Rheological Studies, Mathematical Analysis, and Numerical Methods for Multiphase and Non-Newtonian Fluid Flows

Dear Colleagues,

We are pleased to present this special issue of our journal, dedicated to the exploration of "Rheological Studies, Mathematical Analysis, and Numerical Methods for Multiphase and Non-Newtonian Fluid Flows". This edition brings together a curated selection of cutting-edge research articles, review papers, and technical notes that advance our understanding and capabilities in the dynamic field of complex fluid flow analysis.

The study of non-Newtonian fluids, with their unconventional flow behaviors, and multiphase flows, with their intricate interfacial dynamics, has remained a domain of considerable academic and industrial interest. The considered phenomena include phase change processes, and non-Newtonian fluids behavior, such as blood, slurry transports and polymer solutions. These flows are encountered in a multitude of processes ranging from environmental phenomena to the most sophisticated engineering systems. The articles featured in this issue offer a glimpse into the profound complexities of these fluids, whose behaviors challenge traditional rheological models and necessitate the development of robust mathematical and numerical approaches.

This issue highlights innovative rheological investigations that reveal the nuanced stress-strain relationships in complex fluids, pushing the boundaries of what we know about their flow and deformation characteristics. Theoretical advancements in the mathematical modeling of these fluids provide a framework for understanding their unique behaviors under various conditions and geometries. A special focus on 1D problems and exact solutions constitutes a guide to understanding the phenomena by simplifying the model while keeping the main characteristics.

Moreover, we delve into the numerical realm, showcasing the latest developments in computational methods tailored for the simulation of multiphase and non-Newtonian flows. From finite volume schemes to advanced computational fluid dynamics (CFD) techniques, our contributors demonstrate the effectiveness of numerical tools in capturing the intricacies of these challenging flow systems.

In recognition of the increasing need for precision and efficiency in simulations, this issue also explores the intersection of traditional numerical methods with innovative computational paradigms, including machine learning and high-performance computing. These synergies pave the way for more accurate, stable, and efficient simulation approaches that promise to revolutionize the field.

Each contribution within this issue not only stands as a testament to the individual expertise and innovative spirit of its authors but also as a collective milestone in our continuous quest to model and manipulate the enigmatic nature of multiphase and non-Newtonian fluids. This compendium is intended to serve as a vital resource for researchers, engineers, and practitioners in the field, inspiring new questions and fostering collaborative endeavors to address the numerous challenges that remain.

As we present this special issue, we invite our readers to engage with the research findings and critical discussions contained within, which we hope will serve as catalysts for further discovery and innovation in the fascinating world of multiphase and non-Newtonian fluid flow research.

Prof. Dr. Fayssal Benkhaldoun
Prof. Dr. Abderrahim Maazouz
Guest Editors

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• rheological studies
• mathematical analysis
• numerical methods
• multiphase flows
• non-Newtonian fluids
• fluid mechanics
• computational fluid dynamics (CFD)
• finite volume schemes
• interfacial dynamics
• complex fluids
• machine learning in fluid dynamics
• high-performance computing
• conservation laws
• phase transition
• viscosity models
• industrial processes
• theoretical modelling