I am interested broadly in numerical methods and biofluids with particular emphasis on Stokes flow. I have two active projects and the details of these can be viewed using the tabs below

Singly-periodic Stokes Flow with a Wall

There are many real world phenomena of interest that involve viscous fluid near a wall or surface such as the beating of cilia and blood flow through small capillaries. There are often situations that involve many repeated structures, like carpets of cilia and flow past obstacles. It can be computationally expensive to the extent of being prohibitive to model a large number of these structures individually. One approach to try and still capture the influence of many structures is to assume that they are periodically repeated. In this project I obtained the exact flow due to an infinite array of regularized Stokeslet in 2 dimensions. Using the method of images this result was extended to enforce zero flow along a wall. A few applications were looked at, such as simulating an infinite array of cilia (the beat shape of a single cilia is shown here) as well as flow past periodic objects near a wall (the streamlines of two periods of an example configuration is shown below)


Simulating Cilia in 3 Dimensions

Cilium play a diverse and important role in biology, from facilitating the transport of the ovum through the Fallopian tubes to the movement of mucus and particles in the lungs and mechanotransduction. The biological structure of cilium has been fairly well documented (the so called "9+2" axoneme structure), but it is still unkown how the individual parts interact to form a cohesive and regular beat. This projects looking at modeling cilia where the beat shape arises organically from attempting to simulate the internal mechanisms. This approach means that the motion of the cilium itself is coupled with the fluid and properties that depend on hydrodynamic coupling such as how the beat frequency depends on the spacing between cilia and the synchronization of cilia beat patterns can be investigated.