Skip navigation

Unsteady evolution of slip and drag in surfactant-contaminated superhydrophobic channels

Unsteady evolution of slip and drag in surfactant-contaminated superhydrophobic channels

Tomlinson, Samuel D. ORCID logoORCID: https://orcid.org/0000-0002-7180-9443, Gibou, Frédéric ORCID logoORCID: https://orcid.org/0000-0001-7022-5262, Luzzatto-Fegiz, Paolo ORCID logoORCID: https://orcid.org/0000-0003-3614-552X, Temprano-Coleto, Fernando ORCID logoORCID: https://orcid.org/0000-0002-2179-3148, Jensen, Oliver E. ORCID logoORCID: https://orcid.org/0000-0003-0172-6578 and Landel, Julien R. ORCID logoORCID: https://orcid.org/0000-0003-3159-8749 (2024) Unsteady evolution of slip and drag in surfactant-contaminated superhydrophobic channels. Journal of Fluid Mechanics, 1000 (A62). A62-1-A62-39. ISSN 0022-1120 (Print), 1469-7645 (Online) (doi:10.1017/jfm.2024.676)

[thumbnail of Open Access Article]
Preview
PDF (Open Access Article)
51095 TOMLISON_Unsteady_Evolution_Of_Slip_And_Drag_In_Surfactant-Contaminated_Superhydrophobic_Channels_(OA)_2024.pdf - Published Version
Available under License Creative Commons Attribution.

Download (2MB) | Preview

Abstract

Recognising that surfactants can impede the drag reduction resulting from superhydrophobic surfaces (SHS), we investigate the impact of spatio–temporal fluctuations in surfactant concentration on the drag-reduction properties of SHS. We model the unsteady transport of soluble surfactant in a channel flow bounded by two SHS. The flow is laminar, pressure driven and the SHS are periodic in the streamwise and spanwise directions. We assume that the channel length is much longer than the streamwise period, the streamwise period is much longer than the channel height and spanwise period, and bulk diffusion is sufficiently strong for cross-channel concentration gradients to be small. By combining long-wave and homogenisation theories, we derive an unsteady advection–diffusion equation for surfactant-flux transport over the length of the channel, which is coupled to a quasi-steady advection–diffusion equation for surfactant transport over individual plastrons. As diffusion over the length of the channel is typically small, the surfactant flux is governed by a nonlinear wave equation. In the fundamental case of the transport of a bolus of surfactant, we predict its propagation speed and describe its nonlinear evolution via interaction with the SHS. The propagation speed can fall below the average streamwise velocity as the surfactant adsorbs and rigidifies the plastrons. Smaller concentrations of surfactant are advected faster than larger ones, so that wave-steepening effects can lead to shock formation in the surfactant-flux distribution. Our asymptotic results reveal how unsteady surfactant transport can affect the spatio–temporal evolution of the slip velocity, drag reduction and effective slip length in SHS channels.

Item Type: Article
Uncontrolled Keywords: Marangoni convection, drag reduction, microfluidics
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Faculty / School / Research Centre / Research Group: Faculty of Engineering & Science
Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS)
Last Modified: 26 Sep 2025 15:23
URI: https://gala.gre.ac.uk/id/eprint/51095

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics