Dissipative anomaly in sliding drops*

We use volume of fluid-based direct numerical simulations to compare drop sliding on ideal superhydrophobic and lubricant-impregnated surfaces. Ideal superhydrophobic surfaces conceptualize a thin air cushion between drop and substrate, but maintaining this layer's stability proves challenging. Consequently, current approaches often employ lubricating oils, creating a thin film on the substrate using which the drops can slide--an approach that subsequently generates a meniscus where viscous dissipation can occur. Remarkably, even for vanishingly small lubricant viscosity, we find that the drop's terminal velocity is lower on the lubricated surface than on a dry superhydrophobic surface. This phenomenon is attributed to persistent viscous dissipation in the lubricant meniscus, despite negligible viscosity, mirroring the ``dissipative anomaly" observed in turbulent flows. Our findings reveal fundamental limitations in mimicking ideal superhydrophobic behavior with lubricated surfaces and provide insights for optimizing self-cleaning technologies. Additionally, we uncover intriguing parallels between microscale interfacial flows and macroscale turbulence, suggesting broader implications for understanding dissipation in multiscale fluid systems.