A sub-grid-scale viscous force model for simulating moving contact lines

Simulations of two-phase flows with moving contact lines are often reported to be mesh-dependent [Afkhami et al., 2009] due to the diverging viscous stress at the contact line [Huh and Scriven, 1971]. Strategies such as the Navier-slip boundary condition and the Cox-Voinov dynamic contact-angle model have been proposed to alleviate this issue. However, the Navier-slip boundary condition requires an unrealistically large slip-length to achieve better mesh-independency, and no clear reason justifies the improved mesh-independency of the Cox-Voinov dynamic model [Legendre and Maglio, 2015]. In this talk, we volume-filter the Navier-Stokes equations for two-phase flows with moving contact lines, and identify two unclosed terms: a sub-grid scale (SGS) surface tension force and a SGS viscous force. The SGS surface tension force is closed by the uncompensated Young’s force model [Wang and Desjardins, 2017], and a new physics-based closure is derived for the SGS viscous force. Both models are flexible and easily implementable in any numerical framework. Simulations using both SGS models are verified to be mesh-independent, and the utility of the model is demonstrated across a number of examples, including drop spreading on a plane and drop sliding down an inclined plane.