| Abstract: |
| Using the Stokes equations with variable density, we derive a first-principle model for a sphere settling in stratified viscous fluid. Taking advantage of the linearity of the governing equations, we split the fluid flow into the Stokes flow with static density distribution and the stratification induced flow. The solution reduces to a highly coupled system involving a convolution over the fluid domain of the fundamental solution and the forcing term. We discuss the challenges of the Greens function solution to the system, the difficulty that arises from integrating the three dimensional integral, and the appearance of removable singularities. In the cases where the stratification induced flow is not dominant, we propose an asymptotic approach that simplifies the computation. Diffusion effects of the entrainment will also be discussed and explained. |
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