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

Abstract

Using numerical simulations, we investigate the effects of Marangoni stresses induced by surfactants on the effective slip length of liquid-infused surfaces (LIS) with transverse grooves. The surfactants are assumed soluble in the external liquid shearing the surface and can adsorb onto the interfaces. Two different adsorption models are used: a classical Frumkin model and a more advanced model that better describes the decrease of surface tension for minuscule concentrations. The simulations show that LIS may face even more severe effects of surfactants than previously investigated superhydrophobic surfaces. Constructing an analytical model for the effective slip length, we can predict the critical surfactant concentration for which the slip length decreases significantly. This analytical model describes both adsorption models of LIS on a unified framework if properly adjusted. We also advance the understanding of when surfactant advection gives rise to highly skewed interfacial concentrations: the so-called partial stagnant cap regime. To a good approximation, this regime can only exist below a specific surfactant concentration given by the Marangoni number and the strength of the surfactants.

A single parameter can predict surfactant impairment of superhydrophobic drag reduction

“…Recently, independent experimental studies have reported time-dependent and spatially complex interfacial dynamics that unequivocally demonstrate the importance of surfactant-induced stresses on SHSs ( 13 , 14 ). Theoretical and computational works have confirmed the extent to which trace amounts of these surface-active contaminants can reduce slip ( 15 – 18 ). This slip reduction is also consistent with broader findings for small-scale multiphase flows, where environmental levels of surfactants, often extremely difficult to avoid or control, play a central role ( 19 ); prominent examples are given by small bubbles rising in water (e.g., refs.…”

Laminar drag reduction in surfactant-contaminated superhydrophobic channels

“…However, the drag reduction of LISs decreases as the viscosity ratio between internal and external fluids increases (Schönecker et al 2014). Furthermore, recent numerical simulations by Sundin & Bagheri (2022) have indicated that LISs may be more susceptible to surfactant effects than SHSs. Sundin & Bagheri (2022) extended the theory introduced in Landel et al (2020) to account for surfactants in a 2D shear flow, predicting the critical surfactant concentration for the slip to be reduced appreciably: Ĉc = 4 × 10 −4 mol m −3 for water-air SHSs and Ĉc = 5 × 10 −5 mol m −3 for water-dodecane LISs.…”

“…Furthermore, recent numerical simulations by Sundin & Bagheri (2022) have indicated that LISs may be more susceptible to surfactant effects than SHSs. Sundin & Bagheri (2022) extended the theory introduced in Landel et al (2020) to account for surfactants in a 2D shear flow, predicting the critical surfactant concentration for the slip to be reduced appreciably: Ĉc = 4 × 10 −4 mol m −3 for water-air SHSs and Ĉc = 5 × 10 −5 mol m −3 for water-dodecane LISs. For low applied shear stresses, Sundin & Bagheri (2022) found that the distribution of surfactant at the interface is approximately uniform and a scaling theory was used to derive an expression for the slip length.…”

“…Sundin & Bagheri (2022) extended the theory introduced in Landel et al (2020) to account for surfactants in a 2D shear flow, predicting the critical surfactant concentration for the slip to be reduced appreciably: Ĉc = 4 × 10 −4 mol m −3 for water-air SHSs and Ĉc = 5 × 10 −5 mol m −3 for water-dodecane LISs. For low applied shear stresses, Sundin & Bagheri (2022) found that the distribution of surfactant at the interface is approximately uniform and a scaling theory was used to derive an expression for the slip length. For high applied shear stresses, surfactant accumulates at the downstream stagnation point and forms a stagnant cap.…”

“…For high applied shear stresses, surfactant accumulates at the downstream stagnation point and forms a stagnant cap. Sundin & Bagheri (2022) employed numerical simulations to find that the stagnant cap regime only exists below a particular bulk concentration (above which the scaling theory once again becomes valid). Considering a typical surfactant, e.g.…”