The flow of layered fluids in microchannels plays a key role in several micro devices aimed at solvent extraction, chemical processing, bio-chemical diagnosis, etc. Despite the viscous, low-Re nature of these flows, quite complex dynamics can arise due to an interplay between the two fluids, as well as interfacial forces acting at the liquid-liquid interface, or elastic forces in cases where the fluids are separated by a membrane (as in membrane extraction or the organ-on-a-chip device, see adjoined figure). Our work in this area will focus on developing and analysing mathematical models of these systems, in order to understand the physical principles governing their dynamics. This work will point to strategies for improving system performance. Moreover, the elasto-hydrodynamic fluid-membrane-fluid problem serves as a simple model system for understanding how low-Re viscous flows interact with a thin, deformable solid plate/membrane, which is relevant to flow past cells and in the heart and lungs.
This project will involve understanding and applying mathematical methods like reduced-order modelling, and stability analysis. Simulations will also be needed, but of simplified models. To get started, a knowledge of fluid dynamics, mathematics of ODEs and preferably also of PDEs is important. Experience using Matlab or Python is also useful. If you don't have a background in some of these areas, then don't worry---you can learn, but you must have a strong interest in them.
For information on the other problems my group works on, you can visit my personal and group webpages.