Molecular Hydrodynamics of the Moving Contact Line in Two-Phase Immiscible Flows (Communications in Computational Physics, 2018)
The no-slip boundary condition, i.e., zero fluid velocity relative to the solid at thefluid-solid interface, has been very successful in describing many macroscopic flows. A problemof principle arises when the no-slip boundary condition is used to model the hydrodynamicsof immiscible-fluid displacement in the vicinity of the moving contact line, where the interfaceseparating two immiscible fluids intersects the solid wall. Decades ago it was already knownthat the moving contact line is incompatible with the no-slip boundary condition, since thelatter would imply infinite dissipation due to a non-integrable singularity in the stress nearthe contact line. In this paper we first present an introductory review of the problem. Wethen present a detailed review of our recent results on the contact-line motion in immiscibletwo-phase flow, from molecular dynamics (MD) simulations to continuum hydrodynamicscalculations. Through extensive MD studies and detailed analysis, we have uncovered theslip boundary condition governing the moving contact line, denoted the generalized Navierboundary condition. We have used this discovery to formulate a continuum hydrodynamicmodel whose predictions are in remarkable quantitative agreement with the MD simulationresults down to the molecular scale. These results serve to affirm the validity of the generalizedNavier boundary condition, as well as to open up the possibility of continuum hydrodynamiccalculations of immiscible flows that are physically meaningful at the molecular level.