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The stability of a homogeneous suspension of chemotactic bacteria
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10.1063/1.3580271
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Affiliations:
1 Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
2 School of Chemical and Bio-molecular Engineering, Cornell University, Ithaca, New York 14853, USA
Phys. Fluids 23, 041901 (2011)
/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

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.

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).

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.

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 .

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.

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, .

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.

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.

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 .

/content/aip/journal/pof2/23/4/10.1063/1.3580271
2011-04-11
2014-04-24

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