Thin-finger growth and droplet pinch-off in miscible and immiscible displacements in a periodic network of microfluidic channels

Abstract

We report the results of experimental and numerical studies of two-phase flow in a periodic, rectangular network of microfluidic channels. This geometry promotes the formation of anisotropic, dendrite-like structures during viscous fingering experiments. The dendrites then compete with each other for the available flow, which leads to the appearance of hierarchical growth pattern. Combining experiments and numerical simulations, we analyze different growth regimes in such a system, depending on the network geometry and fluid properties. For immiscible fluids, a high degree of screening is present which results in a power-law distribution of finger lengths. Contrastingly, for miscible fluids, strong lateral currents of displaced fluid lead to the detachment of the heads of the longest fingers from their roots, thus preventing their further growth.