Spheres Passing Through the Interface of Stratified Corn Syrup (2009)

Undergraduates: Claudia Falcon, Nicholas Mykins Joyce Lin Roberto Camassa

Faculty Advisor: Richard McLaughlin
Department: Mathematics

---

Settling rates of particles through stratified fluids affect many aspects of life, from air quality to distribution of biomass in the upper ocean. We study the behavior of a sphere falling through a two-layer stratification of miscible viscous fluids. Motivated by the above applications and by the levitation and velocity reversal found in similar saltwater experiments, we focus on the low Reynolds number regimes. This simplifies the physics by making the fluid inertia negligible, which is reflected mathematically by the linearization of the governing motion equations, thus making them more accessible to analysis and numerics. In this experimental study, we use corn syrup, a highly viscous fluid, to match this approximation. The analysis of these experiments provides us with a velocity profile. In this regime, we find a novel phenomenon in which the sphere slows down beyond the terminal velocity of the bottom layer. This behavior is dictated by the complicated interplay between the entrained fluid and the downward moving sphere. We can emphasize this effect in a tortoise-and-hare like race, in which a sphere falling in a tank of stratified fluid exhibits a longer travel time than a sphere falling the same distance in a tank of only the bottom denser fluid. Our experiments have revealed other interesting phenomena, including studies of the wall effects, convection, entrainment, and reflux.