The moving contact line problem

When two immiscible fluids are placed on a substrate, the line where the interface of the two fluids intersects the solid substrate is called the contact line. The equilibrium configuration of the static contact line is described by the Young's relation which relates the three coefficients of interfacial tension to the contact angle formed by the fluid-fluid interface with the solid surface. The moving contact line problem, however, has for many years remained an issue of controversy and debate. The main difficulty stems from the fact that classical hydrodynamic equations coupled with the conventional no-slip boundary condition predicts a singularity for the stress that results in a non-physical divergence for the energy dissipation rate. Recently, we systematically investigated the physical processes near a moving contact line using molecular dynamics. Based on the molecular dynamics study, continuum theory and multiscale techniques, we formulated simple and effective continuum models. These models not only remove the non-physical singularities, but also give a faithful description of the physical process near the moving contact line .
  • On the distinguished limit of the Navier slip model of the moving contact line problem, W. Ren, P. Trinh and W. E, J. Fluid Mech., 772, 107 (2015)  
  • Derivation of a continuum model and the energy law for moving contact lines with insoluble surfactants, Z. Zhang, S. Xu and W. Ren, Phys. Fluids, 26, 062103 (2014)  
  • A level set method for two-phase flows with moving contact lines and insoluble surfactants, J.-J. Xu and W. Ren, J. Comput. Phys., 263, 71 (2014)  
  • Contact line dynamics on heterogeneous surfaces, W. Ren and W. E, Phys. Fluids, 23, 072103 (2011)
  • Continuum models for the contact line problem, W. Ren, D. Hu and W. E, Phys. Fluids, 22, 102103 (2010)  
  • Derivation of continuum models for the moving contact line problem based on thermodynamic principles, W. Ren and W. E, Commun. Math. Sci. 9, 597 (2011)  
  • Boundary conditions for the moving contact line problem, W. Ren and W. E, Phys. Fluids, 19, 022101 (2007)  

Last modified: Thur Oct 15 20:55:34 EST 2015