Experimental evidence for surface tension origin of the circular hydraulic jump

Abstract

For more than a century, the consensus has been that the thin-film hydraulic jump that can be seen in kitchen sinks is created by gravity. However, we recently reported that these jumps are created by surface tension, and gravity does not play a significant role. In this paper, {we present experimental data for hydraulic jump experiments conducted in a micro-gravity environment ($\approx 2\%$ of Earth's gravity) (Avedisian \& Zhao 2000; Painter et al. 2007; Phillips et al. 2008). The existence of a hydraulic jump in micro-gravity unequivocally confirms that gravity is not the principal force causing the formation of the kitchen sink hydraulic jump.} We also present thirteen sets of experimental data conducted under terrestrial gravity reported in the literature for jumps in the steady-state for a range of liquids with different physical parameters, flow rates and experimental conditions. There is good agreement with {Bhagat et al.}'s theoretical predictions. We also show that beyond a critical flow rate, $Q_C^* \propto \gamma^2 /\nu \rho^2 g$, gravity does influence the hydraulic jumps. At lower flow rates, at the scale of the kitchen sink, surface tension is the dominating force. We discuss previously reported phenomenological and predictive models of hydraulic jumps and show that the phenomenological model -- effectively a statement of continuity of radial momentum across the jump -- does not allow the mechanism of the origin of the jump to be identified. However, combining the phenomenological model and {Bhagat et al.}'s theory allows us to predict the height of the jump.