  Recent experimental and computational investigations have shown that trace
amounts of surfactants, unavoidable in practice, can critically impair the drag
reduction of superhydrophobic surfaces (SHSs), by inducing Marangoni stresses
at the air-liquid interface. However, predictive models for realistic SHS
geometries do not yet exist, which has limited the understanding and mitigation
of these adverse surfactant effects. To address this issue, we derive a model
for laminar, three-dimensional flow over SHS gratings as a function of geometry
and soluble surfactant properties, which together encompass 10 dimensionless
groups. We establish that the grating length $g$ is the key geometric parameter
and predict that the ratio between actual and surfactant-free slip increases
with $g^2$. Guided by our model, we perform synergistic numerical simulations
and microfluidic experiments, finding good agreement with the theory as we vary
surfactant type and SHS geometry. Our model also enables the estimation, based
on velocity measurements, of a priori unknown properties of surfactants
inherently present in microfluidic systems. For SHSs, we show that surfactant
effects can be predicted by a single parameter, representing the ratio between
the grating length and the interface length scale beyond which the flow
mobilizes the air-water interface. This mobilization length is more sensitive
to the surfactant chemistry than to its concentration, such that even
trace-level contaminants may significantly increase drag if they are highly
surface active. These findings advance the fundamental understanding of
realistic interfacial flows and provide practical strategies to maximize
superhydrophobic drag reduction.
