Slurry Flow

When particles are suspended in a highly viscous oil and allowed to flow down an incline, there are two qualitatively distinct regimes: at low particle concentration / inclination angle, the fluid and particles separate; at high particle concentration / inclination angle, the particles stay mixed in the fluid and become more concentrated at the leading front. In some experiments we ran, we noticed the particles and fluid stayed well mixed and didn't bifurcate over the length of the incline. It seemed odd...

We have used a Suspension Balance Model, a model for shear-induced migration (how shear can overcome gravity), and studied the system on a 'fast timescale'. Our model allowed us to explain why the bifurcation didn't take place: in our experimental regime, we were very close to a 'critical particle concentration', where the lengthscale for the bifurcation becomes very large. Given some fitting parameters, we could also qualitatively match other experimental data of similar systems.

physical mechanisms and results of shear induced migration
Given a well-mixed slurry, initially particles are either driven to the top or begin to settle out: this comes from a battle between gravity and shear induced migration, the latter driving particles from regions of higher (closer to substrate) to lower (at the free surface) shear rate. Depending on the "winner", we either observe a settled regime or a ridged regime. The well-mixed regime is only transient.
prediction/fit for how far a slurry must travel before the well-mixed regime ends
One of our models qualitatively matches the inclination angles and particle concentrations where a well-mixed state is observed over the length of our experimental track, without turning to the settled or ridged regimes.

We are currently investigating more exotic systems with multiple species present. Already some unexpected phenomena can emerge. We are working on develping a general theory of these more complicated systems.