A dynamic Cassie-Baxter model

Contact-angle hysteresis of a liquid suspended on surface microstructures, namely in a Cassie-Baxter state, is determined mainly by the receding contact line although not fully understood. Existing modified Cassie-Baxter models predict some but not most experimental data in the literature. Noting that most models were based on the two-dimensional (2-D) principle whereas the experiments were under three-dimensional (3-D) conditions, here we develop a 2-D experiment. While 3-D experiments measure the receding contact lines averaged over space and time, 2-D experiments eliminate the spatial averaging and can further eliminate the temporal averaging by high-speed visualization. The resulting details of the contact line motion lead us to propose a 2-D model, which incorporates the contact-line friction. The new 2-D model matches the 2-D experimental results excellently while all existing models show significant deviation. By introducing a line solid fraction term, the 2-D model is further generalized to a 3-D model, which successfully predicts a wide range of 3-D data in the literature regardless of their distinct microstructures and receding modes.