2D Dynamics of a Drop Falling in a Miscible Fluid

Abstract

Abstract. -The dynamics of the fragmentation of a liquid drop falling in a miscible fluid is studied in a Hele-Shaw geometry. We show that this configuration allows quantitative measurements of the characteristic sedimentation velocity and internal velocity of the drop. The break-up process observed in 3D is also found in this quasi-2D configuration. The relation between the internal circulation pattern and this process is also discussed.Fluid instabilities occur in many natural phenomena (flows in porous media, dynamics of earth mantle, atmospheric currents) as well as industrial processes (stirring tanks, mixing processes). In the last few years considerable attention has been devoted to basic hydrodynamical instabilities (convective, centrifugal, gravitational) that could offer insight on the basic instability mechanisms under quite well-regulated conditions.Instabilities can be found even at small Reynolds number and for open flows. One of the simplest instabilities of this kind is the fragmentation of a drop falling in a miscible fluid. This instability was fist described by von Helmholtz and inspired Lord Kelvin his works on vorticity. A detailed phenomenological description can be found in ref. [l]. These authors reported the fragmentation process in a wide variety of miscible liquids and also discussed the case of immiscible liquids. The process could be summaxized as follows. A drop is deposited on the free surface of a lighter liquid. After a short period, it begins to fall, leaving a tail at the rear. After some time the drop breaks up forming a torus that expands radially. 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. If the second one is faster than the first, the drop breaks up. But diffusion efficiency grows as the area increases and the transfer rate of velocity is inversely proportional to the radius, so the fragmentations eventually stop and dfision becomes dominant. Moreover Baumann et al.(*) Also at CITEFA/CONICET

The self-similar rise of a buoyant thermal in very viscous flow

“…There is a loose link here with work on the rise of a compositionally buoyant viscous drop for which diffusion is negligible (e.g. Kojima, Hinch & Acrivos 1984;Koh & Leal 1989;Pozrikidis 1990;Garcimartin, Mancini & Perezgarcia 1992). In the absence of surface tension, such a drop is found to be unstable, with a thin filamentlike tail left behind the rear of an initially almost spherical head.…”

Formation of Polymeric Toroidal-Spiral Particles

“…During the subsequent sedimentation, viscous forces overwhelm any small miscible interfacial tension existing between the polymer and the bulk solutions to roll up the interface into an intricate T-S shape that automatically entrains the surrounding liquid. Although sedimentation of drops in the same solutions has been previously studied for understanding rainfall and mixing and the vortex-ring structure has been observed, − the present study goes beyond the previous literature on this phenomenon in its detailed geometric characterization and control of the channels and their dependence on viscosity ratio and other flow parameters (to be described below). In the study of drop sedimentation in immiscible solutions, , the effects of viscosity ratio and rheological properties of the polymer have been considered, but the doughnut/ring shape only forms with high injection velocity, drop interactions, or a viscoelastic instability, and does notin any casecontain any internal channels.…”