Effective slippage on superhydrophobic trapezoidal grooves

TL;DR

This study combines simulations and theoretical analysis to understand how the geometry of superhydrophobic trapezoidal grooves influences effective slip, providing insights for designing microfluidic surfaces with optimized flow properties.

Contribution

It introduces a validated approach combining DPD simulations and theoretical estimates to accurately predict effective slip lengths on trapezoidal superhydrophobic surfaces.

Findings

Effective slip depends on area-averaged slip and roughness amplitude.

Flow singularities near heterogeneities inhibit slip and increase flow anisotropy.

Guidelines for designing optimal superhydrophobic surfaces are proposed.

Abstract

We study the effective slippage on superhydrophobic grooves with trapezoidal cross-sections of various geometries (including the limiting cases of triangles and rectangular stripes), by using two complementary approaches. First, dissipative particle dynamics (DPD) simulations of a flow past such surfaces have been performed to validate an expression [E.S.Asmolov and O.I.Vinogradova, J. Fluid Mech. \textbf{706}, 108 (2012)] that relates the eigenvalues of the effective slip-length tensor for one-dimensional textures. Second, we propose theoretical estimates for the effective slip length and calculate it numerically by solving the Stokes equation based on a collocation method. The comparison between the two approaches shows that they are in excellent agreement. Our results demonstrate that the effective slippage depends strongly on the area-averaged slip, the amplitude of the roughness, and on the fraction of solid in contact with the liquid. To interpret these results, we analyze flow singularities near slipping heterogeneities, and demonstrate that they inhibit the effective slip and enhance the anisotropy of the flow. Finally, we propose some guidelines to design optimal one-dimensional superhydrophobic surfaces, motivated by potential applications in microfluidics.