Hydrodynamic Focusing of an Elastic Capsule in Stokes flow: An Exploratory Numerical Study

Abstract

We study numerically the motion of an elastic capsule in a simple microfluidic device, a sheath flow focuser, designed to align (or focus) particles at the center of a microchannel. The geometry of the device is given, while the flow conditions are varied, and the outflux is constant. The efficiency is expressed in terms of the distance required to achieve focusing and the functioning is characterized by the deformations and stresses undergone by the capsule membrane. Calculations are performed for a ‘stiff’ and ‘soft’ capsule, corresponding to a capillary number equal to Ca = 0.05 and Ca = 0.3 based on the outflow rate. We report that as the sheath flow is increased the focusing efficiency grows and plateaus beyond a certain threshold, displaying a drop in the efficiency gain. Differently, the deformations and stresses undergone by the capsule membrane grow for the entire range of the flow parameters considered. This should be kept in mind if the stresses exerted on the membrane have to be minimized or need to be below certain characteristic thresholds typical of the specific application considered. Especially large initial offsets and stiff capsules benefit from focusing.