Influence of insoluble surfactants on shear flow over a surface in Cassie state at large Péclet numbers

Baier, Tobias; Hardt, Steffen

doi:10.1017/jfm.2020.814

Cited by 18 publications

(19 citation statements)

References 28 publications

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“…In the present study, we have assumed a flat liquid/air interface at the SH walls, following the recent works in the relevant literature (Yu, Teo & Khoo 2016;Crowdy 2017a;Hodes et al 2017;Patlazhan & Vagner 2017;Arenas et al 2019;Fairhall, Abderrahaman-Elena & García-Mayoral 2019;Schnitzer & Yariv 2019;Vagner & Patlazhan 2019;Landel et al 2020;Nayak et al 2020;Baier & Hardt 2021;Tomlinson & Papageorgiou 2022). This simplifying assumption has enabled us to tackle the problem of a viscoplastic fluid flow over the groovy SH wall, while addressing the complexities arising due to the yield stress effects, in a systematic way.…”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

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Poiseuille flow of a Bingham fluid in a channel with a superhydrophobic groovy wall

Rahmani

Taghavi

2022

J. Fluid Mech.

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Plane Poiseuille flow of a Bingham fluid in a channel armed with a superhydrophobic (SH) lower wall is analysed via a semi-analytical model, accompanied by complementary direct numerical simulations (DNS). The SH surface represents a groovy structure with air trapped inside its cavities. Therefore, the fluid adjacent to the wall undergoes stick–slip conditions. The model is developed based on introducing infinitesimal wall-induced perturbations into the motion equations, followed by Fourier series expansions, and solving the resulting equations as a boundary value problem. The Navier slip law accounts for the slip at the liquid/air interface (assuming the Cassie state). The presented analysis is fairly comprehensive, covering the creeping and inertial regimes for thick channels (via the semi-analytical and DNS solutions). The main dimensionless numbers are the Reynolds ( $Re$ ), Bingham ( $Bi$ ) and slip ( $b$ ) numbers, as well as the groove periodicity length ( $\ell$ ) and the slip area fraction ( $\varphi$ ). By increasing $Bi$ , the perturbation and slip velocity fields grow. As $Re$ increases, the perturbation and slip velocity fields become asymmetric. For certain flow parameters, an unyielded plug zone may appear on the SH wall liquid/air interface, while its formation is accelerated by inertial effects. The results classify the regimes of creeping and inertial flows via predicting the onset of the unyielded plug zone formation at the SH wall.

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Section: Summary and Concluding Remarksmentioning

confidence: 99%

“…2020; Nayak et al. 2020; Baier & Hardt 2021; Tomlinson & Papageorgiou 2022). This simplifying assumption has enabled us to tackle the problem of a viscoplastic fluid flow over the groovy SH wall, while addressing the complexities arising due to the yield stress effects, in a systematic way.…”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

Poiseuille flow of a Bingham fluid in a channel with a superhydrophobic groovy wall

Rahmani

Taghavi

2022

J. Fluid Mech.

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“…Recently, independent experimental studies have reported time-dependent and nonlinear dynamics that unequivocally demonstrate the importance of surfactant-induced stresses on SHSs [13][14][15]. Theoretical and computational works have then confirmed the extent to which trace amounts of these surfactant contaminants can influence liquid slip [15][16][17]. Indeed, ambient levels of surfactants, often extremely difficult to avoid or control in common experimental settings, are known to play a central role altering the behavior of numerous smallscale multiphase flows [18].…”

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confidence: 99%

“…The concentration gradients that induce interfacial Marangoni stresses appear in the streamwise direction, owing to stagnation points at the downstream ends of the interfaces where surfactants advected by the flow can accumulate. Initial theoretical studies only considered two-dimensional flows over transverse SHS gratings, since this is the simplest geometry to capture the negative effect of streamwise surfactant-induced Marangoni stresses [16,17]. However, these models cannot capture any three-dimensional effect.…”

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confidence: 99%

A single parameter can predict surfactant impairment of superhydrophobic drag reduction

Temprano-Coleto,

Smith,

Peaudecerf

et al. 2021

Preprint

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Trace amounts of surfactants have been shown to critically prevent the drag reduction of superhydrophobic surfaces (SHSs), yet predictive models including their effects in realistic geometries are still lacking. We derive theoretical predictions for the velocity and resulting slip of a laminar fluid flow over three-dimensional SHS gratings contaminated with surfactant, which allow for the first direct comparison with experiments. The results are in good agreement with our numerical simulations and with measurements of the slip in microfluidic channels lined with SHSs, which we obtain via confocal microscopy and micro-particle image velocimetry. Our model enables the estimation of a priori unknown parameters of surfactants naturally present in applications, highlighting its relevance for microfluidic technologies.

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“…Understanding how surfactants equilibrate near contact lines is also important for flows over superhydrophobic surfaces, and slippery-liquid-infused porous surfaces (Wang & Guo 2020). As recently shown, surfactants can significantly affect the drag-reducing properties of superhydrophobic surfaces when a flow concentrates them at stationary contact lines (Landel et al 2020;Baier & Hardt 2021;Peaudecerf et al 2017). Surfactants are amphiphilic materials that accumulate at interfaces, where they lower surface tension.…”

Section: Introductionmentioning

confidence: 99%

Surfactant spreading in a two-dimensional cavity and emergent contact-line singularities

2021

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We model the advective Marangoni spreading of insoluble surfactant at the free surface of a viscous fluid that is confined within a two-dimensional rectangular cavity. Interfacial deflections are assumed small, with contact lines pinned to the walls of the cavity, and inertia is neglected. Linearising the surfactant transport equation about the equilibrium state allows a modal decomposition of the dynamics, with eigenvalues corresponding to decay rates of perturbations. Computation of the family of mutually orthogonal two-dimensional eigenfunctions reveals singular flow structures near each contact line, resulting in spatially oscillatory patterns of shear stress and a pressure field that diverges logarithmically. These singularities at a stationary contact line are associated with dynamic compression of the surfactant monolayer. We show how they can be regularised by weak surface diffusion. Their existence highlights the need for careful treatment in computations of unsteady advection-dominated surfactant transport in confined domains.

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Influence of insoluble surfactants on shear flow over a surface in Cassie state at large Péclet numbers

Abstract: Abstract

Cited by 18 publications

References 28 publications

Poiseuille flow of a Bingham fluid in a channel with a superhydrophobic groovy wall

Poiseuille flow of a Bingham fluid in a channel with a superhydrophobic groovy wall

A single parameter can predict surfactant impairment of superhydrophobic drag reduction

Surfactant spreading in a two-dimensional cavity and emergent contact-line singularities

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