Creeping flow dynamics over superhydrophobic ball: Slip effects and drag reduction

摘要

Slip and drag over superhydrophobic ball in the creeping flow regime (Reynolds number < 0.1) are investigated due to its relevance in physiological systems. Experiments involve comparing the settling velocities of superhydrophobic (SH) balls (3 mm-11.96 mm) fabricated using etching method with that of smooth balls, in highly viscous Newtonian mediums: golden syrup and honey. Due to the high Capillary number (Ca > 1) of the system, air is trapped in the surface asperities without formation of film (plastron). The flow over SH ball is modeled using the stream function formulation, that incorporates wall-slip and relates it to the enhanced settling velocities and drag reduction. Slip length decreases (178-24 mu m) with the increase in Reynolds number, establishing the dependence of slippage on flow apart from surface morphology. The drag reduction is comparatively low 8% due to the absence of plastron. A component based analysis reveal that form drag contributes towards one-third of the total drag while skin drag and normal stress drag contribute towards the remaining two-third. The skin drag takes over the normal stress drag with the increase in Reynolds number, eventually replacing it. The experimental method and modeling constitute a generic technique for evaluating the potential of SH surface to reduce drag.