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Instabilities and nonlinear dynamics of concentrated active suspensions
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10.1063/1.4812822
/content/aip/journal/pof2/25/7/10.1063/1.4812822
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/7/10.1063/1.4812822

Figures

Image of FIG. 1.
FIG. 1.

(a) Solutions of the equation (δ) = 0, where is defined in Eq. (31) , as functions of ξ = 2 ν/. Full lines show the branches that, at a given value of ξ, minimize the steric interaction energy. (b) Steric interaction energy (ξ) along each of the three branches found in (a). (c) Orientation distributions for ξ = 20 corresponding to the three solution branches.

Image of FIG. 2.
FIG. 2.

Marginal stability curve in the long-wave limit ( → 0) in terms of effective volume fraction ν and dimensionless dipole strength αν/30, for various values of 2 / [see Eq. (68) ]. In this plot, β = 1.75, corresponding to a particle aspect ratio of ≈ 10.

Image of FIG. 3.
FIG. 3.

Numerical solutions of the dispersion relations Eqs. (60) and (61) for the complex growth rates λ, λ, and λ of azimuthal modes = 0, 1, 2 as functions of the wavenumber . (a)–(c) show the real parts, while (d)–(f) show the imaginary parts. In (b) and (e), we set β = 0 to isolate the leading-order effect of the steric torque, and α/4 = −0.2 (pushers).

Image of FIG. 4.
FIG. 4.

Unstable range of wavenumbers as a function of ξ = 2 ν/ for azimuthal modes = 0 (a), 1 (b), and 2 (c). For mode 1, we set β = 0 to isolate the leading-order effect of the steric torque.

Image of FIG. 5.
FIG. 5.

Dependence of the maximum reduced growth rate Re(λ) governing the stability of the nematic base states on the dimensionless active stress magnitude α, for ξ = 20: (a) branch 2 and (b) branch 3. Results for two different wave orientations Θ are shown. Insets show close-ups on the region near the origin.

Image of FIG. 6.
FIG. 6.

Dependence of the maximum reduced growth rate Re(λ) on the parameter ξ, along both nematic branches, for two different wave directions Θ: (a) branch 2, Θ = 0; (b) branch 2, Θ = π/2; (c) branch 3, Θ = 0; and (d) branch 3, Θ = π/2.

Image of FIG. 7.
FIG. 7.

Dependence of the maximum reduced growth rate Re(λ) on: (a) wave direction Θ (in the limit of → 0), and (b) wavenumber (for a wave with orientation Θ = 0). Both plots were obtained on branch 2, with ξ = 20.

Image of FIG. 8.
FIG. 8.

Stability diagrams for: (a) movers (α = 0), (b) pushers (α < 0), and (c) pullers (α > 0). A branch is labeled unstable if there exists a positive growth rate Re(λ) > 0. In the case of movers, branch 2 is only weakly unstable, as the growth rates on that branch are very low (two orders of magnitude lower than on other unstable branches).

Image of FIG. 9.
FIG. 9.

Simulation results for pushers and pullers. Panels (a)–(d) show the concentration fields (, ) at an arbitrary time after the initial transient for the following cases: (a) pushers at ν = 0.05, (b) pushers at ν = 0.07, (c) pushers at ν = 0.2, and (d) pullers at ν = 0.2. Panels (e)–(h) show the corresponding nematic parameter fields (, ) defined in Eq. (70) , for the same cases. Panels (i)–(l) show the nematic orientation fields in a two-dimensional slice, obtained by taking the eigenvector of with largest eigenvalue (enhanced online). [URL: http://dx.doi.org/10.1063/1.4812822.1]doi: 10.1063/1.4812822.1.

Image of FIG. 10.
FIG. 10.

Spatially averaged nematic parameter ⟨(, )⟩, defined in Eq. (70) , as a function of time in suspensions of pushers (α = −1), pullers (α = +1), as well as shakers ( = 0, α = ±1) at various volume fractions.

Image of FIG. 11.
FIG. 11.

Time evolution of the spatial averages of (a) |(, )|, (b) |(, )|, and (c) |(, ) + (, )|, in suspensions of pushers at ν = 0.05, 0.07, and 0.2, and pullers at ν = 0.2.

Image of FIG. 12.
FIG. 12.

Time evolution of the correlation defined in Eqs. (72)–(74) : (a) (), (b) (), and (c) (), in suspensions of pushers at ν = 0.05, 0.07, and 0.2, and pullers at ν = 0.2.

Image of FIG. 13.
FIG. 13.

Mean active power () defined in Eq. (75) as a function of time, in suspensions of pushers at ν = 0.05, 0.07, and 0.2, and pullers at ν = 0.2. The plot also shows results for shakers ( = 0, α = ±1) at ν = 0.2.

Image of FIG. 14.
FIG. 14.

Simulation results for shakers ( = 0) at an effective volume fraction of ν = 0.2 (ξ = 26.92). Panels (a)–(c) are for pushers (α = −1) and (d)–(f) for pullers (α = +1). (a) and (d) show the nematic parameter (, ) defined in Eq. (70) ; (b) and (c) show the nematic orientation fields in a two-dimensional slice, obtained by taking the eigenvector of with largest eigenvalue; and (c) and (f) show the hydrodynamic velocity fields in a two-dimensional slice.

Image of FIG. 15.
FIG. 15.

Standard deviation of the concentration field (, ) as a function of time, in suspensions of pushers (α = −1), pullers (α = +1), and shakers ( = 0) of both types, at ν = 0.2.

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/content/aip/journal/pof2/25/7/10.1063/1.4812822
2013-07-18
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Instabilities and nonlinear dynamics of concentrated active suspensions
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/7/10.1063/1.4812822
10.1063/1.4812822
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