Power-Law Slip Profile of the Moving Contact Line in Two-Phase   Immiscible Flows
  Large scale molecular dynamics (MD) simulations on two-phase immiscible flows show that associated with the moving contact line, there is a very large $1/x$ partial-slip region where $x$ denotes the distance from the contact line. This power-law partial-slip region is verified in large-scale adaptive continuum simulations based on a local, continuum hydrodynamic formulation, which has proved successful in reproducing MD results at the nanoscale. Both MD and continuum simulations indicate the existence of a universal slip profile in the Stokes-flow regime, well described by $v^{slip}(x)/V_w=1/(1+{x}/{al_s})$, where $v^{slip}$ is the slip velocity, $V_w$ the speed of moving wall, $l_s$ the slip length, and $a$ is a numerical constant. Implications for the contact-line dissipation are discussed. 
Tiezheng Qian, Xiao-Ping Wang, Ping Sheng