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Pair-particle dynamics and microstructure in sheared colloidal suspensions: Simulation and Smoluchowski theory
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10.1063/1.4812799
/content/aip/journal/pof2/25/7/10.1063/1.4812799
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/7/10.1063/1.4812799
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Angle definitions defined in a simple-shear flow (): 0 ⩽ θ ⩽ 2π is the azimuthal angle measured clockwise from the positive axis, and −π/2 ⩽ φ ⩽ π/2 is the polar angle measured from plane.

Image of FIG. 2.
FIG. 2.

Dispersion of pair trajectories for different starting points in shear plane obtained by sampling the configuration from ASD simulation for ϕ = 0.40 and = 10. The thick lines are the average trajectories and the average motion is from left to right along these trajectories.

Image of FIG. 3.
FIG. 3.

Pair distribution function in shear plane for ϕ = 0.40 and = 50 conditions. (a) Previous theory, (b) current theory, (c) simulation results. The color bars are identical for all the figures and are only presented for simulation results. Values of pair distribution function are truncated to ⩽ 10 to enhance visualization. Figures 3(a) and 3(b) were reprinted with permission from Nazockdast and Morris, “Microstructural theory and the rheology of concentrated colloidal suspensions,” J. Fluid Mech.713, 420–452 (Year: 2012)10.1017/jfm.2012.467. .

Image of FIG. 4.
FIG. 4.

Comparison of angular variations of pair distribution in shear plane at contact, ( = 2; θ, 0), for ϕ = 0.40 and = 50 suspension from theory and simulation.

Image of FIG. 5.
FIG. 5.

Angular variations of pair distribution function for ϕ = 0.40 in shear plane (a) = 0.1, 1, (b) = 10, (c) = 100.

Image of FIG. 6.
FIG. 6.

Angular variations of pair distribution function in shear plane (a) ϕ = 0.20 and = 100, (b) ϕ = 0.30 and = 100, (c) ϕ = 0.45 and = 25.

Image of FIG. 7.
FIG. 7.

Brownian () and hydrodynamic () contributions and total value () of (a) normalized shear viscosity, , (b) first normal stress difference, , and (c) second normal stress differences, , of a ϕ = 0.40 suspension as a function of . The results of previous theory are shown by symbol “-*-” for comparison. The dotted lines are the results of the perturbation solution at ⩽ 0.20. The solid straight lines near the axis are the predictions at = ∞. The Brownian contributions to normal stress differences are presented in inset figures.

Image of FIG. 8.
FIG. 8.

Theory predictions and simulation results for nonlinear rheology of sheared suspensions at at different volume fractions. The error bars are approximately the same value for first and second normal stress difference and are only presented for at selected ϕ.

Image of FIG. 9.
FIG. 9.

Average pair trajectories in shear plane of a ϕ = 0.20 suspension at = 100: (a) predictions, (b) simulation results. (c) Pair trajectories of an isolated pair in simple shear flow.

Image of FIG. 10.
FIG. 10.

The predictions and simulated results of average pair trajectories alongside () for the same conditions in shear plane: (a) the predicted pair trajectory for ϕ = 0.40, and = 50, (b) the predicted () at ϕ = 0.40 and = 50, (c) the pair trajectory obtained from simulation results for relative velocity at ϕ = 0.50 and = 100, (d) the computed values of () from sampling the simulation results at ϕ = 0.50 and = 100.

Image of FIG. 11.
FIG. 11.

The mean disturbance of the relative hydrodynamic velocity from the bulk relative velocity, ⟨ , in the shear plane at ≫ 1. (a) Predictions of radial relative velocity, , at ϕ = 0.40 and = 50, (b) simulation results for radial relative velocity at ϕ = 0.40 and = 1000, (c) predictions of angular relative velocity, , at ϕ = 0.40 and = 50, (d) simulation results for angular relative velocity at ϕ = 0.40 and = 1000. The color bars for theory and simulation results are identical and they are shown next to the theoretical results.

Image of FIG. 12.
FIG. 12.

Average relative radial velocity fluctuations, , in the shear plane from simulation: (a) ϕ = 0.20, (b) ϕ = 0.40, (c) ϕ = 0.50, (d) variations of radial velocity fluctuations with separation distance, , in shear plane along compressional axis, θ = 3π/4 for ϕ = 0.20, 0.40 and ϕ = 0.50, all at = 1000.

Image of FIG. 13.
FIG. 13.

Average angular velocity fluctuations, in the shear plane from simulation: (a) ϕ = 0.20, (b) ϕ = 0.40, and (c) ϕ = 0.50, all at = 1000.

Image of FIG. 14.
FIG. 14.

Dispersion of trajectories starting from = 3.5, θ = 5π/6 and φ = 0 for a ϕ = 0.40 suspension from samplings of simulation configurations projected to shear plane: (a) = 1, (b) = 10, (c) = 100, (d) = 1000. The solid line represents the mean trajectory and motion is from left to right along this trajectory.

Image of FIG. 15.
FIG. 15.

Spatial variations of radial dispersion of pair trajectories with time, ⟨ (). Figures (a)– (d) are variations at different strains related to = 1 and ϕ = 0.40: (a) , (b) , (c) = 0.4, and (d) . Figures (e)– (h) show the spatial variations for = 10 and 100 at ϕ = 0.40: (e) , (f) , (g) , and (h) .

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/content/aip/journal/pof2/25/7/10.1063/1.4812799
2013-07-18
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Pair-particle dynamics and microstructure in sheared colloidal suspensions: Simulation and Smoluchowski theory
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/7/10.1063/1.4812799
10.1063/1.4812799
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