A generalized examination of capillary force balance at contact line: On rough surfaces or in two-liquid systems.

We investigate the capillary force balance at the contact line on rough solid surfaces and in two-liquid systems. Our results confirm that solid-liquid interactions perpendicular to the interface have a significant influence on the lateral component of the capillary force exerted on the contact line. Surface roughness of the solid substrate reduces the mobility of liquid and alters how the perpendicular solid-liquid interactions transfer into a force acting parallel to the interface. A quantitative relation between surface roughness and the transfer strategy is proposed. Moreover, when a liquid is in coexistence with another immiscible liquid on a solid, the capillary forces exerted on liquids of both sides are involved in our theoretical model. The contact angle can be predicted by calculating three interfacial tensions. These arguments are then verified by molecular dynamics simulations. Our findings set up the generalized theoretical framework for the capillary force balance at the contact line and broaden its application in more realistic scenarios.