Roughening transition in receding contact lines

The interplay between the contact line elasticity, surface disorder, and dissipation leads to complex and unexpected observations in immiscible flows. Here, we use the Cox–Voinov law to formulate a dynamical evolution equation considering all these effects. We then investigate the roughening transition that occurs in the receding contact lines when the contact line velocity exceeds a critical value. This transition is accompanied by deposition of a macroscopic film on the plate, known as Landau-Levich film. Using a perturbative renormalization group approach, we further investigate the flow equations of the coupling constants in the vicinity of the fixed point corresponding to the roughening transition. Our results suggest that Cox–Voinov relation leads to a phase diagram that is entirely different from that obtained using de Gennes’ relation. It predicts a second-order continuous transition as opposed to a first-order discontinuous behavior predicted by de Gennes’ model. The critical exponents further hint to the breakdown of the perturbative approach.