[Paper Review] Experimental evidence for surface tension origin of the circular hydraulic jump

Rajesh K. Bhagat, D.I. Wilson+1 more|arXiv (Cornell University)|Oct 8, 2020

Hydraulic flow and structures30 references4 citations

TL;DR

This paper provides experimental evidence that surface tension, not gravity, is the primary force driving the formation of circular hydraulic jumps in kitchen sinks. Using micro-gravity experiments and extensive terrestrial data, the authors confirm that jumps persist in near-zero gravity, validating a theory that surface tension dominates at typical kitchen sink flow rates, with excellent agreement between predictions and measurements across diverse fluids and conditions.

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, $Q_C^* \propto γ^2 /νρ^2 g$, 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.

Motivation & Objective

• To challenge the long-standing consensus that gravity is the dominant force in circular hydraulic jump formation.
• To provide direct experimental evidence using micro-gravity environments to test the role of gravity in jump formation.
• To validate Bhagat et al.'s surface tension-based theory against a broad range of independent experimental data from the literature.
• To identify the critical flow rate above which gravity becomes significant in hydraulic jump dynamics.
• To demonstrate that combining phenomenological momentum balance with surface tension theory enables prediction of jump height, a previously unmodeled feature.

Proposed method

• Conducted hydraulic jump experiments in micro-gravity environments (~2% Earth gravity) using data from Avedisian & Zhao (2000), Painter et al. (2007), and Phillips et al. (2008).
• Collected and analyzed 13 sets of terrestrial experimental data from the literature, covering diverse liquids (water, surfactants, glycols, silicone oils, glycerin solutions, lubricating oil) with varying surface tension, viscosity, and density.
• Applied Bhagat et al.'s theoretical model, which posits that surface tension dominates at low flow rates, with jump radius governed by $ R \propto \sqrt{\gamma / \rho \nu g} $, where $\gamma$ is surface tension, $\rho$ density, $\nu$ kinematic viscosity, and $g$ gravity.
• Derived a critical flow rate $ Q_C^* \propto \gamma^2 / (\nu \rho^2 g) $, above which gravity becomes influential, using scaling analysis.
• Combined phenomenological momentum conservation (radial flow continuity) with the surface tension-based theory to predict jump height, yielding $ H \approx \sqrt{2\gamma / \rho g} $.
• Compared theoretical predictions with experimental jump radii and heights across all fluid types and conditions, assessing model accuracy.

Experimental results

Research questions

• RQ1 Is gravity the dominant force responsible for the formation of circular hydraulic jumps in kitchen sinks?
• RQ2 Can hydraulic jumps form in micro-gravity environments, and what does this imply about the role of gravity?
• RQ3 Does Bhagat et al.'s surface tension-based theory accurately predict jump radii across a wide range of liquids and flow conditions?
• RQ4 At what flow rate does gravity begin to significantly influence hydraulic jump formation?
• RQ5 Can the jump height, a previously unmodeled feature, be predicted by combining phenomenological momentum balance with surface tension theory?

Key findings

• Hydraulic jumps were observed in micro-gravity environments (~2% Earth gravity), providing direct experimental evidence that gravity is not the principal force behind the jump formation.
• The jump radius predicted by Bhagat et al.'s surface tension-based theory showed excellent agreement with experimental data across 13 diverse fluid systems, including water, surfactant solutions, ethylene glycol, silicone oils, and glycerin solutions.
• For typical kitchen sink flow rates, where $ Q \ll Q_C^* $, surface tension alone determines the jump radius, with gravity playing a negligible role.
• The critical flow rate $ Q_C^* \approx 3058 \, \text{cm}^3\text{s}^{-1} $ was identified, above which gravity begins to influence the jump, particularly for high-viscosity, low-surface-tension fluids.
• The combined model of phenomenological momentum conservation and surface tension theory successfully predicted the jump height, yielding $ H \approx \sqrt{2\gamma / \rho g} $, in good agreement with experimental observations.
• The model of Wang & Khayat (2019) over-predicted jump radii, especially for low-viscosity, high-surface-tension fluids, indicating limitations in its physical assumptions compared to the surface tension-based theory.