The flow of suspensions in channels: Single files of drops

Abstract

The flow of a periodic suspension of two-dimensional viscous drops between two parallel plane walls is considered, and a framework for performing dynamic simulations with suspensions of increasingly complex structure is developed. The computations are based on an improved implementation of the boundary integral method which is coined the method of interfacial dynamics. An elementary configuration is considered in detail in which the suspension is composed of a periodic array of suspended drops arranged on a single file, and the flow is driven by the relative motion of the two walls. The motion is studied as a function of the capillary number, the viscosities of the fluids, and the drop size. The transition from the small-drop behavior, where the effects of the walls are insignificant, to the large-drop behavior, where the drops occupy almost the whole of the clearance between the walls, is illustrated. It is found that, in all cases, the suspension exhibits a shear-thinning behavior and some type of elasticity. The single-file arrangement is unstable to subharmonic perturbations in which the drops are displaced in an alternating fashion across the centerline of the channel. The evolution of the perturbed array may lead to oscillatory motions including orbiting and bypassing, or to formation of a double file of nearly stationary drops. The effects of drop interactions on the effective properties of the suspension are discussed.