92
S. Lee et al.
Fig. 4.1 (top left) Schematic of the experimental apparatus; (bottom left) The thin film of fluid
of ρ l and μ l that contains two particle species of equal diameter d and variant densities, such that
ρ 2 > ρ 1 > ρ l . Two sets of experimental results are shown on the right. In the bottom right panel,
as time evolves (images from left to right), clear fingers form on the flow front, indicating that both
particle species have settled to the channel walls with a clear fluid layer on top that moves ahead.
On the other hand, the particles appear to remain aggregated and well-mixed on the front in the
‘ridged’ regime, as shown in the top right panel
0
0.5
1
0
0.2
0.4
0.6
0
0.5
1
0
0.2
0.4
0.6
Fig. 4.2 Transition from settled to ridged solutions in φ for the monodisperse system, for X = 1
(left) and X = 0 (right). The critical concentrations are φ c,1 = 0.459 and φ c,2 = 0.521
Settled (0 < φ 0 < φ A ): In the settled regime, the heavy particles settle to the
substrate, with a layer of the lighter particles above, and then a clear fluid layer up to
the free surface. The upper bound for the settled region, φ A decreases from φ c,2 to
φ c,1 as X 0 increases from 0 to 1. If φ 0 < φ c,1 , then the ODE system guarantees that
φ is monotonically decreasing regardless of X 0 .
S. Lee et al.
Fig. 4.1 (top left) Schematic of the experimental apparatus; (bottom left) The thin film of fluid
of ρ l and μ l that contains two particle species of equal diameter d and variant densities, such that
ρ 2 > ρ 1 > ρ l . Two sets of experimental results are shown on the right. In the bottom right panel,
as time evolves (images from left to right), clear fingers form on the flow front, indicating that both
particle species have settled to the channel walls with a clear fluid layer on top that moves ahead.
On the other hand, the particles appear to remain aggregated and well-mixed on the front in the
‘ridged’ regime, as shown in the top right panel
0
0.5
1
0
0.2
0.4
0.6
0
0.5
1
0
0.2
0.4
0.6
Fig. 4.2 Transition from settled to ridged solutions in φ for the monodisperse system, for X = 1
(left) and X = 0 (right). The critical concentrations are φ c,1 = 0.459 and φ c,2 = 0.521
Settled (0 < φ 0 < φ A ): In the settled regime, the heavy particles settle to the
substrate, with a layer of the lighter particles above, and then a clear fluid layer up to
the free surface. The upper bound for the settled region, φ A decreases from φ c,2 to
φ c,1 as X 0 increases from 0 to 1. If φ 0 < φ c,1 , then the ODE system guarantees that
φ is monotonically decreasing regardless of X 0 .