Deformation and Breakup of a Droplet Falling into a Viscous Fluid

Abstract

When a droplet with a higher density falls in a miscible solution with lower density, the droplet deforms and breaks up spontaneously. Instability of a vortex ring, formed by droplet deformation in the falling process, causes the breakup. An origin of the instability, however, is not understood yet. We investigated a relationship between a wavelength of the instability and a thickness of the ring when the instability occurred. The relationship almost agrees with an evaluation of Rayleigh-Taylor (RT) instability. Thus, it is considered that RT instability plays an important role for the instability of the ring. Next, we investigated the number of the breakup. The number depends on a non-dimensional parameter which is a ratio between a driving force by gravity due to a density difference between two solutions and a viscosity dissipation. This means that a balance between the driving force and the viscosity dissipation determines the number.