Generalized Navier Boundary Condition for the Moving Contact Line∗
نویسندگان
چکیده
From molecular dynamics simulations on immiscible flows, we find the relative slipping between the fluids and the solid wall everywhere to follow the generalized Navier boundary condition, in which the amount of slipping is proportional to the sum of tangential viscous stress and the uncompensated Young stress. The latter arises from the deviation of the fluid-fluid interface from its static configuration. We give a continuum formulation of the immiscible flow hydrodynamics, comprising the generalized Navier boundary condition, the Navier-Stokes equation, and the CahnHilliard interfacial free energy. Our hydrodynamic model yields near-complete slip of the contact line, with interfacial and velocity profiles matching quantitatively with those from the molecular dynamics simulations.
منابع مشابه
Molecular Hydrodynamics of the Moving Contact Line in Two-Phase Immiscible Flows
The no-slip boundary condition, i.e., zero fluid velocity relative to the solid at the fluid-solid interface, has been very successful in describing many macroscopic flows. A problem of principle arises when the no-slip boundary condition is used to model the hydrodynamics of immiscible-fluid displacement in the vicinity of the moving contact line, where the interface separating two immiscible ...
متن کاملThe Sharp Interface Limit of a Phase Field Model for Moving Contact Line Problem
Abstract. Using method of matched asymptotic expansions, we derive the sharp interface limit for the diffusive interface model with the generalized Navier boundary condition recently proposed by Qian, Wang and Sheng in [9, 11] for the moving contact line problem. We show that the leading order problem satisfies a boundary value problem for a coupled Hale-Shaw and Navier-Stokes equations with th...
متن کامل3d Adaptive Finite Element Method for a Phase Field Model for the Moving Contact Line Problems
In this paper, we propose an adaptive finite element method for simulating the moving contact line problems in three dimensions. The model that we used is the coupled Cahn-Hilliard Navier-Stokes equations with the generalized Navier boundary condition(GNBC) proposed in [1]. In our algorithm, to improve the efficiency of the simulation, we use the residual type adaptive finite element algorithm....
متن کاملA variational approach to moving contact line hydrodynamics
In immiscible two-phase flows, the contact line denotes the intersection of the fluid– fluid interface with the solid wall. When one fluid displaces the other, the contact line moves along the wall. A classical problem in continuum hydrodynamics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a non-integrable singularity. The rec...
متن کاملUnified slip boundary condition for fluid flows.
Determining the correct matching boundary condition is fundamental to our understanding of several everyday problems. Despite over a century of scientific work, existing velocity boundary conditions are unable to consistently explain and capture the complete physics associated with certain common but complex problems, such as moving contact lines and corner flows. The widely used Maxwell and Na...
متن کامل