title: Effective slip-length tensor for a flow over weakly slipping stripes.
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 steplike 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 formulas are tested by numerical solutions and are in agreement with results of dissipative particle dynamics simulations.
authors.affiliation: A.N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, 31 Leninsky Prospect, 119071 Moscow, Russia and Central Aero-Hydrodynamic Institute, 140180 Zhukovsky, Moscow region, Russia and Institute of Mechanics, M. V. Lomonosov Moscow State University, 119071 Moscow, Russia.
authors.forename: Evgeny S
authors.initials: ES
authors.lastname: Asmolov
authors.forename: Jiajia
authors.initials: J
authors.lastname: Zhou
authors.forename: Friederike
authors.initials: F
authors.lastname: Schmid
authors.forename: Olga I
authors.initials: OI
authors.lastname: Vinogradova