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The stability of a homogeneous suspension of chemotactic bacteria
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10.1063/1.3580271
/content/aip/journal/pof2/23/4/10.1063/1.3580271
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/4/10.1063/1.3580271
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The physical mechanism of mutual reinforcement of the fluid velocity and bacterial orientation perturbation fields in the absence of a chemical gradient. The solid arrows indicate the local extensional component of the imposed velocity perturbation, while the dashed arrows indicate the disturbance velocity produced by the bacterium force dipole, which reinforces the imposed flow. As the Fourier (velocity) mode grows in amplitude, the orientation distribution in the vicinity of the nodes of the velocity wave becomes increasingly peaked along the local extensional axis; this anisotropy, in turn, reinforces the velocity perturbation.

Image of FIG. 2.
FIG. 2.

The variation of (a measure of the critical bacterial concentration) as a function of for . The dashed line corresponds to Eq. (26) and the dotted line corresponds to Eq. (27).

Image of FIG. 3.
FIG. 3.

The variation of (a measure of the critical bacterial concentration) as a function of . The solid line denotes Eq. (28) corresponding to an attractant-aligned wavevector, while the dotted-dashed line denotes Eq. (31), the nominal stability criterion.

Image of FIG. 4.
FIG. 4.

Schematic representations of the modal structure for a suspension of random tumblers for differing values of . Note that the hatched region, which denotes the neutral continuous spectrum modes for straight swimmers, is absent for finite .

Image of FIG. 5.
FIG. 5.

The real and imaginary parts of the scaled growth rate, , as a function of for a suspension of straight swimmers. The filled and hollow symbols denote the mode 1 and mode 2 branches, respectively.

Image of FIG. 6.
FIG. 6.

The real and imaginary parts of the growth rate, , as a function of for a suspension of random tumblers in the absence of a chemoattractant. The filled and hollow symbols denote the mode 1 and mode 2 branches, respectively; here, .

Image of FIG. 7.
FIG. 7.

The real and imaginary parts of the growth rate, , as a function of for chemotactic bacteria with and ; the symbols are the same as in Fig. 5. The analytical prediction for , in the limit of small , given by Eq. (73), is plotted as a dashed line.

Image of FIG. 8.
FIG. 8.

The real and imaginary parts of as a function of for chemotactic bacteria with and ; the symbols are the same as in Fig. 5. The analytical prediction for , in the limit of small , is plotted as a dashed line.

Image of FIG. 9.
FIG. 9.

The function , denoting the inverse of the highest (scaled) growth rate, as a function of ; here, . The highest growth rate corresponds to a stationary mode in the interval and to a propagating mode for .

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/content/aip/journal/pof2/23/4/10.1063/1.3580271
2011-04-11
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The stability of a homogeneous suspension of chemotactic bacteria
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/4/10.1063/1.3580271
10.1063/1.3580271
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