Path selection of liquid fronts in junctions of branching channels

Abstract

We consider how a liquid front propagating through an initially dry channel network selects its path when encountering branch junctions. We employ both experimental observation and theoretical analysis to investigate the path selection dynamics depending on liquid properties, pressure-driven flow rate, and channel geometry. We identify three distinct front propagation types at the junction, namely, straight, diverging, and diverting flows, and construct their regime map with theoretical regime boundaries. These flow types at the junction determine the subsequent channel-filling patterns, which we also identify and categorize. Our results allow us to design small-scale channel networks to precisely deliver or distribute functional liquids, which can be applied to lab-on-a-chip systems, liquid sculpture, and porous flow control.