Boundary-integral algorithm for drop squeezing through a granular material

A multipole-accelerated algorithm is developed to simulate squeezing of an emulsion of many deformable drops through a granular material; the drops non-deformed diameter is much bigger than the interparticle constriction diameters. The algorithm features Hebeker representation for solid particle contributions to boundary integrals combined with novel desingularization techniques, "passive" mesh stabilization and a triply-periodic Green function. Multipole acceleration facilitates calculations with very high resolution essential for squeezing phenomena and allows us to achieve up to 2-order-of magnitude advantage over the standard boundary integral method. Squeezing of a drop through a cluster of four close spheres in free space is demonstrated. Also considered is squeezing of an emulsion through a periodic lattice of solid particles to determine the pressure gradient-flow rate relationship and critical conditions for squeezing to occur. Our first simulations for motion of many deformable drops through a random granular material in a periodic box are also presented.