DETERMINATION OF THE SLIP BOUNDARY-CONDITION BETWEEN A GAS AND A SOLID-SURFACE WITH A RANDOM ARRAY OF ROUGH PATCHES

The macroscopic boundary condition for a gas flow with a randomly roug h solid surface is determined in a limit where the gas molecules are r eflected specularly from the solid surface. The rough surface is, for simplicity, assumed to be flat except for a sparse random array of mic roscopic defects of single typical dimension. These assumptions lead t o extremely simple results, having no numerically determined constants . This complements work on moving contact lines that uses the same mod el rough surface. To highlight the important physical processes, the g as is assumed to have a mean free path that is both much greater than a defect dimension and much less than the typical distance between def ects. The slip length and slip velocity are determined explicitly for a solid surface with hemispherical hump defects.