Sheared colloids and emulsions
studied with confocal microscopy
Eric R. Weeks
Emory University (Physics)
Chen 陈丹丹
* DandanClara Rahola* Joaquim
Denis Semwogerere
In collaboration with:

Victor Breedveld (Georgia Tech)
Jun Sato (Georgia Tech)John Crocker (Univ. Pennsylvania)
Klebert Feitosa (Univ. Pennsylvania)
Funding by NSF-DMR
Colloidal particles from Andrew Schofield,
University of Edinburgh

Overview• Study dense amorphous (“jammed”) samples• How do they deform microscopically undershear?

Colloidal particles: hard,monodisperse

Emulsion droplets: soft,polydisperse(Dandan Chen’s work)(Joaquim Clara Rahola’s work)Basic problem: particles collide, mustfind way to rearrange
shear

Like the “David Pine” effect. For dense amorphous samples,even small strains cause collisions. Unlike David’s talk, ourparticles are influence by Brownian motion.
“shear-induced cage breaking” – Akira Furukawa

One possibility: shear transformation zones(ML Falk and JS Langer, Phys. Rev. E 57, 7192 (1998)]

2D Lennard-Jones simulations of Falk & Langer

One possibility: shear transformation zones(ML Falk and JS Langer, Phys. Rev. E 57, 7192 (1998)]

3D colloidal experiments: 1.5 µm dia monodisperse particles
Blue = negative strain, red = position (direction of shear)
Total strain γ = 0.01
[P Schall, DA Weitz, & F Spaepen, Science (2007)]Can also have “avalanches” ofrearranging particles
H Shiba & A Onuki PRE 2010
Sheared glassy 2D binary
mixture, black X’s markrearranging particles, Δγ = 0.005
See poster: Hayato Shiba

Controlled strain, parallel plate shear cellsample

stick colloids and/or Scotchgard to plates to diminish slip

Confocal microscopy for 3D pictures
Scan many 2D slices,
reconstruct 3D image

0.2 µm

2D and 3D images of 2.3 µm diameter PMMA particles

Microscopy and Tracking
software: http://www.physics.emory.edu/~weeks/idl/
Dinsmore, Weeks, Prasad, Levitt, & Weitz, Appl. Optics ’01

Microscopy:• 30 images/s (512×480 pixels, 2D)• one 3D “chunk” per 2 - 20 s
• 67 × 63 × 20 µm3• 100× oil / 1.4 N.A. objective• Identify particles within 0.03 µm (xy), 0.05 µm (z)Particle tracking:• Follow 3000-5000 particles, in 3D• 200-1000 time steps = hours to days
• ≈ 4 GB of images per experimentPart 1: Shear of dense
colloidal suspensions
D Chen et al., Phys Rev E 81, 011403 (2010)Colloidal System• 2.3 mm diameter PMMA colloids• density matched solvent (cyclohexylbromide + decalin)• slightly charged hard spheres• provided by A Schofield & WCK Poon, Univ. of Edinburgh

one of Andrew Schofield’s cabinets

Colloidal glass transition
 Control parameter is volume fraction φ Glass exists when φ > φg ≈ 0.58
(agrees with simulations with slight polydispersity) Diffusion constant  0
 See aging behavior(Courtland & Weeks ’03; Cianci, Courtland, Weeks ’06;Lynch, Cianci, & Weeks ’08)

Our experiments:φ ≈ 0.51-0.57

How fast do we shear?
Use triangle wave driving, strain rate

, period 150-450 sCompare with time scale to diffuse radius a in unsheared sample,

Define Peclet number
Shear-induced motion is more significant than thermal motion!
.
(same idea as γτ > 1)

Aside: we have shear bands• Focus on region wherevelocity gradient is linear• Define local (mesoscopic)
strain rate:•is control parameterMovie and tracking
Top view

Side viewzyx
3.7 µmx0-3.3 µm
Relative rearrangements between neighbors makes structure change.

Examine nonaffine motion: Δx~

1. Initial
unstrained sample

2. Strained
sample4. Motion in y, z left unchanged

3. Remove affine
motion of strain
fieldExamine nonaffine motion: Δx~

2. Strained
sample3. Remove affine
motion of strain
field

φ = 0.51, γmeso = 0.43, Pe ≈ 20

Shear-induced motion:
accumulated strain is key

Shear-induced motion:
accumulated strain is key
Comments:• Has been seen before(Yamamoto & Onuki 1998; Pine 2005;
Maloney & Robbins 2008)• Our result implies(agrees with Eisenmann 2010, Ovarlez 2010)• Prior work found(Besseling, Weeks, Schofield & Poon 2007)• Prior work was larger strains,
glassy samples

question:
Are shear-induced rearrangements
spatially isotropic?
zyx

~Nonaffine motion: Δxdeshearz(µm)

deshearx(µm)Δx-3.3 µm

3.7 µmz(µm)

real datax(µm)~|Δx|

0.2 µm

1.6 µmφ = 0.51, γmeso = 0.43, Pe ≈ 20

Nonaffine displacements have isotropic distributionzyx

φ = 0.51, γmeso = 0.43, Pe ≈ 20

Nonaffine displacements have isotropic distribution

our data

Yamamoto & Onuki simulations
PRE 1998(also, Miyazaki et al PRE 2004)

φ = 0.51, γmeso = 0.43, Pe ≈ 20

Nonaffine rearrangement is spatially heterogeneous~|Δx| (µm)
1.6Sheary(µm)
Y-slice
ZX
0.2x (µm)
Mobile particles cluster together
Do they spread in a particular direction?

YExamine extent of largest highly mobile regionZXY

A non-affine mobile cluster: a network of neighboring
particles with large non-affine mobility ( Δr~ > 1 µm).

Examine extent of largest highly mobile region

Zextent
ZXXextent

Yextent

A non-affine mobile cluster: a network of neighboring
particles with large non-affine mobility ( Δr~ > 1 µm).

Y

Mobile clusters have no preferential orientation

zyx

Note 1: Plausible that more subtle analysis would show anisotropy[4p correlations: A Furukawa, K Kim, S Saito, and H Tanaka, PRL (2009)]

Note 2: We checked other measures of deformation: similar results

Summary part 1 of talk:• Examined shear of dense monodisperse
colloidal suspensions• Shear results in deformations which are
isotropic in several senses• Length scales of ~ 2 particle diameters
For more details:
D Chen et al., Phys Rev E 81, 011403 (2010)

Part 2: Shear of polydisperse emulsions*Joaquim Clara Rahola, K Feitosa, JC Crocker, ER Weeks

Compared to first part of the talk:• Highly polydisperse• Droplets are soft• High volume fractions (jammed samples)• Smaller strains• Elastic deformations rather than plasticrearrangements• Sinusoidal driving rather than triangle
wave• Mostly 2D analysis of 3D samples

Decane in water/glycerol emulsions (with SDS)
rheology results in collaboration with Rut Besseling & Wilson Poonmicroscopy data to be shown in talk all taken at f = 1 Hz, ω = 6.3 s-1

G’ G”

Droplet size distribution(image analysis: K Feitosa, algorithm similar to R Penfold et al., Langmuir 2006)

Decay length = 0.5 µm(perhaps unimportant)Long tail(important)φ = 0.80

look at movie…
• 2D movie in real-time• φ = 0.65
• Driving frequency f = 1 Hz
• depth = 12 µm, γ ≈ 0.12

movie “2Vpp-A.tif”, show with ImageJ, \ to start animation

Use Hough transform to identify droplets

Caveat: true radius ofdroplet might be larger
than we observe

Droplet trajectories are sinusoidal

x(t) = ax sin(ωt + θx )y(t) = ay sin(ωt + θy )φ = 0.65, γ = 0.07

Amplitude distributions
to be shown: small droplets are the outliers〈ax〉 = 2.4 µm

φ = 0.65, γ = 0.07, z = 24 µm

What we think is happening:

Large droplet in otherwise
homogeneous strain field
droplet velocity = mean flow velocity

What we think is happening:
Small droplet
constrained bylarge droplet,moves slower
than “normal”

Small droplet pushed by large
droplet, moves faster than “normal”
Summary: Smaller droplets pushed around by larger
droplets; their “anomalous” motion results in “correct”
average flow field around largest dropletsWhat we think is happening:
Small droplet
constrained bylarge droplet,moves slower
than “normal”

Small droplet pushed by largedroplet, moves faster than “normal”
Summary: Smaller droplets pushed around by larger
droplets; their “anomalous” motion results in “correct”
average flow field around largest dropletsSmall droplets are outliers: ax

φ = 0.65, γ = 0.07, z = 24 µm

Small droplets are outliers: ay

φ = 0.65, γ = 0.07, z = 24 µm

Small droplets are outliers

φ = 0.65, γ = 0.07, z = 24 µm

Phase angle distributions
x(t) = ax sin(ωt + θx )Again, the small droplets
are the outliers

Use 〈θx〉 as referenceφ = 0.65, γ = 0.07, z = 24 µm

Do neighbors move in similar ways?
answer will be yes…

Calculate correlation functionΔrΔr center-to-center: NO!

Δr surface-to-surface: YES!

Correlations have exponential decayax, γ = 0.08

Δray, γ = 0.08ay, γ = 0.02ax, γ = 0.02

φ = 0.65, z = 24 µm

Decay length increases with increasing strain

Droplet sizes:
mean r = 1.2 µm
r < 2.6 µm = 50% of volumer < 10 µm = 85% of volume

φ = 0.65, z = 24 µm

SummaryShear of jammed soft materials:• Monodisperse – see locally deforming
regions, isotropic, results depend primarily
on total accumulated strain• Polydisperse – see extremely non-affine
response of smaller droplets, correlation
length that grows with shear rate

colloids: Chen et al., PRE 81, 011403 (2010)
emulsions: Clara Rahola et al., hopefully on arXiv soon
Movies, reprints, & free particle tracking software:www.physics.emory.edu/~weeks/lab/Extraslides

Find length scale for rearrangements: correlation functions
based on Doliwa & Heuer, PRE (2000);ER Weeks, JC Crocker, DA Weitz, JP:CM (2007)

Vector correlation function:

Scalar correlation function:• use nonaffine displacements• use Δtmax

Correlations decay exponentially in spacedecay length = 6.1aResults shown are
typical; no clear
dependence on φ.
or γ seen

decay length = 2.4a

φ = 0.51, γmeso = 0.43, Pe ≈ 20

Droplet size distribution(image analysis: K Feitosa, algorithm similar to R Penfold et al., Langmuir 2006)
Volumeweighteddistribution

φ = 0.80

Confocal Microscopy
rotatingmirrors

laser

screen withpinholedetector (PMT)

microscope

See review article:
fluorescent sample“Confocal microscopy of colloids”
Prasad, Semwogerere, & Weeks
J. Phys.:Cond. Mat. 19, 113102 (2007)