A single parameter can predict surfactant impairment of superhydrophobic drag reduction

Abstract

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.

Slip of submerged two-dimensional liquid-infused surfaces in the presence of surfactants

“…At these desorption rates, diffusion of bulk surfactants becomes the limiting process (Damköhler number Da δ 1). Temprano-Coleto et al (2021) recently discussed this independence, using κ d = 0.75 s −1 with good agreement with the experimental results of SHS with surfactants naturally occurring in their experimental setting.…”

“…The analytical model has been developed for two-dimensional transverse grooves. However, similar surfactant transport processes are expected to be present for LIS with three-dimensional longitudinal grooves (Landel et al 2020;Temprano-Coleto et al 2021). Therefore, the analytical model is expected to provide an indication of the effects of surfactants on the slip length also for such configurations, commonly used in experimental LIS studies (Jacobi et al 2015;Wexler et al 2015;Fu et al 2019).…”

“…where Da = κ a w/(ωD) is the Damköhler number (Temprano-Coleto et al 2021). From (5.2), a characteristic adsorption flux is given by…”

“…Using numerical simulations, a significant slip length reduction of SHS has been observed at bulk concentrations c 0 ≈ 10 −3 mol m −3 using properties of the surfactant sodium dodecyl sulphate (SDS) (Peaudecerf et al 2017). Most recent experimental studies of SHS, which propose that surfactant gradients lead to slip degradation, have not added surfactants artificially (Kim & Hidrovo 2012;Bolognesi, Cottin-Bizonne & Pirat 2014;Peaudecerf et al 2017;Song et al 2018;Temprano-Coleto et al 2021). Instead, the fluid systems have likely been contaminated by the surrounding environment.…”

Shear flow over a surface containing a groove covered by an incompressible surfactant phase

“…Special attention has been given to liquid flow over 'superhydrophobic' surfaces with gas-filled (or liquid-filled) cavities due to their potential for drag reduction (Rothstein 2010;Schönecker, Baier & Hardt 2014;Lee, Choi & Kim 2016). The influence of surfactants on such flows has been observed experimentally (Kim & Hidrovo 2012;Bolognesi, Cottin-Bizonne & Pirat 2014;Schäffel et al 2016;Peaudecerf et al 2017;Song et al 2018;Li et al 2020) and analysed theoretically (Gaddam et al 2018;Landel et al 2020;Baier & Hardt 2021;Temprano-Coleto et al 2021). Also in this case, surfactant molecules stack up at stagnation points and can severely impede the drag reduction compared with expectations based on a surfactant-free situation.…”