Asymptotic formulae for flow in superhydrophobic channels with longitudinal ridges and protruding menisci

Author: 

Kirk, T

Publication Date: 

1 February 2018

Journal: 

Journal of Fluid Mechanics

Last Updated: 

2021-10-10T21:24:26.223+01:00

Volume: 

839

DOI: 

10.1017/jfm.2018.73

abstract: 

This paper presents new asymptotic formulae for flow in a channel with one or both walls patterned with a longitudinal array of ridges and arbitrarily protruding menisci. Derived from a matched asymptotic expansion, they extend results by Crowdy (J. Fluid Mech., vol. 791, 2016, R7) for shear flow, and thus make no restriction on the protrusion into or out of the liquid. The slip length formula is compared against full numerical solutions and, despite the assumption of small ridge period in its derivation, is found to have a very large range of validity; relative errors are small even for periods large enough for the protruding menisci to degrade the flow and touch the opposing wall.

Symplectic id: 

1105830

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article