Although the no-slip boundary condition, which requires fluid adjacent to a solid substrate to move with the same velocity as the substrate, serves reliably to model fluid behavior in most circumstances, recent experiments and numerical simulations have shown that, in fact, there is a relative velocity between the fluid and the substrate. While the effects of this slip may remain negligible in some flows, accounting for slip is a prerequisite for predicting the correct behavior in many other types of flows, such as those in small geometries, flows in which an interface (between two fluids) moves along a solid, and flows in which particles must pass through an interface. This project seeks to develop models of the slip boundary condition. The formulation will incorporate results of recent experiments and numerical simulations to construct the equations of flow in the neighborhood of a solid substrate. Preliminary work indicates that such a model, as well as related useful simpler approximations, can be developed. The simplicity of the equations and consequent efficient numerical procedures for evaluating the dynamics near the wall should provide insight into how slip occurs and how the characteristics of the fluid and the substrate determine the amount and nature of slip. The recent availability of high quality experimental data and simulation results, as well as the advent of technologies demanding flow in small geometries, make this a timely undertaking.
This project concerns mathematical modeling of the behavior of fluids where they adjoin solids. The results will allow highly accurate computation of fluid flow, which is essential for the design of small hydrodynamical instruments, including "lab-on-a-chip" devices.
