Normalizing study on the characteristic size of the stable cavity induced by a gas-jet penetrating into a liquid sheet

Generating a stable cavity accompanying with a dry spot on the solid substrate by a gas-jet penetrating into a liquid sheet is commonly required in various industrial fields. In-depth study to the impact of the characteristic size of the stable cavity (i.e. the dry spot diameter) from the penetrating conditions is still lacked. In this paper, a series of experiments were carried out to study stable cavities created by vertical gas-jet penetrating into and rupturing a shallow liquid sheet (spread in a container with the thickness of 3-5 mm), in which a dry spot (a circular dry area after the liquid displaced) was produced on the solid flat substrate. The effects on the dry spot diameter by the penetrating parameters including nozzle diameter, liquid sheet thickness, gas flow rate and jet height were systemically studied. In addition, further dimensionless analysis was implemented on the experimental results to normalize the dry spot diameter with all penetrating parameters. To realize the normalization, a mechanical equilibrium model of the dry spot boundary line was built according to gas-liquid-solid interface action mechanism, and further simplified according to Young-Dupré law based on the experimentally monitored results of the cavity contact angle. Based on the simplified model, the ratio of dry spot diameter to jet height was expressed by a linear function of a combined dimensionless parameter of the Froude number and the ratio of nozzle diameter to jet height as normalization, where the slope of the function could be determined by curve fitting of the experimental results. The normalizing study on the characteristic size of the stable cavity in this paper can provide useful criteria for the jet controls in actual industry applications.