Cornell Fluids Seminar (CFS): Monika Nitsche, Ph.D. (University of New Mexico), "Boundary Integral Formulation for Stokes Equations in Multi-Fluid Domains"

Description

Our motivation is to study the evolution of double emulsions exiting from a tapered nozzle, driven by a background flow in the nozzle. Laboratory experiments have shown that in certain cases the drops break as they exit, thus releasing the inside phase to the outside (Chen et al, Softmatter 2011, Vol 7, no 6, 2345). Important applications of this process include drug delivery through atomized sprays (eg, a nose spray), inkjet printing, food processing and cosmetics. Whether or not the drops break was observed to depend on the angle of the nozzle at the exit. Here, we propose to study the dependence of the flow on the various flow parameters using numerical simulations. The flow is well described by Stokes Equations. We first outline the derivation of the coupled boundary integro-differential formulation of the problem, starting with the basics. We then describe several of the numerical issues that arise in evaluating the boundary integrals, including regular integrals, singular integrals, and near-singular integrals. We conclude by showing a few numerical results, building from simple geometries, where we can compare against known results for validation, to more complex geometries, leaving us well-positioned for the proposed parameter study.