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

TL;DR

This study uses numerical simulations and analytical modeling to explore how surfactants affect the slip length of liquid-infused surfaces with grooves, revealing conditions under which surfactants significantly impair slip performance.

Contribution

It introduces a unified analytical framework for predicting surfactant effects on LIS slip length, incorporating advanced adsorption models and the partial stagnant cap regime.

Findings

Surfactants can severely reduce LIS slip length, more than previously thought.

The analytical model predicts critical surfactant concentrations for slip reduction.

Partial stagnant cap regime occurs below a specific surfactant concentration, influenced by Marangoni number.

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.