Effect of stiffness of the base on impact-induced liquid jet velocity

Dropping a liquid-filled test tube onto various bases generates a focused liquid jet. This study aims to clarify the relationship between the stiffness of the base and the jet velocity. Previous research focused on finding that jet velocity is proportional to the gas-liquid interface velocity just before ejection and developing a model for jet velocity on a metal base. We measured the jet velocity for various bases with elastic modulus from 0.186 MPa to 206 GPa. For elastic modulus between 7.50 MPa and 206 GPa, the jet velocities agree with the values obtained from the model equation. However, when the elastic modulus was below 1.15 MPa, the jet velocities were up to 66% lower than the values obtained from the model equation, which does not account for the effects of the stiffness of the base. Assuming that the gas-liquid interface velocity depends on the impact velocity of the test tube, the elastic modulus of the base, and the density of the liquid-filled test tube, dimensional analysis revealed an intriguing finding: the jet velocity is determined by the ratio of the inertial force of the test tube filled with liquid to the elastic force of the bases. Furthermore, we could describe the jet velocity using a model equation that considers the effect of the base's elasticity by applying the Cauchy number, which represents the ratio of the inertial force to the elastic force.