Predicting slip degradation due to traces of surfactant in laminar flows over superhydrophobic surfaces*

In recent years, surfactants have been identified as one of the most influential factors affecting the performance of drag-reducing superhydrophobic surfaces (SHS). Trace amounts of these substances, virtually unavoidable in practical applications and even in nominally clean experiments, induce Marangoni forces that can completely negate slip (Peaudecerf et al. PNAS 2017; Song et al. PRF 2018). Models inclusive of surfactant initially considered flows over transverse SHS gratings (Landel et al. JFM 2020), since this is the simplest 2D flow that allows for the streamwise accumulation of surfactant ultimately responsible for the loss of performance. Here, we present a theory for longitudinal gratings, the most widely used configuration, which necessarily requires considering a 3D flow field (Temprano-Coleto et al. arXiv 2021). Predictions of the slip as a function of the SHS geometry are in good agreement with our simulations and experimental measurements, which we perform using confocal microscopy and micro-PIV in microfluidic channels. In addition, we show how our model can be used to estimate the concentration and physicochemical properties of the unknown surfactants naturally present in experimental setups, which are otherwise extremely challenging to measure directly.