Influence of interfacial coupled flow on slip boundary over a microstructured surface

A slip boundary is usually realized by micro-structured surfaces, where primary fluid flows over the microstructures being filled with a secondary immiscible fluid. We establish a theoretical framework for interfacial coupled flow on a slip boundary over a micro-structured surface. Coupled flow of two fluids, which is the key problem for the study of slip boundary, is solved by finding the approximate integral relation between the slip velocity and the slip velocity gradient.