(591g) A Universal Stress Dependent Slip Boundary Condition for Steady Fluid Flows

Interfaces are ubiquitous in nature and technology. The asymmetry in forces that is experienced by molecules and atomic species in the vicinity of the interface, is one of the primary factors that governs the extent to which mass, momentum, and energy are transported across it. The boundary condition, used to define the tangential momentum transfer at the fluid-solid interface, has been the subject of many investigations for more than a century. The widely used no-slip boundary condition is known to produce velocity and stress singularity for problems such as spreading of fluid, extrusion of polymer melts in capillary tubes and corner flows, resulting in a breakdown of the boundary condition. We show that the Navier and Maxwell slip model that is widely used to overcome these singularities, make an implicit assumption of velocity variation in only wall normal direction and hence are not applicable to flow problems mentioned above. We present a generalized boundary condition that is not limited by this constraint and therefore applicable to a wide spectrum of steady flow problems. It is shown that slip velocity at an interface is a function of the velocity gradient tensor for a general steady flow problem, instead of only the shear rate as given by Navier and Maxwell slip models. In addition using molecular dynamic simulations we simulate a moving contact line problem and a corner flow problem, and present a universal relation that relates slip length to principal strain rate of fluid near the wall. The general slip model along with the universal relationship for slip length provides a unified boundary condition which could be used to model various types of single and two phase flow over solid surfaces without having to perform computationally expensive molecular dynamic simulations.