Fluid Dynamics Research


Saffman-Taylor Flow Evolution over Time

Saffman-Taylor Flow Evolution over Time

During my work as a Pillsbury Summer Research Scholar in 2012 and continued research through spring 2014, I studied viscous fluid dynamics with Dr. Patrick Bunton. I learned fluorescence imaging techniques, image processing, and optics. The experiment involved fluids trapped in a thin gap between glass plates. This apparatus, called a Hele-Shaw cell, approximates two-dimensional flow because of the size of the gap between the plates – less than a millimeter in thickness. An injection port in the center of one glass plate enabled me to inject one fluid into another fluid that was already sandwiched between the plates, creating a radial flow from the center outward. Prior to the flow, I added a viscosity-sensitive fluorescent molecular probe to each solution. As the two fluids mixed, I took images of the solution fluorescence to determine the viscosity in an interfacial region between the two fluids. When the injected fluid was more viscous than the displaced fluid, the interface was stable (just a plain circle, expanding with time). However, if the injected fluid was less viscous than the displaced fluid, then the Saffman-Taylor instability (also known as viscous fingering) occurs, creating a pattern like that shown above. This measurement technique was unique because it works in situ, as the flow is happening in real time. The technique was published in 2014 in Physics of Fluids, in collaboration with the De Wit group from ULB in Brussels, Belgium.

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I was fascinated by the theoretical and computational work performed by the De Wit group, and was invited to study with their group in January 2015. During my time in Brussels, I learned how to perform computational fluid dynamics of reactive-diffusive-convective systems. I wrote simulations in C++ and openFrameworks to produce live visualizations of complex fluid flows and chemical reactions like the famous Brusselator reaction (discovered in Brussels!) that vary with space and time. The simulations were parameterized, allowing a user to discover the effect of each parameter by simply moving a slider.