Effective slip lengths for longitudinal shear flow over partial-slip circular bubble mattresses

The problem of longitudinal shear flow over a circular bubble mattress with partial slip and protrusion angle 90o is solved in a quasi-analytical fashion by a novel transform scheme recently devised by the author. The general approach can be readily adapted to other mixed boundary value problems. From the analysis explicit approximations for the effective slip lengths are found as a function of the Navier-slip parameter and the area fraction of the surface covered by protrusions. These new approximation formulas for the slip lengths both unify and extend those based on empirical polynomial fits to numerical data given recently by Ng and Wang (2011 Fluid Dyn. Res. 43 065504).