An Integral Boundary Layer Model for Superhydrophobic Drag Reduction in General Flows*

There have been major recent advances in understanding and achieving superhydrophobic drag reduction. For practical applications (e.g. watercraft), a low-order model valid for flow over curved surfaces and with pressure gradients is still needed. Although no-slip versions of these flows can be handled by integral boundary layer (IBL) techniques, such methods rely on closures that apply only to no-slip flows. To extend the applicability of existing closures, we introduce a mapping between the properties of a "slip" boundary layer and those of an "equivalent" no-slip flow. In laminar flow, we test our approach using Falkner-Skan solutions with slip, and find that slip-flow properties are correctly mapped onto the no-slip parametrization, for any pressure gradient. For turbulent flow, model predictions with slip are consistent with published DNS and with prior log-law models (e.g. Tomlinson et al 2023). To examine general geometries, the mapping is incorporated into a code that hierarchically considers the outer flow, the IBL, and the sublayer, inclusive of air viscosity and of surfactant-induced stresses. The model's predictions compare favorably to turbulent experiments. The resulting code can predict superhydrophobic flow past general slender bodies.