Algorithm for flow of highly-concentrated emulsions through a narrow constriction

Abstract

Abstract A multipole-accelerated 3D boundary-integral algorithm is developed to model pressure-driven flow of a highly-concentrated emulsion of many deformable drops through a periodic channel with tight constrictions. The drops are monodisperse, free from surfactant, and the Reynolds number is small for Stokes equations to apply. The channel surface consists of four solid panels: front and back parallel to each other, and band-like top and bottom panels with an arbitrary profile. The algorithm is for arbitrary channel aspect ratios, but the results are obtained for extreme cases, when the channel depth (front-back distance) is the same as the minimum channel height and both can be much smaller than the non-deformed drop diameter, making the drops flow as a monolayer. Strong hydrodynamic interactions (especially, drop-wall) necessitate very high surface resolutions combined with novel desingularization tools for the boundary integrals. Multipole acceleration gives, at least, two orders of magnitude gain over direct summations and facilitates long-time simulations, with many drop rearrangements. Examples for homoviscous emulsions with 40-92 drops in two types of channels at 80-90% drop volume fractions and different capillary numbers demonstrate single-file drop motion intermittent with pairs or triplets of drops in the constriction. Such squeezing interactions can result in extreme drop elongations, but are still not sufficient to promote breakup for the channel geometries, capillary numbers and drop confinements considered. Integral properties (the entire drop-phase and constriction flow velocities) are also analyzed.