Biomedical Engineering Reference
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small molecules like sodium chloride is very nearly the same in TEP and in
seawater (Ploug and Passow 2007).
Previous investigations of solid spheres settling through step-like strati-
fications at comparable Reynolds numbers,
Re
=
O
(1), reported a reduction
in settling speed at the pycnocline associated with an increase in drag. This
excess drag resulted from the buoyancy of a wake of lighter fluid attached
to and dragged downward by the particle (Srdic-Mitrovic et al. 1999). The
magnitude of this “tailing” effect is governed by the relative importance of
inertial and buoyancy forces, measured by the Froude number
Fr
=
U/
(
aN
).
A related effect has been observed for solid particles settling in linear strati-
fications, where a shell of lighter fluid is entrained by the particle, exerting a
buoyancy force on the particle that retards its descent (Yick et al. 2007).
To study the effect of porosity on the settling process at a pycnocline,
Kindler et al. (2010) recently conducted experiments with hydrogel spheres
settling through a thin density interface with
N
=7
.
2s
−
1
, using salt as the
stratifying agent (Figure 10.16). The Reynolds number
Re
0
, based on the ter-
minal velocity in the upper (lighter) phase
U
0
,was
O
(0
.
1
1). The porosity of
the spheres was
φ
=0
.
955 and the permeability
k
=10
−
15
m
−
2
, in general agree-
ment with those of marine snow. The settling of porous, impermeable spheres
through a pycnocline is based on two processes: the entrainment of lighter
fluid from above, and the relaxation of the interstitial fluid (Figure 10.16).
Depending on the initial particle excess density with respect to the lower
(denser) layer, ∆
ρ
p
=
ρ
1
−
−
ρ
p
0
, two limiting scenarios were identified. First,
(a)
(b)
r
p
0
r
0
r
0
a
r
const
=
U
z
r
p
U
r
1
r
1
r
FIGURE 10.16
(a) Schematics of the density stratification. (b) Schematic illustration of the
behavior of porous particles settling through a density interface, depending on
the initial particle excess density
ρ
p
0
with respect to the lower phase density
ρ
1
. (From Kindler et al. (2010)).
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