry to improve data quality [27].

Collectively, these approaches point toward the need to develop models that balance complexity, predictive capability, and experimental feasibility.

The results indicate that rheological modeling in the literature is broad in scope; however, its application to recycled systems remains comparatively limited. This disparity does not arise from the absence of suitable models but rather from the difficulty of adapting them to heterogeneous and variable materials with limited characterization. In this context, the main challenge is not the mathematical formulation of the models themselves but their transferability and adaptation to real systems, particularly in the recycling of polyolefins.

Overall, the findings of this review suggest that progress in the rheological modeling of recycled polyolefins will depend on the development of integrative approaches capable of effectively linking material structure, rheological behavior, and processing performance under realistic industrial conditions.

Based on the analyzed studies, a simplified roadmap for the application of rheological modeling in post-consumer polyolefins can be proposed:

• Initial characterization using melt flow index (MFI) and viscosity curves to establish baseline flow behavior and detect major variations due to degradation.
• Identification of key rheological parameters such as zero-shear viscosity, flow behavior index, and viscoelastic moduli as indicators of structural and compositional changes.
• Selection of an appropriate modeling level based on system complexity, using generalized Newtonian models for process-oriented analysis and more advanced approaches when sufficient data are available.
• Integration of rheological data into process simulation and formulation strategies, enabling indirect assessment of material behavior in systems with unknown composition.

This framework highlights the potential of rheology not only as a characterization tool but as a practical basis for decision-making in the design of recycled polymer systems.

5. Conclusions

This review analyzed 50 studies addressing rheological modeling in thermoplastic systems, with a particular focus on polyolefins and their recycled counterparts. The results demonstrate that rheological models can be organized into a hierarchical framework ranging from indirect flow parameters to advanced multiscale and hybrid approaches, with model selection strongly dependent on system complexity and data availability.

Analysis reveals that while generalized Newtonian and empirical approaches are widely applied in recycled systems due to their robustness and limited data requirements, more advanced viscoelastic and structural models remain predominantly restricted to compositionally controlled materials. This imbalance highlights a key limitation in the current literature: the systems that would benefit most from predictive modeling, namely, heterogeneous post-consumer polyolefins, are often addressed using more simplified or descriptive approaches.

Furthermore, although rheological parameters such as viscosity, storage modulus, and loss modulus are frequently used to characterize material behavior, their integration into predictive frameworks for formulation remains limited. In most cases, rheological modeling is applied to describe flow behavior or support process simulations rather than to establish quantitative relationships between composition, structure, and performance. In addition, variability in experimental conditions across studies limits the comparability and generalization of rheological data.

Based on these findings, we propose that rheological parameters can be interpreted as integrative state variables capturing the combined effects of molecular structure, degradation, compositional variability, and interfacial interactions in complex polymer systems. This perspective provides a conceptual basis for extending the role of rheology beyond characterization, enabling its use as a tool for formulation and decision-making in systems with unknown or variable composition.

Finally, a simplified roadmap for the application of rheological modeling in recycled polyolefins is identified, emphasizing the progressive use of experimental characterization, parameter identification, and model selection according to system complexity. Future research should focus on developing integrative approaches that combine rheological measurements with structural analysis and data-driven methods in order to bridge the gap between descriptive modeling and predictive material design in recycled polymer systems. Future research should also prioritize standardizing rheological testing conditions and reporting protocols in order to enhance reproducibility and enable more robust cross-study comparisons, particularly in heterogeneous recycled systems.