A general condition for spontaneous capillary flow in uniform cross-section microchannels

Abstract

Spontaneous capillary flow (SCF) is a powerful method for moving fluids at the microscale. In modern biotechnology, composite channels—sometimes open—are increasingly used. The ability to predict the occurrence of a SCF is a necessity. In this work, using the Gibbs free energy, we derive a general condition for the establishment of SCF in any composite microchannel of constant cross section, i.e., a microchannel comprising different wall materials and even open parts. It is shown that SCF occurs when the Cassie angle is smaller than π/2 (θ* < π/2). For a homogeneous confined channel, this relation collapses to the well-known hydrophilic contact angle θ < π/2.