Environmental Engineering Reference
In-Depth Information
50
40
30
20
0
0.5
1
Fig. 4.5
(
Left
) Bifurcation
ʱ
A
(
X
0
)
(
dashed line
) between settled and ridged regimes for fixed
ˆ
0
=
.
ʱ
and
X
0
. The symbols indicate experimental results identified as ridged
(
star
) or settled (
circle
). The
triangles
mark results for which the particles did not equilibrate in the
duration of the experiment. (
Right
) Photographs of the experiment in the settled and ridged regimes
are shown on the
right
for experimental parameters, (i)
0
4 with varying
20
ⓦ
,
X
0
50
ⓦ
,
ʱ
=
=
0
.
5 and (ii)
ʱ
=
X
0
=
0
.
5
buoyant particle species of the equal diameter,
d
, and variant densities, such that
ˁ
2
>ˁ
1
>ˁ
l
. In the monodisperse case of the same geometry, heavy particles in the
viscous fluidwere shown to either settle rapidly to the channel walls ('settled' regime)
or collect on the free surface ('ridged'), depending on the channel inclination angle
and the total volume fraction. This bifurcation behaviour was explained by [
2
,
15
,
16
]
by balancing particle fluxes due to sedimentation and drift diffusion. The analogous
bifurcation behaviour was observed in bidensity suspensions experimentally by [
10
]
and is explained by our current equilibrium model.
Notably, additional complexities arise due to the presence of a second particle
species. For instance, the ridged regime in the bidensity suspensions now consists
of three sub-regimes (
R
A
,
R
B
, and
R
C
) that display different profiles of
ˆ
2
,
depending on the relative particle volume fraction,
X
0
. It would be interesting to
explore the sub-regimes in future experiments, which would require new experi-
mental techniques to measure the volume concentration of different particle species
through the layer. In addition, the mixing behaviour between particle species is inves-
tigated by incorporating tracer diffusion in our model. This mixing effect is shown
to depend on the inclination angle, such that lower angles lead to less mixing. This
behaviour has been observed experimentally in [
10
] where they found the biden-
sity mixture to stratify into separate layers forming three distinct fronts at smaller
inclination angles. Therefore, our equilibrium model and experimental observations
suggest that particle segregation is more pronounced in the 'settled' regime, while
particles remain well-mixed in the 'ridged' regime.
Particle segregation is fundamentally important in oil refinement, waste-water
treatment, and mineral processing via a spiral separator. However, these applications
lack quantitative models that are important for predictive design. Recently, [
8
,
9
]
demonstrated that the equilibrium model for monodisperse slurries on an incline is
valid in spiral geometries to leading order and derived a simple steady state model.
We believe the present model could lead to a valid equilibrium theory for more
ˆ
1
and
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