Advancing modes on regularly patterned substrates

Abstract

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 θ_o 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 θ_a. 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 θ_a 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 θ_o, 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 θ_o between 45 and 55° where interfacial instabilities due to liquid coalescence and contact line depinning compete.