Research

Flow dominated by viscous dissipation—or "creeping flow"—is commonplace in micro-scale systems like microfluidic chips and in capillaries which carry blood to every part of the human body. While the equations of fluid motion are simplified in this case (Stokes instead of Navier-Stokes), there is still great need for efficient methods for simulation and analysis of these systems, especially if one is concerned with flows in complex biological settings, many-body hydrodyanmic interactions, or systems involving additional physics due to electromagnetic fields, chemical potential gradients, etc.

The method of regularized Stokeslets (MRS) [1] is a robust method for the numerical solution of creeping flow problems that is popular in biological fluid mechanics and fluid-structure interaction problems. The method works by representing the action of moving boundaries as a collection of "point forces", or "Stokeslets", placed on the boundary and acting on the fluid. For numerical reasons, these point forces must be spread or "regularized" over a small but finite volume of fluid, and the choice of regularization critically affects the accuracy and computational expense of the method. I have developed an easy way to generate families of regularized Stokeslets with low computational cost and favorable error properties [2]. This research allows for more efficient and accurate MRS simulations of flow in a variety of systems under viscous flow.

Fluid interfaces are ubiquitous in nature and in a variety of industries. Microscopic colloidal particles can adsorb to these interfaces, creating a physically rich system useful for creating manufacturing tools and consumer products [3]. One may also take advantage of interfacial physics to deliver drug-carrying particles to parts of the human body like the lung [4]. Moreover, these particles can be driven into motion by external forces or internal chemical or mechanical activity, adding another dimension of physical richness and potential applications to these "active" particle-laden interfaces [5], [6].

While working as a Postdoctoral Researcher in the Stebe Lab at the University of Pennsylvania, I performed fundamental research to push our theoretical understanding of these systems to new levels [7]. My results laid groundwork for the new experimental methods to measure key properties of fluid interfaces [8]. They also predict fluid flows generated by bacteria adsorbed to oil-water interfaces, which has implications for oil remediation and bacterial infections [9].

The understanding the locomotion of small organisms is important for our understanding of their biology. It is also important for designing biomimetic swimmers in the form of autonomous microrobots or millirobots, which have potential uses in drug delivery, microfluidic chips, and environmental remediation [10].

My PhD thesis investigated how a spherical "squirmer" a mathematical model of a tiny swimmer, self-propels through a fluid [11]. Swimmers can be categorized by their swimming stroke, which can either be that of a "puller", which is breast-stroke-like and propelled from the trailing end, or a "puller", which is propelled from the leading end. Simulations that I performed revealed fundamental differences in these two cases, with pullers leading to turbulent flow at larger Reynolds number— that is, for faster or larger swimmers—and pushers maintaining steady, laminar flow.

I also studied how these swimmers mix the surrounding fluid by analyzing their wake structures using asymptotic methods [12]. In particular, I showed that that the drift volume—the volume of fluid entrained by the swimmer [12], [13]—can be many times larger than the swimmer's own volume. This finding has potential consequences for the mixing of large bodies of water—lakes or oceans—by living things and for the use of artificial swimmers as fluid mixing agents.