Effective slip in pressure-driven flow past super-hydrophobic stripes

Abstract

Super-hydrophobic array of grooves containing trapped gas (stripes), have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused on idealized cases of stick-perfect slip stripes. Here, we analyze the experimentally more relevant situation of a pressure-driven flow past striped slip-stick surfaces with arbitrary local slip at the gas sectors. We derive approximate formulas for maximal (longitudinal) and minimal (transverse) directional effective slip lengths, that are in a good agreement with the exact numerical solution for any surface slip fraction. By representing eigenvalues of the slip length-tensor, they allow us to obtain the effective slip for any orientation of stripes with respect to the mean flow. Our results imply that flow past stripes is controlled by the ratio of the local slip length to texture size. In case of a large (compared to the texture period) slip at the gas areas, surface anisotropy leads to a tensorial effective slip, by attaining the values predicted earlier for a perfect local slip. Both effective slip lengths and anisotropy of the flow decrease when local slip becomes of the order of texture period. In the case of small slip, we predict simple surface-averaged, isotropic flows (independent of orientation).

Underwater Restoration and Retention of Gases on Superhydrophobic Surfaces for Drag Reduction

“…To start, the slip lengths on non-wetted surfaces were measured to be consistent with theoretical values for grates [25,26] and posts [6,27] ("Never-wetted" in Fig. 4).…”

Superhydrophobic drag reduction in laminar flows: a critical review

“…Analytical models and numerical simulations are useful tools in understanding slip lengths in laminar flows on a few simple surface patterns such as grates (ridges, trenches) (Philip 1972a, b;Lauga and Stone 2003;Belyaev and Vinogradova 2010a;Asmolov and Vinogradova 2012), posts (pillars) (Ybert et al 2007;Davis and Lauga 2010), and holes (Ybert et al 2007;Davis and Lauga 2009a), as shown in Fig. 2.…”

Electro-osmosis on Anisotropic Superhydrophobic Surfaces

“…Let then φ 1 and φ 2 = δ/L be the area fractions of the solid and gas phases with φ 1 + φ 2 = 1. Pressure-driven flow past such stripes has been shown to depend on the direction of the flow, and the eigenvalues of the slip-length tensor [20] read [21] …”