Emerging perspectives in non-Newtonian fluid dynamics: Research gaps, evolving methods, and conceptual limitations

This paper primarily focuses on areas within non-Newtonian fluid mechanics that remain underexplored or inadequately investigated. It highlights research domains that have not received sufficient attention or detailed study, while also considering the emergence of new areas unexplored by recent scientific and technological advancements. For example, this study explores research directions and innovative modeling and theoretical strategies for understanding fluid dynamics in complex, deformable, and branched flow systems across multiple scales. The elastoviscoplastic behavior of fluids under external forcing is used to model droplet spreading, coalescence, and filtering over porous and soft substrates. Wall slip and junction resistance effects of the flow are in a tree-like structure. The study also highlights and explores research directions in the flow physics of non-Newtonian fluids that exhibit odd viscosity and odd elasticity, focusing on their unconventional stress–strain responses and the resulting unique flow behaviors. The objective of this paper is to raise awareness about these relatively neglected or unexplored areas of research, encouraging researchers to put efforts toward these promising domains. By doing so, they can contribute to advancing the field in ways that diverge from which have already been sufficiently explored and may lead to breakthroughs and novel discoveries by generalizing the existing laws or creating new models and laws. Moreover, addressing these under-explored areas could have far-reaching implications for both theoretical and practical applications in non-Newtonian fluid mechanics. Investigating these areas more deeply could uncover new insights, enhance existing models, and drive forward technological advancements that were previously overlooked. In addition, this paper will briefly discuss the potential introduction of novel tools, techniques, and methodologies that could be applied to these research areas, as well as to the broader field of non-Newtonian fluid mechanics. Furthermore, we also discuss the current and upcoming applications using non-Newtonian fluids. These innovations could open up new avenues of exploration and help overcome some of the existing limitations in past and current research.