A Falling Sphere through Stratified Karo (2008)

Undergraduates: Claudia Falcon, Claudia Falcon Joyce Lin

Faculty Advisor: Richard McLaughlin
Department: Mathematics

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This experimental study models the behavior of a sphere falling under gravity through a two-layer fluid. The study began when it was found that a sphere undergoes levitation– sharp acceleration to near zero speed, and sometimes even a directional (velocity) reversal, when falling under specific conditions through a sharply stratified fluid. These experiments were done in saltwater and fresh water stratifications using a glass bead. Explaining this phenomenon is a fundamental problem in fluid dynamics and can be applied to sedimentation in stratified fluids, such as the ocean. Simplifying to low-Reynolds numbers, the equations that model these experiments become linear and thus more accessible to study them analytically and numerically. In order to match this approximation in the experiments, we use corn syrup, a highly viscous fluid. In this new medium, we look for the same phenomenon of levitation. Our stratification involves pure corn syrup as the bottom layer and diluted corn syrup for the top layer. Due to the nature of corn syrup, we must heat it and stir in distilled water until homogeneous, and then allow to cool overnight to room temperature. The analysis of these experiments provides us with a velocity profile of the falling sphere. We have found that the stratification slows the bead down beyond its terminal velocity in the bottom layer. This is being explored to find the specific conditions under which the bead will levitate.