Liquid entrainment of the toroidal bubble crossing the interface between two immiscible liquids

Abstract

We experimentally investigate the transport of liquid by a toroidal bubble that rises vertically and penetrates a horizontal interface between two immiscible liquids. Experiments are conducted with various strengths of vortex circulation in the bubble, and with different liquid densities and viscosities. In contrast to a spherical bubble, a rising toroidal bubble carries a great amount of the lower liquid by virtue of the self-induction of circulating flow. The lower liquid is entrained by the toroidal bubble and forms an ellipsoidal body enclosing the bubble after it penetrates the interface. The downward net force acting on the ellipsoidal body results in the radial contraction of the bubble, reducing the volume of the entrained lower liquid. As the entrained volume decreases, the nearby upper liquid eventually pierces the ellipsoidal body, making the bubble unstable. At this instant, the net force acting on the ellipsoidal body approaches zero, and the volume ratio of the entrained lower liquid and bubble converges to a specific value. For smaller vortex circulation and larger density difference between the liquids, the volume of the entrained lower liquid within the ellipsoidal body becomes smaller and the travel distance of the bubble from the initial interface until it becomes unstable decreases. The effective Froude number, which accounts for both the inertial effect of vortex circulation and the gravitational effect of liquid density difference, is found to characterise the temporal changes in the ring radius, propagation speed and entrained volume.