An Efficient Algorithm for Hydrodynamical Interaction of Many Deformable Drops

An efficient and accurate 3D algorithm for dynamical simulations of many deformable drops with strong hydrodynamical interactions at zero Reynolds numbers is developed. The drop-to-medium viscosity ratio, λ, and the Bond number are arbitrary, and the drops are subject to gravity with stationary triply periodic boundary conditions. The algorithm, at each step, is a hybrid of boundary-integral and economical multipole techniques, with extensive use of rotational transformations and economical truncation of multipole expansions to optimize near-field interactions. A significant part of the code is the new, “best paraboloid-spline” technique for calculating the normal vectors and curvatures on drop surfaces, which greatly improves the quality of long-time simulations. Examples show the phenomenon of clustering in a concentrated sedimenting emulsion for λ=0.25 and 1, which leads to an increase in the average sedimentation velocity with time. A high efficiency of the method is demonstrated, with two orders-of-magnitude gains over the standard O(N2N2▵) boundary-integral technique for N∼102 drops in a periodic cell with N▵∼103 triangular boundary elements per drop, so that typical long-time dynamical simulations can be performed in a few days or weeks on a standard workstation (as compared to the several years which would be required for the same simulations using standard boundary-integral techniques). The effects of drop triangulation and truncation of multipole expansions on dynamical simulations are assessed.