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Using numerical simulations, we investigate the effects of Marangoni stressesinduced by surfactants on the effective slip length of liquid-infused surfaces(LIS) with transverse grooves. The surfactants are assumed soluble in theexternal liquid shearing the surface and can adsorb onto the interfaces. Twodifferent adsorption models are used: a classical Frumkin model and a moreadvanced model that better describes the decrease of surface tension forminuscule concentrations. The simulations show that LIS may face even moresevere effects of surfactants than previously investigated superhydrophobicsurfaces. Constructing an analytical model for the effective slip length, wecan predict the critical surfactant concentration for which the slip lengthdecreases significantly. This analytical model describes both adsorption modelsof LIS on a unified framework if properly adjusted. We also advance theunderstanding of when surfactant advection gives rise to highly skewedinterfacial concentrations - the so-called partial stagnant cap regime. To agood approximation, this regime can only exist below a specific surfactantconcentration given by the Marangoni number and the strength of thesurfactants.

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