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 on 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 explores innovative modeling strategies for understanding fluid dynamics in complex, deformable, and branched flow systems across multiple scales. The elastoviscoplastic (EVP) behavior of fluids under external forcing to model droplet spreading, coalescence, and filtering over porous and soft substrates. Wall slip and junction resistance effects of the flow in tree-like structure. The objective of this paper is to raise awareness about these relatively neglected or unexplored areas of research, encouraging researchers to put efforts towards 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. 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. These innovations could open up new avenues of exploration and help overcome some of the existing limitations in past and current research.