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Mesoscale hydrodynamic modeling of a colloid in shear-thinning viscoelastic fluids under shear flow
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10.1063/1.3646307
/content/aip/journal/jcp/135/13/10.1063/1.3646307
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/13/10.1063/1.3646307
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Velocity (■) and density (▲) profiles in simple shear flow as a function of position y in the gradient direction. The shear rate is , the density of MPC particles is ρ = 10, and the collision time is h = 0.02. The spring constant of the FENE dumbbell is k = 0.2, and the FENE parameter is b = 8.

Image of FIG. 2.
FIG. 2.

Density distribution of dumbbell monomers relative to the dumbbell's center of mass (arb. units) for the indicated reduced shear rates . The other parameters are the same as in Fig. 1. The maximum extension is . The integrated probability is the same in all three plots.

Image of FIG. 3.
FIG. 3.

Extension R/R 0 (•) and inclination tan (2θ) (▼) as a function of the reduced shear rate Γ. The other parameters are the same as those in Fig. 1. The numbers indicate the exponents of power-law regimes.

Image of FIG. 4.
FIG. 4.

Probability distribution of the dumbbell extension for various shear rates Γ = 0 (▲), 0.92 (+), 1.84 (▼), 4.6 (•), and 9.2 (✦). The solid line is obtained from the Boltzmann factor with the FENE potential. The other parameters are the same as in Fig. 1.

Image of FIG. 5.
FIG. 5.

Reduced rotation frequency of dumbbells as a function of reduced shear rate Γ. The other parameters are the same as those in Fig. 1. The green and black dashed lines indicate the asymptotic behavior for small and large reduced shear rates, respectively.

Image of FIG. 6.
FIG. 6.

The reduced viscosity η r as a function of the reduced shear rate Γ. The parameters are the same as Fig. 1. The solid line shows a fit to the Carreau-type function (18) with the parameters μ = 0.60, q = 1.38, and Γ0 = 3.24, the dashed line indicates the asymptotic scaling law for high Weissenberg numbers.

Image of FIG. 7.
FIG. 7.

The reduced viscosity η r as a function of the reduced shear rate Γ for dumbbells with (a) same FENE parameter b = 8 but different spring constant k; (b) same spring constant k = 0.2 but different FENE parameters. Dashed lines show fits to the Carreau-type expression (18) with the parameters μ = 0.60, q = 1.38, and Γ0 = 3.24 for b = 8, Γ0 = 4.40 for b = 18, Γ0 = 8.27 for b = 50, and Γ0 = 27.5 for b = 200.

Image of FIG. 8.
FIG. 8.

The reduced coefficient of the first normal stress difference as a function of the reduced shear rate Γ. The other parameters are the same as those in Fig. 1. The solid line is a guide to the eye, the dashed line indicates the asymptotic scaling law.

Image of FIG. 9.
FIG. 9.

The reduced viscosity η r as a function of the reduced shear rate Γ in three dimensions. The parameters are collision time h = 0.02, density ρ = 10, spring constant k = 0.2, and FENE parameter b = 8. The solid line shows a fit to the Carreau-type function (18) with the parameters μ = 0.60, q = 1.38, and Γ0 = 3.61, the dashed line indicates the asymptotic scaling law for high Weissenberg numbers.

Image of FIG. 10.
FIG. 10.

Reduced rotation frequency of a colloid in a Newtonian fluid with indicated collision time h and particle density ρ. The size of the simulation box is L x = 120, L y = 80.

Image of FIG. 11.
FIG. 11.

Snapshot of dumbbell conformations in shear flow near a colloidal particle (blue circle). Only a fraction of 0.6% of dumbbells is shown. The reduced shear rate is Γ = 23.5 (). Note that the dumbbells in the interior of the colloid are not stretched. The parameters are collision time h = 0.01, density ρ = 50, spring constant k = 0.2, and FENE parameter b = 8. The system size is L x = 120, L y = 80.

Image of FIG. 12.
FIG. 12.

Reduced rotation frequency of a colloid in a viscoelastic and Newtonian fluid, respectively. The parameters are the same as in Fig. 11.

Image of FIG. 13.
FIG. 13.

Streamlines in Newtonian fluids with (a) , (b) , and in viscoelastic fluids with (c) Γ = 2.35 (), (d) Γ = 23.5 (). The parameters are the same as in Fig. 11.

Image of FIG. 14.
FIG. 14.

Net velocity fields vv ideal and corresponding streamlines of (a) a Newtonian fluid with shear rate , (b) a viscoelastic fluid with Γ = 2.35 (), and (c) a viscoelastic fluid with Γ = 23.5 (). Parameters are ρ = 50, h = 0.01, and for the viscoelastic case k = 0.2, and b = 8. The blue circle indicates the position and size of the colloid.

Image of FIG. 15.
FIG. 15.

Reduced rotation velocity of FENE dumbbells spatially resolved in the vicinity of a colloid in shear flow for the shear rates (a) Γ = 2.35 () and (b) Γ = 23.5 (). The other parameters are ρ = 50, h = 0.01, k = 0.2, and b = 8.

Image of FIG. 16.
FIG. 16.

Average extension R of FENE dumbbells spatially resolved in the vicinity of a sphere in shear flow for the shear rates (a) Γ = 2.35 () and (b) Γ = 23.5 (). The other parameters are ρ = 50, h = 0.01, k = 0.2, and b = 8.

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/content/aip/journal/jcp/135/13/10.1063/1.3646307
2011-10-06
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Mesoscale hydrodynamic modeling of a colloid in shear-thinning viscoelastic fluids under shear flow
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/13/10.1063/1.3646307
10.1063/1.3646307
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