  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.
