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Advances in Computational Mechanics of Non-Newtonian Fluids, 2nd Edition

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A special issue of Fluids (ISSN 2311-5521). This special issue belongs to the section "Non-Newtonian and Complex Fluids".

Deadline for manuscript submissions: 31 August 2026 | Viewed by 7385

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Dr. Chengcheng Tao

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Guest Editor

School of Construction Management Technology, Purdue University, West Lafayette, IN 47907, USA
Interests: multiscale modeling of materials; hazard-resilient infrastructure; machine learning application; multi-objective optimization; computational fluid dynamics (CFD); sustainable construction materials
Special Issues, Collections and Topics in MDPI journals

Dr. Mehrdad Massoudi

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Guest Editor

Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Interests: multi-component flows; non-Newtonian fluids; granular materials; heat transfer; mathematical modelling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Non-Newtonian (non-linear) fluids are common in nature (mud, honey, avalanches, etc.), but are also found in many petroleum, geotechnical, chemical, biological, food, pharmaceutical, and personal care processing industries. This Special Issue of Fluids is dedicated to the recent advancements in the mathematical, physical, and computational aspects of non-linear fluids with industrial applications, especially those concerned with computational fluid dynamics (CFD) studies. These fluids include traditional non-Newtonian fluid models, electro- or magneto-rheological fluids, granular materials, slurries, drilling fluids, polymers, blood and other biofluids, mixtures of fluids and particles, etc.

Dr. Chengcheng Tao
Dr. Mehrdad Massoudi
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fluids is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

non-Newtonian fluids
rheology
multiphase flow
computational fluid dynamics (CFD)
mathematical modeling
viscoelasticity
thixotropy
slurries
suspensions
polymers
biofluids
geofluids

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Advances in Computational Mechanics of Non-Newtonian Fluids in Fluids (13 articles)

Published Papers (6 papers)

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Research

17 pages, 3950 KB

Open AccessArticle

Friction Drag Characteristics of Non-Newtonian Weighted Fracturing Fluids in Pipe Flows

by Jianxin Peng, Liwei Wang, Xin Qiao, Ju Liu, Sixin Li, Wen Zhang, Yanyan Feng, Zhanying Zheng and Yu Zhou

Fluids 2026, 11(4), 101; https://doi.org/10.3390/fluids11040101 - 17 Apr 2026

Abstract

Non-Newtonian weighted fracturing fluids are used to carry out hydraulic fracturing operations into the deep and ultra-deep earth for oil and gas extraction, though their flow and friction drag characteristics are largely unknown. This study aims to understand the abovementioned characteristics. An engineering-oriented cost-effective numerical scheme is deployed, incorporating LES with a generalized Newtonian fluid constitutive equation, for predicting the non-Newtonian pipe flow and friction drag coefficient C_f. The weighted fracturing fluid is described as a power-law fluid, i.e., viscosity

μ (\dot{γ}) = K {\dot{γ}}^{n - 1}

, where both K and n are coefficients related to fluid rheology, and

\dot{γ}

is the shear rate. The influences of fluid density ρ, mean velocity U and pipe diameter D, as well as K and n on C_f were documented and compared with a water pipe flow. It was found that C_f = f₁ (K, n, ρ, U, D) may be reduced to C_f = f₂ (Re_g), where the scaling factor Re_g = ρU²⁻ⁿDⁿ/(K8ⁿ⁻¹) is the generalized Reynolds number. This scaling law can reasonably well predict the friction drag variation in the pipe flow of non-Newtonian weighted fracturing fluids throughout a range of interests and engineering applications. Full article

(This article belongs to the Special Issue Advances in Computational Mechanics of Non-Newtonian Fluids, 2nd Edition)

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24 pages, 11871 KB

Open AccessArticle

MCV-Driven Effective Viscosity Modulation and Its Hemodynamic Impact in an Idealized Carotid Bifurcation: A Computational Fluid Dynamics Study

by Arif Çutay, Hakan Bayrakcı, Özdeş Çermik and Muharrem İmal

Fluids 2026, 11(2), 40; https://doi.org/10.3390/fluids11020040 - 29 Jan 2026

Viewed by 453

Abstract

Mean corpuscular volume (

M C V

) is a routinely measured hematological parameter that influences blood viscosity by altering red blood cell volume and packing density. Although

M C V

is physiologically linked to hemorheological behavior, to the authors’ knowledge, its direct [...] Read more.

Mean corpuscular volume (

M C V

) is a routinely measured hematological parameter that influences blood viscosity by altering red blood cell volume and packing density. Although

M C V

is physiologically linked to hemorheological behavior, to the authors’ knowledge, its direct role in modulating large-artery hemodynamics has not been systematically quantified. This study introduces an

M C V

-driven effective Newtonian viscosity mode to evaluate the first-order impact of

M C V

variation on carotid bifurcation flow. Rather than employing shear-dependent constitutive laws, blood viscosity was scaled through an

M C V

-based formulation, yielding three Newtonian fluids corresponding to clinically relevant

M C V

levels of 70, 90, and 110 fL. Pulsatile CFD simulations were performed in four idealized carotid bifurcation geometries (40°, 50°, 65°, and 100°) to assess the combined influence of vascular geometry and

M C V

-dependent viscosity variation. Hemodynamic indices including time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and relative residence time (RRT) were quantified, and a two-way analysis of variance (ANOVA) was employed to distinguish the relative contributions of geometric configuration and

M C V

. Across the investigated

M C V

range, increasing

M C V

produced a geometry-dependent modulation of shear-based indices, with TAWSS increasing by up to approximately 11%, while OSI and RRT decreased by about 20–25% and 10%, respectively, particularly in geometries exhibiting pronounced flow separation. Although vascular geometry remained the dominant determinant of overall hemodynamic patterns,

M C V

-induced viscosity scaling significantly modulated low-shear and recirculation regions. These findings suggest that

M C V

-dependent viscosity scaling can complement patient-specific hemodynamic assessments and provide a rational baseline for future shear-dependent and personalized rheological modeling frameworks. Full article

(This article belongs to the Special Issue Advances in Computational Mechanics of Non-Newtonian Fluids, 2nd Edition)

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25 pages, 5300 KB

Open AccessArticle

CFD Analysis of Non-Isothermal Viscoelastic Flow of HDPE Melt Through an Extruder Die

by Aung Ko Ko Myint, Nontapat Taithong and Watit Pakdee

Fluids 2025, 10(9), 238; https://doi.org/10.3390/fluids10090238 - 8 Sep 2025

Cited by 1 | Viewed by 1830

Abstract

The optimization of polymer extrusion processes is crucial for improving product quality and manufacturing efficiency in plastic industries. This study aims to investigate the viscoelastic flow behavior of high-density polyethylene (HDPE) through an extrusion die with an internal mandrel, focusing on the effects of die geometry and flow parameters. A two-dimensional (2D) numerical model is developed in COMSOL Multiphysics using the Oldroyd-B constitutive equation, solved using the Galerkin/least-square finite element method. The simulation results indicate that the Weissenberg number (Wi) and die geometry significantly influence the dimensionless drag coefficient (Cd) and viscoelastic stress distribution along the die wall. Furthermore, filleting sharp edges of the die wall surface effectively reduces stress oscillations, enhancing flow uniformity. These findings provide valuable insights for optimizing die design and improving polymer extrusion efficiency. Full article

(This article belongs to the Special Issue Advances in Computational Mechanics of Non-Newtonian Fluids, 2nd Edition)

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18 pages, 1911 KB

Open AccessArticle

Rapid Assessment of Relative Hemolysis Amidst Input Uncertainties in Laminar Flow

by Nasim Gholizadeh, Ryan Wang, Gayatri Gautham and Gautham Krishnamoorthy

Fluids 2025, 10(9), 228; https://doi.org/10.3390/fluids10090228 - 29 Aug 2025

Viewed by 1082

Abstract

Predicting absolute values of hemolysis using the power law model to guide medical device design is hampered by uncertainties stemming from four sources of model inputs: incoming/upstream velocity profiles, blood viscosity models, power law hemolysis coefficients, and obtaining accurate stress exposure times. Amidst all these uncertainties, enabling rapid assessments and predictions of relative hemolysis would still be valuable for evaluating device design prototypes. Towards achieving this objective, hemolysis data from the Eulerian modeling framework was first generated from computational fluid dynamics simulations encompassing five blood viscosity models, four sets of hemolysis power law coefficients, fully developed as well as developing velocity flow conditions, and a wide range of shear stresses, strain rates, and stress exposure times. Corresponding hemolysis predictions were also made in a Lagrangian framework via numerical integration of shear stress and residence time spatial variations under the assumption of fully developed Newtonian fluid flow. Absolute hemolysis predictions (from both frameworks) were proportional to each other and independent of the blood viscosity model. Further, relative hemolysis trends were not dependent on the hemolysis power law coefficients. However, accuracy in wall shear stresses in developing flow conditions is necessary for accurate relative hemolysis assessments. Full article

(This article belongs to the Special Issue Advances in Computational Mechanics of Non-Newtonian Fluids, 2nd Edition)

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21 pages, 3783 KB

Open AccessArticle

Fluid–Structure Interaction Effects on Developing Complex Non-Newtonian Flows Within Flexible Tubes

by Sheldon Wang, Dalong Gao and Hassan Pouraria

Fluids 2025, 10(8), 210; https://doi.org/10.3390/fluids10080210 - 10 Aug 2025

Cited by 1 | Viewed by 1147

Abstract

Complex non-Newtonian glues are widely used in electrical vehicle (EV) manufacturing plants. In this paper, we focus on initial transient and compressibility issues which are closely associated with high pressure, boundary conditions, and flexible tubes, as well as their respective fluid–structure interaction effects. Both thixotropic and power law non-Newtonian nearly compressible fluid models have been employed to couple with flexible tubes with two different sets of material properties, namely, Young’s modulus and density. In addition to thick-wall cylindrical pressure vessel solutions, different pressure and velocity boundary conditions have also been studied with the consideration of initial transient and steady solutions for acoustic models. Moreover, the radial direction displacement distributions through the tube wall thickness and axial directions compare well within 4 to 9 percentage points with theoretical solutions of thick-wall cylinders under internal and external pressures. Finally, inverse optimization methods have been employed for the calibration of key parameters in comparison with experimental and computational results. Full article

(This article belongs to the Special Issue Advances in Computational Mechanics of Non-Newtonian Fluids, 2nd Edition)

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19 pages, 3763 KB

Open AccessArticle

Mathematical Study of Pulsatile Blood Flow in the Uterine and Umbilical Arteries During Pregnancy

by Anastasios Felias, Charikleia Skentou, Minas Paschopoulos, Petros Tzimas, Anastasia Vatopoulou, Fani Gkrozou and Michail Xenos

Fluids 2025, 10(8), 203; https://doi.org/10.3390/fluids10080203 - 1 Aug 2025

Cited by 3 | Viewed by 2302

Abstract

This study applies Computational Fluid Dynamics (CFD) and mathematical modeling to examine uterine and umbilical arterial blood flow during pregnancy, providing a more detailed understanding of hemodynamic changes across gestation. Statistical analysis of Doppler ultrasound data from a large cohort of more than [...] Read more.

P S V

) between the 22nd and 30th weeks, while uterine artery velocities remain relatively stable, suggesting adaptations in vascular resistance during pregnancy. By combining the Navier–Stokes equations with Doppler ultrasound-derived inlet velocity profiles, we quantify several key fluid dynamics parameters, including time-averaged wall shear stress (

T A W S S

), oscillatory shear index (

O S I

), relative residence time (

R R T

), Reynolds number (

R e

), and Dean number (

D e

), evaluating laminar flow stability in the uterine artery and secondary flow patterns in the umbilical artery. Since blood exhibits shear-dependent viscosity and complex rheological behavior, modeling it as a non-Newtonian fluid is essential to accurately capture pulsatile flow dynamics and wall shear stresses in these vessels. Unlike conventional imaging techniques, CFD offers enhanced visualization of blood flow characteristics such as streamlines, velocity distributions, and instantaneous particle motion, providing insights that are not easily captured by Doppler ultrasound alone. Specifically, CFD reveals secondary flow patterns in the umbilical artery, which interact with the primary flow, a phenomenon that is challenging to observe with ultrasound. These findings refine existing hemodynamic models, provide population-specific reference values for clinical assessments, and improve our understanding of the relationship between umbilical arterial flow dynamics and fetal growth restriction, with important implications for maternal and fetal health monitoring. Full article

(This article belongs to the Special Issue Advances in Computational Mechanics of Non-Newtonian Fluids, 2nd Edition)

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