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Direct numerical simulations are used to study the drag reduction by superhydrophobic surfaces in laminar channel flow. Resolved multiphase simulations using the volume of fluid methodology are performed to study the effects of groove geometry, interface shear rate, and meniscus penetration independently. An analytical solution for the flow in a laminar channel with a grooved surface with a gas pocket within is obtained. The solution accounts for both the groove geometry and the trapped fluid properties, and shows good agreement with simulation results. The solution is used to propose a scaling law that collapses data across fully wetted to fully gas-filled regimes. The trapped gas is simulated as both flat and meniscal interfaces. The drag reduction initially increases with interface deflection into the groove and then decreases for large deflections as the interface velocity approaches zero due to the proximity to the bottom of the groove.

Feature-resolved computational and analytical study of laminar drag reduction by superhydrophobic surfaces