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

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

Deadline for manuscript submissions: 28 February 2026 | Viewed by 43

Special Issue Editors


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Guest Editor
School of Construction Management Technology, Purdue University, West Lafayette, IN 47907, USA
Interests: multi-scale modeling of materials; hazard-resilient infrastructure; machine learning application; multi-objective optimization; computational fluid dynamics; sustainable construction materials
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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

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Keywords

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

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Published Papers (1 paper)

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Research

19 pages, 3765 KiB  
Article
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 (registering DOI) - 1 Aug 2025
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.
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 200 pregnant women (in the second and third trimesters) reveals significant increases in the umbilical arterial peak systolic velocity (PSV) 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 (TAWSS), oscillatory shear index (OSI), relative residence time (RRT), Reynolds number (Re), and Dean number (De), 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
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