Film flow of a suspension of liquid drops

Abstract

The film flow of a two-dimensional suspension of neutrally buoyant liquid drops down an inclined plane wall is investigated by numerical simulation in the limit of vanishing Reynolds numbers. The results show that well-separated and solitary drops migrate toward an equilibrium position located between the free surface and the wall, for a broad range of the fluid physical properties and flow conditions. The precise location of the equilibrium position is determined by the ratio of the drop viscosity and the viscosity of the film fluid, and by the deformability of the drop interface and free surface expressed by the drop and free-surface capillary numbers. The motion of a periodic file of drops is found to be unstable to periodic perturbations whose amplitude exceeds a critical threshold. The instability leads to periodic accumulation of drops within bands developing in the streamwise direction. Large scale numerical simulations of dilute and concentrated random systems show that the drops spontaneously migrate toward the film interior, thereby causing the development of particle-free zones along the inclined wall and free surface. In contrast to the case of pressure-driven channel flow where peaks in the drop number density distribution are observed near both walls, in the case film flow a peak develops near the inclined plane but not near the free surface.