Vortex ring generation due to the coalescence of a water drop at a free surface

Abstract

The formation of a vortex ring in a pool by contact with a fluid drop is a familiar phenomenon easily generated by milk drops in a glass of water. First observed over a century ago by Thomson and Newall (1885), however, much about the process is not well understood. For simplicity, much of the work done has been restricted to the case of the the drop and pool having identical composition. Chapman and Critchlow (1967) characterize the rings formed by falling drops in terms of the drop shape at the time of impact and propose a quantitative model of the vortex ring's generation process. Peck and Sigurdson (1994) analyze the structure of rings as they penetrate into the pool after a fall. Hsiao, et al. (1988) experimentally determine a critical Weber number for the falling drop (We ≈ 8) above which a jet, rather than a vortex ring, is formed in the pool. It should be noted that the Peck and Sigurdson drops had a We range of 22-25, which seems to contradict the earlier work of Hsiao, et al. To further simplify matters, the degenerate case (We = 0) in which contact between the drop and pool occurs with zero velocity may be examined. Shankar and Kumar (1995) observe the evolutionary behavior of rings so generated, and characterize the zero velocity case as a function of two dimensionless parameters only. In this work we visualize the formation of the ring rather than its evolution, and quantitatively examine a simplified scaling law based on the analyses of Hsiao, et. al and Shankar and Kumar. This scaling law, when valid, allows the flow conditions to be expressed in a single dimensionless parameter. Validity, however, requires that surface tension forces dominate gravitational and viscous ones in the vortex ring formation process.