Overview:- There are no smooth surfaces in nature. Almost all surfaces present in nature are covered with patterned rough elements or rigid/elastic porous coatings in the form of hairs, feathers, and other filamentous features. A few notable scenarios include dermal denticles of shark skins, seal fur, hierarchical roughness on lotus leaves, scales on butterfly wings, feathers of birds and geometry of arterial walls. The geometry of these coatings are so complex and have gone through several cycles of optimization during the course of million years of evolution. With the help of such controlled geometrical coatings, these living creatures modify the surrounding fluid flows to their favour, and achieve energy efficient locomotion by minimizing skin-friction forces acting on them. The present work is focused on developing the essential mathematical framework to aid the design of such nature-inspired surfaces.
Importance:- Researchers in recent years are interested in designing biomimetic complex surfaces that can be useful in aerospace, automobile and energy sector. An essential prerequisite to design tailor-made surfaces is the quantification of the complex interplay between microscale geometrical details of the coating and the associated transport phenomena. Existing mathematical models and computational schemes are very expensive to provide this knowledge. In this work, we derive an accurate mathematical formulation to simulate the coupled interaction between the fluid flow and the surface coatings. The important implication of this project is that it provides a viable computational tool that can be used to understand how geometrical details of the coating will affect the flow field, and aid the design of novel surfaces.
Overall objectives: A major obstacle to simulate flow over complex surface coatings is the multiscale nature of the problem. This is exemplified in figure 1, which shows geometry of flow through a channel of which one wall is covered with rough features. This renders geometry resolved numerical simulations a prohibitively expensive task even with most powerful supercomputers. Hence, they are ‘intractable’ in practice. The objective of this work is to provide an alternative ‘tractable’ computational framework that enables us to model flow over complex surface coatings. To be precise, we derive physics-motivated equivalent mathematical formulations that does not require us to consider all the complex details of the coating (figure 1).
