Effect of converging shape of container on the velocity of impact-induced focused liquid jet

TL;DR

This study demonstrates that the shape of a container, specifically converging geometries, significantly enhances the velocity of impact-induced focused liquid jets, with potential applications in high-viscosity liquid ejection and needle-free injection technologies.

Contribution

It provides a novel insight into how container shape influences jet velocity, supported by numerical and analytical modeling of pressure impulse fields.

Findings

Jet velocity up to 1.6 times higher in converging containers.

Pressure impulse at the bottom drives the jet acceleration.

Container shape alters flow rate and pressure impulse gradient, increasing jet speed.

Abstract

We investigated the effect of container shape on the behavior of the impact-induced focused liquid jets by dropping a converging-shaped container (e.g., Kjeldahl flask) partially filled with liquid onto a floor to develop a method for increasing the jet velocity. Note that a similar well-known experiment, Pokrovski's experiment, in which a focused liquid jet is generated in a test tube, is free from the effect of the converging shape. The results showed that the jet was up to about 1.6 times faster in a converging-shaped container than in a test tube, despite the same impact velocity. To understand the mechanism of the increase in the jet velocity, the Laplace equation on the pressure impulse was solved numerically under the boundary condition that the pressure impulse is given at the bottom of the container. The normalized gas-liquid interfacial velocity obtained from the numerical solution of the pressure impulse field agrees well with the normalized jet velocity in experiments, showing that the jets we observed are driven by the pressure impulse generated at the bottom. In addition, numerical solutions of pressure impulse fields in a simpler-shaped container with different degrees of convergence were compared with analytical solutions obtained from a lower-order model of the pressure impulse field. We confirmed that the gas-liquid interfacial velocity of the impact-induced focused liquid jet is governed by changes in both the flow rate and pressure impulse gradient at the central axis of the container caused by changes in the cross-sectional area of the container. We showed that by changing the container shape, we can increase the velocity of the gas-liquid interface after the container impact. This finding is expected to be applied to the ejection and application of high-viscosity liquids as well as to needle-free injection technology using fast focused liquid jets.