Joyce Lin
                    Dept of Mathematics 
                    UNC Chapel Hill

  Title:      The tortoise and the hare: prolonged residence 
                time of a sphere falling through stratified fluid

 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 the experimental data and assess the importance of different asymptotic terms in the model with respect to which dynamical effect needs to be predicted.