Reverse Washburn dynamics induces flow acceleration during capillary filling

Abstract

We present a corollary to Washburn's equation in capillary dynamics. We show that, during capillary filling, in cases where flow path decreases with time, an accelerating capillary flow or reverse-Washburn flow regime occurs. We provide a description of this phenomenon following Washburn's classic analysis and characterize a “reverse-Washburn” capillary flow regime in both inertial and viscous regimes. This regime is observed and characterized in experiments and numerical simulations of recently discovered self-coalescence flows, opening the door to engineering devices with naturally accelerating capillary inflows.