In the last two decades, microneedles (MNs) have received significant interest due to their potential for painless transdermal drug delivery (TDD) and minimal skin damage. MNs have found applications in a range of research and development areas in drug delivery. They have been prepared using a variety of materials and fabrication techniques resulting in MN arrays with different dimensions, shapes, and geometries for delivery of a variety of drug molecules. These parameters play crucial roles in determining the drug release profiles from the MNs. Developing mathematical modelling, simulation, and optimisation techniques is vital to achieving the desired MN performances. These will then be helpful for pharmaceutical and biotechnological industries as well as professionals working in the field of regulatory affairs focusing on MN based TDD systems. This is because modelling has a great potential to reduce the financial and time cost of both the MNs’ studies and manufacturing. For example, a number of robust mathematical models for predicting the performance of the MNs in vivo have emerged recently which incorporate the roles of the structural and mechanical properties of the skin. In addressing these points, this review paper aims to highlight the current status of the MN modelling research, in particular, the modelling, simulation and optimisation of the systems for drug delivery. The theoretical basis for the simulation of MN enhanced diffusion is discussed within this paper. Thus, this review paper provides a better understanding of the modelling of the MN mediated drug delivery process.

The power-law fluid flow in tree-like self-similar branching networks is prevalent throughout the natural world and also finds numerous applications in technology such as oil recovery and microfluidic devices. We investigate analysis of optimal power-law fluid flow conditions and the optimal structures within tree-like branching networks, focusing on maximizing flow conductance under the constraint of the network tube’s volume and the surface area. The study considered fully developed laminar power-law fluid flow regimes without considering any losses in the network system. A key observation was the sensitivity of the dimensionless effective flow conductance to the network’s geometrical parameters. We found that the maximum flow conductance occurs when a dimensionless radius ratio β∗ satisfies the equation β∗=N−1/3 and β∗=N−(n+1)/(3n+2) under constrained tube-volume and surface-area, respectively. Here, N represents the bifurcation number of branches splitting at each junction, and n is the fluid power-law index. We further find that this optimal condition occurs when pressure drops are equipartition across each branching level. We validated our results with various experimental results and theories under limiting conditions. Further, Hess–Murray’s law is justified and extended for the shear-thinning and shear-thickening fluid flows for an arbitrary number of branches N. Further, in this study, we also derive the relationships between the geometrical and flow characteristics of the parent and daughter tubes as well as the generalized scaling laws at the optimal conditions for the other essential parameters such as tube-wall stresses, length ratios, mean velocities, tube-volume, and surface-area of the tube distributing within the networks. We find that the fluid power-law index n does not influence the constrained tube-volume scaling at the optimal conditions; however, the scaling laws vary with n under the constrained tube’s surface area. These findings offer valuable design principles for developing efficient transport and flow systems.

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.