General criteria for the estimation of effective slip length over corrugated surfaces

Abstract

In this work, we aim to develop an effective hydrodynamic boundary condition over patterned surfaces for the application to microfluidics. Four different criteria to estimate the effective Navier-slip length and their performance are investigated for flows over corrugated surfaces, such as patterned surfaces or porous interfaces, which can be applied for efficient flow simulations. Four distinctive methods were discussed in the estimation of slip length, namely: mass conservation, balance of energy dissipation rate, force balance, and interfacial slip velocity averaging. Expressions of slip length were derived analytically for each criterion in a pressure-driven flat channel flow and the slip length was determined using a combination of analytic and numerical methods. We report that (i) the slip length from force balance appears to be the most accurate and exactly the same as that from interfacial slip velocity averaging, (ii) the slip length from mass conservation deviates from that of force balance, though minor, particularly for a small relative channel height to the length scale of patterns or pores, and (iii) the energy balance yields significantly different slip lengths. The slip length reduces to a single value for a sufficiently large relative channel height, which indicates that it can be considered as a surface property in general, when the pattern dimension is much smaller than the length scale of flow.