Slip length for a viscous flow over spiky surfaces

TL;DR

This paper derives an analytical formula for the slip length of viscous flow over a 3D bi-periodic riblet surface with gaps, validated by numerical solutions, advancing understanding of flow behavior over textured surfaces.

Contribution

It provides a new approximate formula for slip length considering complex 3D riblet geometries with gaps, extending previous 2D results.

Findings

Analytical formula matches numerical solutions.

Formula valid for various gap fractions.

Extends understanding of slip over textured surfaces.

Abstract

For a model of a 3D coating composed of a bi-periodic system of parallel riblets with gaps we analytically derive an approximate formula for the effective slip length (an offset from the flat surface at which the flow velocity would extrapolate to zero) as a function of the geometry of the system (riblet period, riblet height, and relative gap size). This formula is valid for an arbitrary fraction of gaps (i.e from narrow riblets to narrow gaps) and agrees with the known analytical results for the 2D periodic coating of riblets without gaps. We validate our analytical results with the numerical solution of the equations of the viscous (creeping) flow over the riblets with gaps.