Effects of Drop Deformation on Coalescence and Phase Separation in Microgravity

摘要

Two drops of one liquid immersed in a second, immiscible liquid will move relative to one another under a variety of flow conditions. When the drops come close together, they interact under the opposing influences of hydrodynamic disturbances and short-range van der Waals attraction. In addition, interfacial deformation may affect the relative trajectory of the drops, permitting several possible outcomes, including separation of the drops, coalescence of the drops, or even break-up of one drop into two or more drops. If the drops are only slightly deformable, so that they remain spherical except for a small flattening or dimpling in the region of close approach, coalescence is inhibited. If the deformation is more moderate, allowing the interfaces of both liquid particles to distort globally, the behavior depends on the ratio of the viscosity of the drops to that of the surrounding liquid. For viscosity ratios close to zero, moderate deformation actually promotes drop coalescence. However, for viscosity ratios close to unity or greater, moderate deformation may lead to break-up of the smaller drop. It is also possible at 0(l) viscosity ratios for both coalescence and break-up to take place. This project is a theoretical and experimental study. The theoretical work has two parts for the flows being considered: (1) semi-analytical studies for very small capillary numbers for which deformation is significant only in a small region of near contact between two drops, and (2) boundary-integral numerical studies for larger capi.lary numbers for which macroscopic changes in the drop shapes also occur away from the near contact region. One result of the boundary-integral study for moderate capillary numbers is a parameter-space investigation for buoyancy-driven motion to determine critical horizontal offsets for coalescence and drop break-up as functions of the drop-to-medium viscosity ratio, the ration of the smaller to larger drop radius and the capillary number. The critical horizontal offset determines a collision efficiency, which is defined as the ratio of the collision rate including hydrodynamic interactions and possible molecular attraction and deformation to that obtained in their absence. In addition, the critical horizontal offsets for coalescence are used in population dynamics simulations of droplet growth and phase separation for all flows. The experimental component is an investigation to compare with theoretical results. Trajectories of two drops consisting of a mixture of glycerol and water moving through an external medium of castor oil are videotaped and analyzed to check qualitative and quantitative agreement with numerical simulations.