An approximate solution of the hydrodynamic problem associated with receding liquid-gas contact lines

Abstract

An ordinary differential equation, derived previously by the authors to describe liquid-gas menisci in the context of advancing contact lines, is applied to the receding case. The existence of a critical capillary number is demonstrated above which no solution of the differential equations exists. This critical capillary number exhibits a strong dependence on the system scale and true contact angle at the wall. Comparison of critical capillary numbers, predicted by the model and obtained from experiments, suggests that at the critical capillary number the true contact angle at the wall is smaller than the (receding) static contact angle.