A single parameter can predict surfactant impairment of superhydrophobic drag reduction

Trace surfactants, unavoidable in applications, can impair the drag reduction achieved by superhydrophobic surfaces (SHS), as Marangoni stresses can immobilize the air-water interface. For realistic SHS textures, it is not known how this impairment depends on surfactant type and concentration, flow velocity, and SHS geometry; as a result, mitigation strategies are still needed. We introduce a model for finite-length, streamwise SHS gratings, and perform simulations and experiments. Our model also enables the estimation, based on velocity measurements, of a priori unknown properties of surfactants inherently present in microfluidic systems. We find that the interface can be mobilized if it is longer than a critical length scale, which is determined by the surfactant properties. This mobilization length is more sensitive to the surfactant chemistry that to its concentration, such that even trace-level contaminants may significantly increase drag if they are highly surface-active. SHS impairment is thereby predicted from a single parameter, namely the ratio of interface length and mobilization scale, providing fundamental insight and practical guidance to achieve superhydrophobic drag reduction.