Principal Investigator Kenneth Kamrin
Recent work in the fabrication of microfluidic devices has motivated general interest in quantifying the effects of surface texture on bulk low-Reynolds-number fluid flow. In non-trivial ways, wall patterning can be used to impede or expedite adjacent fluid motion, causing non-negligible far-away effects. As such, improved models for textured walls could have impact beyond microfluidics, helping optimize the design of apparati for fluid-like materials in macroscopic environments. One basic goal is to extract a simple boundary condition for the smooth, mean surface, that mimics the effects of the actual condition along the true, corrugated surface. For Stokes fluid, tensorial boundary conditions have been suggested relating the stress traction vector along the mean surface to an “effective slip” velocity. We have carried out an analytical/perturbative study of the Stokes equations along surfaces of small height and/or Navier slip-length fluctuations. This has resulted in a second-order formula, complete with error bound, that converts any such surface to an effective tensorial mobility law on the mean surface. The law can be used to substitute the rough boundary with an approriate slip on the mean surface. We have followed up with additional analytical results pertaining to the symmetry of mobility tensors for arbitrary patterned surfaces.