Slip length for a viscous flow over spiky surfaces

¹ Defence Science and Technology Group - Melbourne, VIC 3207, Australia
² Laboratoire de Physique de la Matiére Condensée, CNRS - Ecole Polytechnique, Institut Polytechnique de Paris 91120 Palaiseau, France
³ Department of Mechanical Engineering, The University of Melbourne - Parkville, VIC 3010, Australia

^(a) E-mail: alexei.skvortsov@defence.gov.au (corresponding author)
^(b) E-mail: denis.grebenkov@polytechnique.edu
^(c) E-mail: lzhchan@unimelb.edu.au
^(d) E-mail: a.ooi@unimelb.edu.au

Received: 12 September 2023
Accepted: 18 September 2023

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.