Mathematical Biology Seminar

Joyce Lin
Math Department, University of Utah
Wednesday, Sept. 23, 2009
3:05pm in LCB 225
Title: An Experimental and Mathematical Study on the Prolonged Residence Time of a Sphere Falling through Stratified Fluids at Low Reynolds Number

Abstract: Particle settling rates in strongly stratified fluids play a major role in describing a wide variety of biological and environmental phenomena, such as the vertical distribution of biomass and pollution clearing times. Applications can extend to medical issues (such as particle settling rates and stratification in centrifugal separations) and are emerging in increasingly important fields such as microfluidics. At low Reynolds number, we discover that the self-entrainment by a particle in stratified miscible fluids causes the particle to experience a significantly prolonged residence time across a density transition. We present data from an experimental investigation, emphasizing the phenomenon using a "tortoise and hare"-like race, and develop a new first-principle theory with several levels of asymptotic approximations of increasing accuracy. We test these levels through direct comparison with experimental data and assess the importance of different asymptotic terms in the model with respect to which dynamical effect needs to be predicted. Analysis of the theoretical model provides the streamlines and instantaneous stagnation points, affording some insight into the behavior of the interior of the fluid. The nondimensional form of the model is used to characterize the entire flow with only four parameters, and the impact of each of these parameters on the flow is studied numerically. The model can be further pressed into a higher Reynolds number regime, which we then compare with experimental data. A brief look is taken at the extension to free space, many-body sedimentation, and linear stratification as the starting point for future work.