Tomlinson, Samuel D. ORCID: https://orcid.org/0000-0002-7180-9443, Gibou, Frédéric ORCID: https://orcid.org/0000-0001-7022-5262, Luzzatto-Fegiz, Paolo ORCID: https://orcid.org/0000-0003-3614-552X, Temprano-Coleto, Fernando ORCID: https://orcid.org/0000-0002-2179-3148, Jensen, Oliver E. ORCID: https://orcid.org/0000-0003-0172-6578 and Landel, Julien R. ORCID: https://orcid.org/0000-0003-3159-8749 (2023) Laminar drag reduction in surfactant-contaminated superhydrophobic channels. Journal of Fluid Mechanics, 963 (A10). pp. 1-48. ISSN 0022-1120 (Print), 1469-7645 (Online) (doi:10.1017/jfm.2023.264)

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Abstract

Although superhydrophobic surfaces (SHSs) show promise for drag reduction applications, their performance can be compromised by traces of surfactant, which generate Marangoni stresses that increase drag. This question is addressed for soluble surfactant in a three-dimensional laminar channel flow, with periodic SHSs made of long finite-length longitudinal grooves located on both walls. We assume that bulk diffusion is sufficiently strong for cross-channel concentration gradients to be small. Exploiting long-wave theory and accounting for the difference between the rapid transverse and slower longitudinal Marangoni flows, we derive a one-dimensional model for surfactant transport from the full three-dimensional transport equations. Our one-dimensional model allows us to predict the drag reduction and surfactant distribution across the parameter space. The system exhibits multiple regimes, involving competition between Marangoni effects, bulk and interfacial diffusion, bulk and interfacial advection, shear dispersion and surfactant exchange between the bulk and the interface. We map out asymptotic regions in the high-dimensional parameter space, and derive explicit closed-form approximations of the drag reduction, without any fitting or empirical parameters. The physics underpinning the drag reduction effect and the negative effect of surfactant is discussed through analysis of the velocity field and surfactant concentrations, which show both uniform and non-uniform stress distributions. Our theoretical predictions of the drag reduction compare well with results from the literature solving numerically the full three-dimensional transport problem. Our atlas of maps provides a comprehensive analytical guide for designing surfactant-contaminated channels with SHSs, to maximise the drag reduction in applications.

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 14:35
URI:	https://gala.gre.ac.uk/id/eprint/51093

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