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Correlations and fluctuations of stress and velocity in suspensions of swimming microorganisms
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10.1063/1.3670420
/content/aip/journal/pof2/23/12/10.1063/1.3670420
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/12/10.1063/1.3670420
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Cs , LL (dark circles (blue online)) and −Cs , NN (light circles (red online)) where r represents the separation of the beads representing the organism bodies (as shown in the inset). The corresponding theoretical predictions using Eq. (47) are shown with the solid line (blue online) and dashed line (red online) in which spatial and orientation correlations are neglected. For comparison, we also show the orientation correlations: Cn , LL (dark squares (blue online)) and −Cn , NN (light squares (red online)).

Image of FIG. 2.
FIG. 2.

(Color online) Cs , LL (dark circles (blue online)) and −Cs , NN (light circles (red online)) where r represents the separation of centers including the body and flagellum (as shown in the inset). The corresponding theoretical prediction using Eq. (47) with q = 0 is shown with the solid line (blue) for the longitudinal correlations. The predicted transverse correlations have the incorrect sign. For comparison, we also show the orientation correlations: Cn , LL (dark squares (blue online)) and −Cn , NN (light squares (red online)).

Image of FIG. 3.
FIG. 3.

(Color online) Cs , LL (dark circles (blue online)) and − Cs , NN (light circles (red online)) where r represents the separation of centers including the body and flagellum. The lines represent Eq. (52) in which q = 0 and C n and C f are both measured in our simulations independently of the swimmer correlations.

Image of FIG. 4.
FIG. 4.

(Color online) Cs , LL (dark circles (blue online)) and −Cs , NN (light circles (red online)) where r represents the separation of the beads representing the organism bodies. The corresponding theoretical predictions using Eq. (52) are shown with the solid lines.

Image of FIG. 5.
FIG. 5.

(Color online) Cs , LL (dark circles (blue online)) and −Cs , NN (light circles (red online)) where r represents the separation of the beads representing the flagella. The corresponding theoretical predictions using Eq. (52) are shown with the solid lines.

Image of FIG. 6.
FIG. 6.

(Color online) Illustration of the key variables in determining how correlations between organisms lead to fluid correlations. The two organisms with orientations n 1 and n 2 are separated by a vector s. The two fluid elements for which the velocity correlation is calculated are separated by a r.

Image of FIG. 7.
FIG. 7.

(Color online) Measured correlation functions A (circles) and C (squares) as a function of s from Eqs. (80) and (81) for pushers (dark (blue online)) and pullers (light (red online)) at ϕe  = 10−2. Because A for pushers and C for pullers are negative over most of the range, − A and −C are plotted for those curves. The dashed line is a power law of s −2 for reference.

Image of FIG. 8.
FIG. 8.

(Color online) Measured correlation function I (triangles) as a function of s from Eq. (82) for pushers (dark (blue online)) and pullers (light (red online)) at ϕe  = 10−2. Because I for pullers is negative over most of the range, −I is plotted. The dashed line is a power law of s −2 for reference.

Image of FIG. 9.
FIG. 9.

Dependence of the mean-squared velocity of fluid elements on system size L for pushers at an effective volume fraction of ϕe  = 10−1.

Image of FIG. 10.
FIG. 10.

(Color online) Comparison of spatial fluid correlations for suspensions of pushers at ϕe  = 10−1 at different system sizes to the theory based on orientational correlations of the organisms. The symbols correspond to the simulations with number of organisms equal to N = 400 (circles), N = 800 (squares), N = 1600 (diamonds), N = 3200 (stars), and N = 6400 (×). The corresponding theory from Eq. (90) is shown by the lines.

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/content/aip/journal/pof2/23/12/10.1063/1.3670420
2011-12-27
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Correlations and fluctuations of stress and velocity in suspensions of swimming microorganisms
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/12/10.1063/1.3670420
10.1063/1.3670420
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