Droplet trajectories in a flat microfluidic network

Motivated by recent experiments, we numerically study the droplet separation in microfluidic channels having a bifurcation with two different branch lengths. The bifurcation is connected to the “mother” channel by two right angled T-junctions. Assuming a flat channel, we employ the boundary element method (BEM) to numerically solve the two dimensional Darcy equation that governs two phase flow in the Hele–Shaw limit. The possibility of an attraction towards the low-flow-rate branch is discussed in terms of flow rate ratio and initial lateral coordinate. The occurrence of different sorting regimes is summarized in a phase diagram spanned by the flow rate ratio and the initial lateral position in the “mother” channel for the case when the mobility ratio of droplet to continuous phase is smaller than one.