Effective slip-length tensor for a flow over weakly slipping stripes

TL;DR

This paper investigates how the effective slip length tensor behaves for flow over weakly slipping striped surfaces, revealing that edge effects can cause anisotropy and reduce slip, contrary to previous isotropic assumptions.

Contribution

It demonstrates that step-like slip variations at stripe edges induce anisotropic effective slip, challenging the assumption of isotropy in weakly slipping surfaces.

Findings

Edge effects cause anisotropy in slip tensor.

Effective slip length is reduced compared to surface average.

Asymptotic formulas agree with numerical and simulation results.

Abstract

We discuss the flow past a flat heterogeneous solid surface decorated by slipping stripes. The spatially varying slip length, $b(y)$, is assumed to be small compared to the scale of the heterogeneities, $L$, but finite. For such "weakly" slipping surfaces, earlier analyses have predicted that the effective slip length is simply given by the surface-averaged slip length, which implies that the effective slip-length tensor becomes isotropic. Here we show that a different scenario is expected if the local slip length has step-like jumps at the edges of slipping heterogeneities. In this case, the next-to-leading term in an expansion of the effective slip-length tensor in powers of ${max}\,(b(y)/L)$ becomes comparable to the leading-order term, but anisotropic, even at very small $b(y)/L$. This leads to an anisotropy of the effective slip, and to its significant reduction compared to the surface-averaged value. The asymptotic formulae are tested by numerical solutions and are in agreement with results of dissipative particle dynamics simulations.