Skip navigation

Drag reduction in surfactant-contaminated superhydrophobic channels at high Péclet numbers

Drag reduction in surfactant-contaminated superhydrophobic channels at high Péclet numbers

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 (2025) Drag reduction in surfactant-contaminated superhydrophobic channels at high Péclet numbers. Journal of Fluid Mechanics, 1010 (A58). A58-1-A58-37. ISSN 0022-1120 (Print), 1469-7645 (Online) (doi:10.1017/jfm.2025.339)

[thumbnail of Open Access Article]
Preview
PDF (Open Access Article)
51096 TOMLISON_Drag_Reduction_In_Surfactant-Contaminated_Superhydrophobic_Channels_(OA)_2025.pdf - Published Version
Available under License Creative Commons Attribution.

Download (1MB) | Preview

Abstract

Motivated by microfluidic applications, we investigate drag reduction in laminar pressure-driven flows in channels with streamwise-periodic superhydrophobic surfaces (SHSs) contaminated with soluble surfactant. We develop a model in the long-wave and weak-diffusion limit, where the streamwise SHS period is large compared with the channel height and the Péclet number is large. Using asymptotic and numerical techniques, we determine the influence of surfactant on drag reduction in terms of the relative strength of advection, diffusion, Marangoni effects and bulk–surface exchange. In scenarios with strong exchange, the drag reduction exhibits a complex dependence on the thickness of the bulk-concentration boundary layer and surfactant strength. Strong Marangoni effects immobilise the interface through a linear surfactant distribution, whereas weak Marangoni effects yield a quasi-stagnant cap. The quasi-stagnant cap has an intricate structure with an upstream slip region, followed by intermediate inner regions and a quasi-stagnant region that is mediated by weak bulk diffusion. The quasi-stagnant region differs from the immobile region of a classical stagnant cap, observed for instance in surfactant-laden air bubbles in water, by displaying weak slip. As exchange weakens, the bulk and interface decouple: the surfactant distribution is linear when the surfactant is strong, whilst it forms a classical stagnant cap when the surfactant is weak. The asymptotic solutions offer closed-form predictions of drag reduction across much of the parameter space, providing practical utility and enhancing understanding of surfactant dynamics in flows over SHSs.

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 14:48
URI: https://gala.gre.ac.uk/id/eprint/51096

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics