Large-scale simulations of concentrated emulsion flows.
Applications of the newly developed hybrid of the boundary integral and economical multipole techniques to large-scale dynamical simulations of concentrated emulsion flows of deformable drops are considered. For N = O(10(2)-10(3)) drops in a periodic cell with O(10(3)) boundary elements per drop, the method has two to three orders of magnitude gain over a standard boundary-integral method at each time-step, thus making long-time large-scale dynamical simulations feasible. In the steady shear flow, large systems N >/= O(10(2)) are imperative for convergence at high drop volume fractions c >/= 0.5. At high concentrations, most of the shear thinning occurs for nearly non-deformed drops; at c approximately 0.55 and small capillary numbers, phase transition is observed in dynamical simulations. In sedimentation of deformable drops from a homogeneous initial state, even larger N >/= O(10(3)) are required to accurately describe the Koch-Shaqfeh type of instability in a wide time range with N up to 1200 and ensemble averaging over the initial conditions. The dynamics of the average sedimentation rate is studied versus concentration c for matching viscosities lambda = 1; for a Bond number of 1.75, systems with c approximately 0.25 are found to be most unstable. Additionally, a low drop-to-medium-viscosity ratio system, lambda = 0.1, is more unstable than those with lambda = 0.25 and lambda = 1. In the third application, buoyancy- or gravity-driven motion of a large bubble/drop through a concentrated emulsion of neutrally buoyant drops is studied by simulations. For a size ratio of two, convergent (box-size independent) results for the bubble/drop settling velocity are obtained in simulations with N </= 800.