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Instability regimes in flowing suspensions of swimming micro-organisms
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10.1063/1.3529411
/content/aip/journal/pof2/23/1/10.1063/1.3529411
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/1/10.1063/1.3529411

Figures

Image of FIG. 1.
FIG. 1.

Problem geometry and coordinate system.

Image of FIG. 2.
FIG. 2.

Effect of shear rate on the (a) real part, and (b) imaginary part of the complex growth rate , for a rotational diffusion coefficient of . : solid line ——, : dashed line ----, : dash-dotted line , and : dash-dot-dotted line .

Image of FIG. 3.
FIG. 3.

Base-state orientation distribution , obtained by solution of Eq. (19), for and two different shear rates: (a) and (b) .

Image of FIG. 4.
FIG. 4.

Effect of rotational diffusion coefficient on the growth rate, or real part of , for (a) and (b) . : solid line ——, : dashed line - - - - .

Image of FIG. 5.
FIG. 5.

Schematic illustrating the deformation of the computational domain with the mean imposed shear flow, after Rogallo (Ref. 57).

Image of FIG. 6.
FIG. 6.

Concentration field isosurfaces for different shear rates: (a) at , (b) at , (c) at , and (d) at (enhanced online). [URL: http://dx.doi.org/10.1063/1.3529411.1]10.1063/1.3529411.1

Image of FIG. 7.
FIG. 7.

Sample disturbance velocity fields in the plane for different shear rates: (a) (no imposed shear flow), (b) , (c) , and (d) .

Image of FIG. 8.
FIG. 8.

Kinetic energy spectrum for different shear rates: from top to bottom, , , , and .

Image of FIG. 9.
FIG. 9.

Vortical structures, identified by isosurfaces of the second invariant of the velocity gradient tensor [Eq. (36)], for different imposed shear rates: (a) at , (b) at , and (c) at (enhanced online). [URL: http://dx.doi.org/10.1063/1.3529411.2]10.1063/1.3529411.2

Image of FIG. 10.
FIG. 10.

plots for different shear rates: (a) (no shear flow) and (b) . In both plots, the black curves correspond to , i.e., uniaxial extensional (left) and compressional (right) flows.

Image of FIG. 11.
FIG. 11.

JPDF of the concentration gradient vector for different shear rates: (a) (no imposed flow), (b) , and (c) .

Image of FIG. 12.
FIG. 12.

JPDF of the vorticity field for different shear rates: (a) (no imposed flow), (b) , and (c) .

Image of FIG. 13.
FIG. 13.

JPDF of the mean director field for different shear rates: (a) (no imposed flow), (b) , and (c) .

Image of FIG. 14.
FIG. 14.

Probability distribution functions of , where denotes the angle between the concentration gradient and the various eigenvectors of the local rate-of-strain tensor, for different shear rates: (a) (no imposed flow) and (b) .

Image of FIG. 15.
FIG. 15.

Probability distribution functions of , where denotes the angle between the vorticity vector and the various eigenvectors of the local rate-of-strain tensor, for different shear rates: (a) (no imposed flow) and (b) .

Image of FIG. 16.
FIG. 16.

Probability distribution functions of , where denotes the angle between the mean director field and the various eigenvectors of the local rate-of-strain tensor, for different shear rates: (a) (no imposed flow) and (b) .

Image of FIG. 17.
FIG. 17.

Time-averaged autocorrelation function of the concentration field in the shear plane ( plane) for different shear rates: (a) (no shear flow), (b) , and (c) .

Image of FIG. 18.
FIG. 18.

Time-averaged autocorrelation function of the disturbance velocity field in the shear plane ( plane) for different shear rates: (a) (no shear flow) and (b) .

Image of FIG. 19.
FIG. 19.

Time-averaged autocorrelation function of the particle director field in the shear plane ( plane) for different shear rates: (a) (no shear flow) and (b) .

Image of FIG. 20.
FIG. 20.

Active power input [Eq. (41)] generated by the swimming particles as a function of time for different shear rates. Solid line ——: , long-dashed line – – –: , dash-dotted line : , dash-dot-dotted line : , and dashed line - - - -: .

Image of FIG. 21.
FIG. 21.

Spatially averaged contraction of the disturbance velocity and director fields [Eq. (42)] as a function of time for different shear rates. Solid line ——: , long-dashed line – – –: , dash-dotted line : , dash-dot-dotted line : , and dashed line - - - -: .

Image of FIG. 22.
FIG. 22.

Time evolution of the eigenvalues , , and of the disturbance rate-of-strain tensor for different imposed shear rates. Solid lines ——: , long-dashed lines – – –: , dash-dotted lines : , dash-dot-dotted lines : , and dashed lines - - - -: .

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2011-01-06
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Instability regimes in flowing suspensions of swimming micro-organisms
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/1/10.1063/1.3529411
10.1063/1.3529411
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