A general boundary integral formulation for compressible Stokes flows is theoretically described within the framework of hydrodynamic potentials. The integral equation is implemented numerically to the study of drop expansion in compressible viscous flows. Marker point positions on the drop interface are involved by using the boundary integral method for calculation of fluid velocity. Surface discretization is adaptive to the instantaneous drops shapes. The interplay between viscous and surface tension and its influence on the evolving emulsion microstructure during its expansion is fundamental to the science and technology of foam processing. In this article the method is applied for 3D simulations of emulsion densification that involves an uniform expansion of a viscous fluid containing spherical drops on a body centered cubic lattice (BCC).

Microstructural changes, that is an important feature for the understanding of the velocity variance in sedimentation is investigated with numerical simulations. The simulations are used to describe velocity fluctuations and hydrodynamic dispersion in a suspension of interacting point-particles sedimenting in a rectangular box with periodic sides and impenetrable bottom and top. It is observed how the positions of the particles evolve in a finite container. The suspension that was initially random in the gravity direction only, tends to be fully randomized as a result of the relative arrangements of the particles and the hydrodynamic interactions between them. The computer simulations, based on statistics over a significant number of particle configurations, suggest velocity variances and diffusivities dependent on the size of the simulated system but with anisotropy in velocity fluctuations and diffusion coefficients nearly independent of the box size.