Boundary-integral study of a freely suspended drop in a T-shaped microchannel

Abstract

The motion of small droplets through microfluidic channels, membrane pores, and other confined geometries presents considerable computational challenge due to drop deformation, small clearances, and complex geometries. This paper addresses the challenge by developing a moving-frame boundary-integral method and demonstrating its utility with simulations of a three-dimensional, freely-suspended deformable drop moving through a T-shaped microchannel at small Reynolds number. The drop size is comparable to the channel height, which is much smaller than the channel depth. The drop is fed into a straight channel or arm of the T-junction, with prescribed flow ratio through the other two branches. This setup typically results in strong drop interaction with the furthest corner of the junction. For computational efficiency, the base flow in the channel without the drop is first determined. Then, a “moving-frame” or computational cell around the drop is dynamically generated, using the first solution to provide the fluid velocity on the cell boundary. This method is used to map the outcomes (movement into one branch or the other, or breakup and partitioning between the branches) as a function of the flow ratio between the two branches and the drop capillary number, size relative to the channel height, and viscosity ratio with the carrier fluid. A critical capillary number or size ratio is observed, below which the drop does not break. Above the critical value, the range of flow ratios over which impending breakup is predicted increases with increasing capillary number and size ratio. The volume partitioning in the range where breakup occurs is essentially unity for equal flow rates between the two branches, even though the geometry is asymmetric, and then the volume partition of the daughter drops favors the branch with higher flow rate and with a stronger dependence on the flow ratio for the smaller drop sizes and capillary numbers. The viscosity ratio has a small but noticeable effect, with drops of similar viscosity to the carrier fluid breaking most easily.