APS DFD 2011 video submission V045

TL;DR

This study investigates inhomogeneous fluid mixing in a tilted-rotating cylindrical tank, revealing how rotation, inclination, and volume influence droplet breakup, vortex behavior, and mixing efficiency at low Reynolds numbers.

Contribution

It provides new insights into the effects of tank tilt and volume on vortex-induced mixing and droplet breakup in inhomogeneous fluids at low Reynolds numbers.

Findings

Vortex transport accelerates mixing below critical volume.

Shallower angles enhance mixing speed and volume capacity.

Droplet breakup and vortex behavior depend on fluid volume relative to Vcrit.

Abstract

Inhomogeneous uid mixing in a tilted-rotating cylindrical tank (radius a = 3:5 cm) is shown at Re(17-40) and low capillary numbers. A water and surfactant solu- tion (1% by mass sodium oleate) is dispersed in soybean oil (95% by volume), through varying the rotation rate, and angle of inclination, the rate of mixing is observed. A planar laser is directed down the tank axis to highlight a cross-sectional area of the fluid volume and as the water droplets begin to break up to sizes on the order of the beam width and less, more light is refracted and the mixture is illuminated. Initially, the water breaks up into large droplets that exhibit approximate solid-body rotation about the bottom of the tank. When the total combined volume is below the critical volume of the tank Vcrit = a^3 tan vortex transport of the water occurs more rapidly, breaking up the water into continually smaller droplets in a process that resembles periodic shearing. When the fluid volume is above critical the water will break up and rotate about the bottom of the tank and vortex-induced mixing is much more reticent, if occurring at all. It is noted that shallower angles with respect to the horizontal produce faster mixing while allowing a greater volume of fluid to be mixed at the sub-critical volume given a constant tank size.