Large dynamic contact angles

Abstract

Abstract The relation between the dynamic contact angle and the capillary number is explored by extending de Gennes’ model where viscous dissipation is equated to the surface work. A cutoff is used to eliminate the contact line singularity. The aim has been to increase the applicability of existing results to include higher contact angles. The flow near the contact line is assumed to be in the creeping flow regime. The results uphold Voinov–Hoffman–Tanner rule at small contact angles but only in the liquid–air system and not in the liquid–liquid system. The more prevalent liquid–air system shows a fold at a dynamic contact angle of 180°. This indicates that at 180° the system jumps out of the dynamic contact line arrangement to an entrained system that has no contact line. Liquid–liquid systems have folds at much lower contact angles. Comparisons with experiments show very good agreement up to contact angles of 120° but the comparisons show only qualitative agreement at large contact angles. Possible explanations have been provided for the latter.