Biomedical Engineering Reference
In-Depth Information
(a)
(b)
40
20
Pe
= 0.1,1
20
30
15
15
k
M
σ
M
20
10
10
5
2
Pe
= 0.1,1
10
5
2
20
5
10
15
0
0
0
0
50
100
150
200
Ra
250
100
200
Ra
(c)
(d)
80
9
8
7
6
5
4
3
2
1
0
0 0 0 0 0 0
Ra*
2
60
σ
∗
M
σ
M
40
20
Pe
= 5, 10, 15, 20
Pe
= 0.1,1
2
0
0
50
100
150
Ra
FIGURE 14.5
(a)
σ
M
versus
Ra
for various
Pe =
0.1-20. (b)
k
M
versus
Ra
for various
Pe
= 0.1-20. (c)
σ
M
versus
Ra
for
Pe =
0.1-2. (d)
σ
M
∗
versus
Ra*
for
Pe
= 2-20.
Figure 14.7 illustrates the temporal evolution of
ψ
and
N
when
Pe
=5
and
Ra
= 52, that is, just above the threshold value
Ra
cr
= 51. Contrary
to thermoconvection, the iso-concentrations and streamlines in this case are
strongly deformed (illustrated in Figure 14.6[d]). This indicates that we are
dealing with a subcritical phenomenon in gravitactic bioconvection.
Bifurcation curves in Figure 14.8 for a range of swimming speed
Pe
from
0.1 to 10 illustrate the occurrence of this subcritical regime from the diffusion
state, showing its dependence on the microorganism mobility. It can be seen
that the higher swimming speed the stronger the subcriticity.
14.2.3.2.2
Supercritical State
In a cavity with an aspect ratio equal to half the critical wavelenghth
F
=
L
cr
,
the bioconvection flow is unicellular, independent of the swimming speed and
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