A generalized, quasi-universal subgrid model for macroscopic moving contact line flows

Abstract

Predictions of moving contact line flows are challenging due to the stress singularity associated with the no-slip boundary condition on solid surfaces and the inherently multiscale nature of the phenomenon. Resolving the microscopic length scale renders the numerical simulations intractable for macroscopic flows due to extremely high computational costs. Affordable and predictive numerical solutions for macroscopic flows require a subgrid model, free of case-specific calibration, that mitigates the grid-dependence observed otherwise. We demonstrate a coupling between Cox's matched asymptotic relation and the empirical contact angle models to obtain a quasi-universal subgrid model. The coupling requires a one-time knowledge of the observation length scale or resolution of the experiments used to formulate the empirical models. The present model eliminates the need for prescribing phenomenological parameters such as the microscopic slip length and wall contact angle, allowing for the predictive simulations of such flows. We demonstrate the reduction in error due to grid-dependence by conducting axisymmetric simulations of droplet spreading for a wide range of Reynolds and Weber numbers for three different contact angle models in the advancing and receding contact line motion scenarios.