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

By A. V. Belyaev, O. Vinogradova. Journal of Fluid Mechanics, 2009

162 citations recorded by the source corpus.

A super-hydrophobic array of grooves containing trapped gas (stripes) has 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 analyse 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, we 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 the 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 a small slip, we predict simple surface-averaged isotropic flows (independent of orientation).

Subfields: Biomedical Engineering, Computational Mechanics, Surfaces, Coatings and Films

View Paper: https://www.semanticscholar.org/paper/d10415a7e6777108c9f692f72115c8a16acb433c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

In Computational Mechanics

In Surfaces, Coatings and Films

Citations in the corpus

Superhydrophobic drag reduction in laminar flows: a critical review (2016, methodology): “…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.…”
Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state (2013, background): “Besides Philip’s results, it is interesting to compare the equations for the effective slip length (2.19) and (2.29) to the equations of Belyaev & Vinogradova (2010), (1.4) and (1.5).”