Scaling law for ventilated air layers modulated by superhydrophobic grooves

An innovative air-layer establishment method is developed and experimentally investigated, where superhydrophobic transverse grooves are introduced to modulate localised minimal-flux ventilation. The results demonstrate that, owing to the modulation by the transverse grooves, the characteristics of multiphase flow undergo a fundamental transition from discrete bubbles to a continuous air layer. This modulation is strictly governed by both the free-stream velocity and the groove size, expressed as Reynolds number (

) and dimensionless groove size (

delta Superscript asterisk δ ∗ $\delta ^*$

), respectively. With a systematic variation in

italic Re Subscript upper D Re D $\textit{Re}_D$

and

delta Superscript asterisk δ ∗ $\delta ^*$

, the macroscopic topology of the air layer evolves through three distinct regimes: (i) continuous air layer (CAL), (ii) partial air layer (PAL) and (iii) bubble shedding (BS). The boundaries for these regimes are delineated within the regime map constructed by

italic Re Subscript upper D Re D $\textit{Re}_D$

and

delta Superscript asterisk δ ∗ $\delta ^*$

. It is established that size effects are negligible for the CAL–PAL transition, whereas the transition from PAL to BS exhibits a pronounced dependence on

delta Superscript asterisk δ ∗ $\delta ^*$

. The two regime transitions therefore follow distinct scaling relations. Neither transition boundary shows a discernible dependence on the solid fraction of the grooves. The dependence of regime transitions on ventilation flux is further examined, and the Weber number (

upper W e Subscript j W e j $We_j$

) is introduced to characterise the competition of the dynamic pressure of injected gas and the capillary force within grooves. The drag-reduction effectiveness of the groove-modulated air layers was also demonstrated. The present findings elucidate the mechanisms of air-layer establishment and provide a robust framework for the design of superhydrophobic grooved surfaces in air-layer drag-reduction applications.