An Experimental Investigation of the Break-up of a Liquid Drop Falling in a Miscible Fluid

Abstract

A liquid drop falling in a lighter miscible fluid either undergoes a cascade of fragmentations, each appearing as a dynamic instability, or it mixes by diffusion, depending on the value of a fragmentation number F . F is the ratio of the diffusion time to the time required for the fluid to convectively mix. We assign an accurate experimental value to the critical fragmentation number F,, which appears to be universal. When the fragmentation occurs, the interfacial area increases via successive splittings which display striking symmetries. We present experimental evidence and a qualitative explanation of such a phenomenon.

2D Dynamics of a Drop Falling in a Miscible Fluid

“…The fact that the elapsed time until the break-up is almost the same as the typical time of internal circulation supports this interpretation; and a quantitative evidence has been presented. We also highlight that the results presented here agree qualitatively with similar studies in 3D [2,3], but give a more precise idea of the time scales that rule the processes, and reinforce the conjecture that the inertia forces are important in the fragmentation mechanism [4].…”

“…This torus in turn is unstable and undergoes a fragmentation in several drops, and these daughter drops follow the same process again. The process is the same if the densities of the fluids are reversed, the drop then moving upward.Recent research [2,3] has thrown light on the phenomenon. The break-up process is explained in terms of competition between diffusion and viscous transfer of momentum along the radius.…”

“…Recent research [2,3] has thrown light on the phenomenon. The break-up process is explained in terms of competition between diffusion and viscous transfer of momentum along the radius.…”

Fragment Formation in the Break-up of a Drop Falling in a Miscible Liquid

“…In the case of miscible liquids considered here, each of these fragments may undergo a similar break-up process, splitting again into secondary fragments. However, the number of successive vertical break-ups remains limited to three.A detailed description of these phenomena including a preliminary explanation was recently presented [4]. Reference [4] is focused on the transition between no splitting and the break-up of the torus into two fragments.…”

“…The p values have been read or interpolated from tables [8]. The D values for each pair of fluid compositions have been measured by a technique described elsewhere [9].…”