A nanodrop on the surface of a lubricating liquid covering a rough solid surface

A two-component fluid consisting of a lubricating fluid (LF) that covers a rough solid surface (surface decorated by periodic array of identical pillars) and a test fluid (TF) as a nanodrop over LF is considered. A horizontal external perturbative force is applied to TF and the density functional theory is used for the treatment of the system. The concepts of advancing and receding contact angles as well as of leading edges of the drop are revisited. Three different definitions of the contact angles are analyzed and the most plausible selected. The contact angles are calculated as functions of drop size and magnitude of the perturbative force. For small drops, both angles change nonmonotonously with increasing perturbative force. For larger drops, the advancing contact angle has the tendency to increase and the receding contact angle to decrease with increasing force. The sticking force which maintains the drop equilibrium in the presence of an external perturbative force is determined as function of the contact angles. It is shown that this dependence is similar to that for a drop on a rough solid surface in the absence of LF. A critical sticking force, defined as the largest value of the perturbative force for which the drop remains at equilibrium, is determined.