Computation of the flow due to entrainment for a sphere settling in stratified fluids

Understanding particle sedimentation in stratified fluids is important in many environmental applications. In particular, we study the cases with long residence times at the density transition layer, similar to the ones of marine snow aggregates in the ocean. A sphere's motion exhibits complex mechanics when falling through a stable stratification of miscible, viscous fluids, due to the deformation of the entrained boundary layer. Following a first principles model, we develop a numerical scheme to compute the stratification-induced flow. Properties of the Oseen tensor and its approximations near and far from the sphere are used to improve computation of the flow. We provide a convergence analysis and comparison of the model with experimental data.