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

Fuente: arXiv
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Main Authors: Tomlinson, Samuel D., Gibou, Frédéric, Luzzatto-Fegiz, Paolo, Temprano-Coleto, Fernando, Jensen, Oliver E., Landel, Julien R.
Format: Preprint
Published: 2024
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author Tomlinson, Samuel D.
Gibou, Frédéric
Luzzatto-Fegiz, Paolo
Temprano-Coleto, Fernando
Jensen, Oliver E.
Landel, Julien R.
author_facet Tomlinson, Samuel D.
Gibou, Frédéric
Luzzatto-Fegiz, Paolo
Temprano-Coleto, Fernando
Jensen, Oliver E.
Landel, Julien R.
contents 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 to 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_15251
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Drag reduction in surfactant-contaminated superhydrophobic channels at high Péclet numbers
Tomlinson, Samuel D.
Gibou, Frédéric
Luzzatto-Fegiz, Paolo
Temprano-Coleto, Fernando
Jensen, Oliver E.
Landel, Julien R.
Fluid Dynamics
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 to 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.
title Drag reduction in surfactant-contaminated superhydrophobic channels at high Péclet numbers
topic Fluid Dynamics
url https://arxiv.org/abs/2406.15251