Applied Math And Analysis Seminar
Monday, March 26, 2012, 4:30pm, 119 Physics
Shilpa Khatri (University of North Carolina at Chapel Hill)
Settling of a Porous Sphere in Stratified Stokes Flow
Abstract:- Marine snow, composed of organic and inorganic aggregates, plays a major
role in marine carbon cycling. Most of these macroscopic particles are
extremely porous, allowing diffusion of salt from the ambient fluid to
affect the density and therefore the settling of these particles. In a first
approximation, these particles can be modeled as spheres. This talk will
present a study of the effect of porosity and salt diffusion in the dynamics
of a sphere settling under gravity in a salt-stratfied fluid analytically
and semi-analytically (depending on the ambient density gradient) in
viscosity dominated regimes. For linear stratification, an explicit solution
for the sphere's position in time is derived. For more general ambient fluid
stratification, the sphere's position can be solved for numerically, under
the asymptotic assumptions about the typical time scales of diffusion and
settling. A parametric study of the settling behaviors and preliminary
comparisons with experiments will be presented. [video]
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