Fluid Mobility over Corrugated Surfaces in the Stokes Regime
Physics of Fluids
American Institute of Physics (AIP)
This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this record.
An exact solution is found for laminar fluid flow along the grooves of a family of surfaces whose shape is given by the Lambert W-function. This simple solution allows for the slip length in the direction parallel to the grooves to be calculated exactly. With this analytical model we establish the regime of validity for a previously untested perturbation theory intended for calculating the surface mobility tensor of arbitrary periodic surfaces, finding that it compares well to the exact expression for nearly all choices of parameters of the conformal map. To test this perturbation theory further, the mobility tensor is evaluated for a simple sinusoidal surface for flow both parallel and perpendicular to the grooves, finding that the perturbation theory is less accurate in the latter of these two cases.
We acknowledge financial support from DSTL, and from the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom, via the EPSRC Centre for Doctoral Training in Electromagnetic Metamaterials (Grant No. EP/L015331/1).
Vol. 28, No. 8, 083101 (2016)