suspensions and suspension mechanics · suspensions may be distinguished by the shape and size of...

Suspensions and suspension mechanics

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Suspensions may be distinguished by the shape and size of the discrete phase

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10-6 10-5 10-4 10-3 10-210-10 10-9 10-8 10-7

[m]

bond length

gap in CP rheometer

gap in PP rheometer

beach sandsiltRBCsclay

Tobacco Mosaic VirusL 300nm

Visible Light

Au nanoparticle

Debye Length in 1mM NaCl

Colloidal silica

(Optical limit)

micro-CT resolution

Size is important: indicates the relevance of various forces

Strong function of volume fraction

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Chong, Christiansen, & Baer J. App. Polymer Sci. 1971

2

1

3

max

Remarks:1. Data from 16 sources2. Divergence at 3. Einstein limit at low4. No rate dependence

max

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Strong function of volume fraction

Entirety of rheology reduced to one

variable.

Is this always the case?

Under what conditions is this valid?

4

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( )rη f φ


Strong function of volume fraction, distribution of sizes

5Chong, Christiansen, & Baer J. App. Polymer Sci. 1971 (adapted)

rs

Monodisperse

0.477dD

0.313dD

0.138dD

spheres

The Farris effect

Contours: volume fraction

5:1 ratio in particle size

6

What are the paths PS and PQ?

<0.75

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Particle shape is also important

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Glass beads, spherical

500um1000um

1000um 2000um

Art glitter, oblate

Wollastoniteprolate, high L/d prolate, low L/d

Mueller, S., et al. Proc. R. Soc. A (2010) 466:1201-1228© The Royal Society. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see https://ocw.mit.edu/help/faq-fair-use/.


Elongated particles have greater hydrodynamic interactions

For the same volume fraction, greater thickening of suspensions

when L/D becomes large.

Particle rotates and sweeps out

a volume

From Barnes, et al. “An Introduction to Rheology”© Elsevier. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see https://ocw.mit.edu/help/faq-fair-use/.


A sample-spanning structure occurs at low volume fractions

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L/D = 7

Require fewer fibers for percolatednetwork

Require more spheres for a percolated network

Increasing ϕ

Percolation threshold != max packing threshold

Garboczi, et al., Phys. Rev. E. (1995) 52:819-828

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Despite this scaling, we still see a shear rate dependence at large Pe#

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Remarks:1. This is a non-colloidal

suspension of spheres2. Brownian diffusion is weak.3. Shear thinning is observed (?)4. How did we construct the

earlier viscosity curves withno rate dependence?

5. Glass particles in aNewtonian matrix

Zarraga, Hill, and Leighton J. Rheol. 2000 (44) © AIP Publishing LLC. All rights reserved. This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use/.


Turn on Brownian motion, dependence on Pe

Laun, H. M. Angew. Makro. Chem. 1984, 124:335-359

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11

asin33

Rectangle



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Limiting trajectories for particle–particle interactions

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• Batchelor & Green result

• C2 accounts for pair interactions,depends on type of flow

• Orbital capture problem,dependence on Pe

Morris, J. F. “A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow” (2009) 48:909-923

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Microstructure is the source of non-Newtonian properties

Microstructure in suspensions: position and orientation of particles

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What is the local density around one particle?

Find 1st, 2nd, 3rd, etc.. nearest neighbors

Count neighboring particles as a function of distance

Radial symmetry is not guaranteed

In general, particle distribution is a function of

an angle and distance

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θ Local density( , )

Bulk densityg r

θr

Investigate hydrodynamics to understand ordering by hydrodynamic forces

Experiments: Parsi & Gadala-MariaHigh Pe # spheres

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Simulations: Péclet number determines symmetry of distribution

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Pe = 0, φ = .45

Color indicates density of particle centers• At low Pe, randomized• At higher Pe, induced structure from flow

Pe = 25, φ = .3

Increased particle density along shoulders of particles, attempting to align in rows




Simulations: Péclet number determines symmetry of distribution

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Pe = 0, φ = .45

Color indicates density of particle centers• At low Pe, randomized• At higher Pe, induced structure from flow

Pe = 25, φ = .3

Increased particle density along shoulders of particles, attempting to align in rows


g(r) depends on the volume fractionSierou and Brady JFM (2002)

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Non-Brownian

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Foss and Brady JFM (2000)Brownian hard spheres

Total

Hydrodynamic

Brownian


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Foss and Brady JFM (2000)Brownian hard spheres

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1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0.001 0.01 0.1 1 10 100 1000 10000

Stre

ss (

less

so

lve

nt)

Pe

Brownian

Hydro

Total

Total

Hydrodynamic

Brownian

Viscosity = f(Pe) Replot asStress = f(Pe)

Brownian

Total

Hydrodynamic

Concentrated suspensions

23Laun, H. M. Angew. Makro. Chem. 1984, 124:335-359



Mechanisms for non-Newtonian suspension behavior

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Vis

cosi

ty

Shear rate or stress

Newtonian plateauStructure not

perturbed by flow: ordering effects washed out by

Brownian motion

Shear thinningStructure is perturbed

aligning particles to flow with decreased

interactions

Shear thickeningStructure strongly

observed

perturbed by flow, strong rise in viscosity

Normal stresses in Brownian suspensions

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1 11 22N σ σ

2 22 33N σ σ

(typically <0)

(typically |N2|>|N1|)


Simulations

1 0.4

2 0.5



Experimental agreement?

26Lee, M., Alcoutlabi, M., Magda, J. J. et al. “The effect of the shear-thickening transition of model colloidal spheres on the sign of N1 and on the radial pressure profile in torsional shear flows” JoR (2006) 50:293-311

Dispersed and stabilized latex particles, 295nm radius

Experiments, Brownian



1N

2N

Experiments, non-Brownian

Experimental agreement?

27Gamonpilas, C., Morris, J. F., Denn, M. M. “Shear and normal stress measurements in non-Brownian monodisperse and bidisperse suspensions” JoR 60 (2016)



Leighton & Acrivos, JFM 1987

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Viscosity decreases in time

Bottom rotates

Upper geometry stationary to measure torque

Pe>>1Re<<1

45% volume fractionDensity matched

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A migration model – Couette flow inside and MRI, ca. 1992

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Good agreement in steady and transient Couette flows

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