Experimental study on the bubble-induced gravity-capillary jet-like surface waves

Abstract

Jet-like surface waves generated by an electric-spark-generated underwater bubble are experimentally studied. Three different motions of jet-like surface waves are observed depending on the inception position of the bubble (d: 0.28–7 mm) below the free surface and the maximum radius of the bubble ($R_m$: 1.5–3.6 mm). When d/$R_m$>1.3, the surface wave shows a simple smooth hump (case 1). When 0.7 < d/$R_m$ < 1.3, a single droplet or multiple droplets are pinched off at the jet-like surface wave (case 2). Finally, when d/$R_m$<0.7, a series of squirting & jetting phenomena are observed (case 3). For the cases 1, a proportional relationship is found between $\rho$gh/$\Delta p$ and $(d/R_m)^{-4}$, where $\rho$ is the density of the fluid, g is the gravitational acceleration, h is the maximum height of the surface wave and $\Delta p$ is the difference between the reference atmospheric pressure and the pressure inside a bubble. This proportional relationship is shown semi-analytically using a scaling argument, conservation of mass, momentum, and energy with the help of the Kelvin impulse theory. In addition, it is found that the resultant surface waves are indeed gravity-capillary waves by comparing the analytical wave solution with the observed surface wave pattern. For the case 2, the discretely proportional relationship between h/$R_m$ and the number of pinched off droplets (n) is observed through the experiment and analysed semi-analytically using a scaling argument and geometrically using conservation of mass.