One-Dimensional Analysis of Gas Diffusion-Induced Cassie to Wenzel State Transition

We develop a one-dimensional model for transient diffusion of gas between ridges into a quiescent liquid suspended in the Cassie state above them. In the first case study, we assume that the liquid and gas are initially at the same pressure and that the liquid column is sealed at the top. In the second one, we assume that the gas initially undergoes isothermal compression and that the liquid column is exposed to gas at the top. Our model provides a framework to compute the transient gas concentration field in the liquid, the time when the triple contact line begins to move down the ridges, and the time when menisci reach the bottom of the substrate compromising the Cassie state. At illustrative conditions, we show the effects of geometry, hydrostatic pressure, and initial gas concentration on the Cassie to Wenzel state transition.