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Apparent slip and drag reduction for the flow over superhydrophobic and lubricant-impregnated surfaces

Edoardo Alinovi and Alessandro Bottaro

  • DICCA, Scuola Politecnica University of Genoa, 1 via Montallegro, 16145 Genoa, Italy

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Phys. Rev. Fluids 3, 124002 – Published 13 December, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.124002

Abstract

The motion of a liquid above textured surfaces, impregnated with either a gas or a lubricant oil, is considered by homogenizing the microscopic near-wall flow to obtain protrusion heights (or Navier slip lengths), which can then be used in (macroscopic) direct numerical simulations of turbulence. The microstructure of the wall consists in longitudinally aligned ridges; this renders the small-scale Stokes problem amenable to decoupling into two problems, solved by the boundary element method with full account of the deformation of the liquid-lubricant interface, finally yielding two different protrusion heights, a longitudinal and a transverse one, respectively h|| and h⊥. Such heights are then employed in direct numerical simulations of the turbulent flow in a channel bounded by superhydrophobic or lubricant-impregnated walls, demonstrating the reduction in skin-friction drag which can be achieved with the rise in protrusion height difference, Δh=h||−h⊥. The results are in good agreement with an analytical approximation, provided Δh+ (Δh scaled in wall units) remains below 2 and the protrusion heights small in magnitude.

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Phys. Rev. Fluids 3, 124002– Published 13 December, 2018
  • Received 19 February 2018
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