Advancing modes on regularly patterned substrates

In this article we study the static advancing contact angle θ+a of a liquid interface in contact with a microstructured substrate equipped with a periodic array of circular posts of height H, diameter W and center to center distance D. Assuming a homogeneous material contact angle θo and gravity to be negligible, we numerically minimize the interfacial energy of an asymptotically plane liquid interface aligned with a row of posts for a fixed value of the apparent contact angle θa. A number of branches of mechanically stable interfacial morphologies are observed and classified by the topology of the liquid interface and the three phase contact line. Increasing θa in small steps, we determined the static advancing contact angle θ+a as the apparent (asymptotic) contact angle, above which no mechanically stable interfacial configuration exists. Specific types of advancing modes can be assigned to certain regions of the control parameter θo, aspect ratio h = H/W, and line fraction w = W/D. A rich spectrum of advancing modes is found in the region of material contact angles θo between 45 and 55° where interfacial instabilities due to liquid coalescence and contact line depinning compete.