Putting the micro into the macro: A molecularly-augmented hydrodynamic model of dynamic wetting applied to flow instabilities during forced dewetting

Abstract

We report a molecularly-augmented continuum-based computational model of dynamic wetting and apply it to the displacement of an externally-driven liquid plug between two partially-wetted parallel plates. The results closely follow those obtained in a recent molecular-dynamics (MD) study of the same problem Toledano (2021) which we use as a benchmark. We are able to interpret the maximum speed of dewetting $U^*_{\mathrm{crit}}$ as a fold bifurcation in the steady phase diagram and show that its dependence on the true contact angle $\theta_{\mathrm{cl}}$ is quantitatively similar to that found using MD. A key feature of the model is that the contact angle is dependent on the speed of the contact line, with $\theta_{\mathrm{cl}}$ emerging as part of the solution. The model enables us to study the formation of a thin film at dewetting speeds $U^*>U^*_{\mathrm{crit}}$ across a range of length scales, including those that are computationally prohibitive to MD simulations. We show that the thickness of the film scales linearly with the channel width and is only weakly dependent on the capillary number. This work provides a link between matched asymptotic techniques (valid for larger geometries) and MD simulations (valid for smaller geometries). In addition, we find that the apparent angle, the experimentally visible contact angle at the fold bifurcation, is not zero. This is in contrast to the prediction of conventional treatments based on the lubrication model of flow near the contact line, but consistent with experiment.