Spatial Pattern Formation of Motile Microorganisms: From Gravitactic Bioconvection to Protozoan Culture Dynamics - Porous Media: Applications in Biological Systems and Biotechnology - page 547

(a) (b)

400 200

300 150

Pe = 0.4

Pe = 20

0.6
0.8
1

Ra Ra

200 100

15

10

8

100 50

5

1

0.01 0.1

0.2

0
0

0

5 10

Wave number k

15 20 0 2 4

Wave number k

6 8 10

(c) (d)

200

200

150

150

Ra c

Ra c
k c

100

Ra*

100

50

50

Pe = 5

100

3

K c

10 2

50

20

0
0

0

5 10

Pe

15 20

0 1 2

Wave number k*

3 4

(e) (f )

10 2

15

Ra c

Ra *

10 1

Ra c

10 Ra *

k c k *

k *

10 0

5

10 -1

k c

0 0

0.25 0.5

Pe

0.75 1 5 10

Pe

15 20

FIGURE 14.3
(a) Stability diagram for various Pe. (b) ( Ra c vs. k ) for Pe ≤ 1 . (c) ( Ra* c vs.

k* ) for Pe 1. (d) ( Ra c vs. Pe ) and ( k c vs. Pe ) for various Pe. (e) ( Ra c vs.

Pe ) and ( k c vs. Pe ) for Pe

≥

2 .
(Nguyen-Quang, T., Nguyen, T.H., Guichard, F., Nicolau, A., Smatzari, G.,
LePalec, et al., Zoo. Sci ., 26, 2009, doi:10.2108/zsj.26.54.)

≤ 1 (F) ( Ra* c vs. Pe ) and ( k* c vs. Pe ) for Pe ≥