(259g) Simulations of Mobilization of Bingham Layers in Agitated Tanks

Derksen, J., University of Alberta

Simulations of mobilization of Bingham layers in agitated

Numerical simulations were used to study mobilization of a
bottom layer of Bingham liquid by agitating a Newtonian liquid above the
Bingham layer. The agitation is done by a pitched-blade impeller at a Reynolds
number of 6000. The Bingham liquid and the Newtonian liquid are miscible. The
parameter space of the simulations has a Bingham number Bn (defined as the
ratio of yield stress over inertial stress) and a Richardson number Ri as
dimensionless variables. The Richardson number quantifies the role of the
density difference between the two liquids. The simulation procedure is based
on the lattice-Boltzmann method for the flow dynamics, and a finite volume
scheme to solve the local and time dependent composition of the liquid mixture.
The moderate Reynolds number allows us to directly simulate the flow, without
the use of turbulence closure or subgrid-scale models.

The simulations show how the bottom layer gets eroded by the
turbulent flow above it (see the figure), and show that there exists a critical
value of the Bingham number beyond which the turbulent flow is not able to
remove the Bingham layer (compare the left and right panel of the figure). The
Richardson number is less important for the mobilization process, but has impact
on the time it takes for homogenization of the liquids after mobilization has occurred.

Figure: cross section through the mixing tank 100 impeller
revolutions after start-up; left Bn=0.8, right Bn=0.1; blue indicates the
Bingham liquid.