We study the forced motion of a tagged soft particle through a jammed suspension of identical soft particles using particle simulations. We relate the local particle dynamics, microstructure, and microrheology to the bulk rheological properties of the suspension. At small forces, the tagged particle is trapped in a cage of other particles that resist the external force whereas at larger forces the tagged particle breaks free of its cage. This is indicative of the macroscopic yielding behavior in these materials. The threshold force from microrheology is quantitatively related to the macroscopic yield stress. The computed microviscosity also follows the shear thinning nature of these glasses and matches the exponent of 0.5 observed in bulk measurements. The semiquantitative agreement between the micro and bulk viscosity is discussed by comparing the microstructural processes involved in both. In microrheology, at moderate forces, the probe displacement causes an accumulation of particles in the direction of motion and a depleted wake behind. In bulk rheology, there are accumulation and depletion of particles along the compression and extension axes, respectively. Despite these differences, the average number of contacts and the elastic contact force on the particles are similar, which justifies why microrheology measurements match bulk rheology data.

1.
Anderson
,
D.
,
D.
Schaar
,
H. G. E.
Hentschel
,
J.
Hay
,
P.
Habdas
, and
E. R.
Weeks
, “
Local elastic response measured near the colloidal glass transition
,”
J. Chem. Phys.
138
,
12A520
(
2013
).
2.
Angelini
,
T. E.
,
E.
Hannezo
,
X.
Trepat
,
M.
Marquez
,
J. J.
Fredberg
, and
D. A.
Weitz
, “
Glass-like dynamics of collective cell migration
,”
Proc. Natl. Acad. Sci. U.S.A.
108
,
4714
4719
(
2011
).
3.
Atapattu
,
D. D.
,
R. P.
Chhabra
, and
P. H. T.
Uhlherr
, “
Creeping sphere motion in Herschel-Bulkley fluids—Flow-field and drag
,”
J. Non-Newtonian Fluid Mech.
59
,
245
265
(
1995
).
4.
Bausch
,
A. R.
,
W.
Moller
, and
E.
Sackmann
, “
Measurement of local viscoelasticity and forces in living cells by magnetic tweezers
,”
Biophys. J.
76
,
573
579
(
1999
).
5.
Beris
,
A. N.
,
J. A.
Tsamopoulos
,
R. C.
Armstrong
, and
R. A.
Brown
, “
Creeping motion of a sphere through a bingham plastic
,”
J. Fluid Mech.
158
,
219
244
(
1985
).
6.
Borrega
,
R.
,
M.
Cloitre
,
I.
Betremieux
,
B.
Ernst
, and
L.
Leibler
, “
Concentration dependence of the low-shear viscosity of polyelectrolyte micro-networks: From hard spheres to soft microgels
,”
Europhys. Lett.
47
,
729
735
(
1999
).
7.
Buitenhuis
,
J.
, and
S.
Forster
, “
Block copolymer micelles: Viscoelasticity and interaction potential of soft spheres
,”
J. Chem. Phys.
107
,
262
272
(
1997
).
8.
Carpen
,
I. C.
, and
J. F.
Brady
, “
Microrheology of colloidal dispersions by Brownian dynamics simulations
,”
J. Rheol.
49
,
1483
1502
(
2005
).
9.
Chen
,
D. T.
,
E. R.
Weeks
,
J. C.
Crocker
,
M. F.
Islam
,
R.
Verma
,
J.
Gruber
,
A. J.
Levine
,
T. C.
Lubensky
, and
A. G.
Yodh
, “
Rheological microscopy: Local mechanical properties from microrheology
,”
Phys. Rev. Lett.
90
,
108301
(
2003
).
10.
Cicuta
,
P.
, and
A. M.
Donald
, “
Microrheology: A review of the method and applications
,”
Soft Matter
3
,
1449
1455
(
2007
).
11.
Cloitre
,
M.
,
R.
Borrega
,
F.
Monti
, and
L.
Leibler
, “
Glassy dynamics and flow properties of soft colloidal pastes
,”
Phys. Rev. Lett.
90
,
068303
(
2003
).
12.
DePuit
,
R. J.
,
A. S.
Khair
, and
T. M.
Squires
, “
A theoretical bridge between linear and nonlinear microrheology
,”
Phys. Fluids
23
,
063102
(
2011
).
13.
Foffano
,
G.
,
J. S.
Lintuvuori
,
K.
Stratford
,
M. E.
Cates
, and
D.
Marenduzzo
, “
Colloids in active fluids: Anomalous microrheology and negative drag
,”
Phys. Rev. Lett.
109
,
028103
(
2012
).
14.
Gardel
,
M. L.
,
M. T.
Valentine
,
J. C.
Crocker
,
A. R.
Bausch
, and
D. A.
Weitz
, “
Microrheology of entangled F-actin solutions
,”
Phys. Rev. Lett.
91
,
158302
(
2003
).
15.
Gazuz
,
I.
,
A. M.
Puertas
,
T.
Voigtmann
, and
M.
Fuchs
, “
Active and nonlinear microrheology in dense colloidal suspensions
,”
Phys. Rev. Lett.
102
,
248302
(
2009
).
16.
Gnann
,
M. V.
,
I.
Gazuz
,
A. M.
Puertas
,
M.
Fuchs
, and
T.
Voigtmann
, “
Schematic models for active nonlinear microrheology
,”
Soft Matter
7
,
1390
1396
(
2011
).
17.
Habdas
,
P.
,
D.
Schaar
,
A. C.
Levitt
, and
E. R.
Weeks
, “
Forced motion of a probe particle near the colloidal glass transition
,”
Europhys. Lett.
67
,
477
483
(
2004
).
18.
Helfer
,
E.
,
S.
Harlepp
,
L.
Bourdieu
,
J.
Robert
,
F. C.
MacKintosh
, and
D.
Chatenay
, “
Microrheology of biopolymer-membrane complexes
,”
Phys. Rev. Lett.
85
,
457
460
(
2000
).
19.
Jack
,
R. L.
,
D.
Kelsey
,
J. P.
Garrahan
, and
D.
Chandler
, “
Negative differential mobility of weakly driven particles in models of glass formers
,”
Phys. Rev. E
78
,
011506
(
2008
).
20.
Jop
,
P.
,
J. R.
Gomez-Solano
,
A.
Petrosyan
, and
S.
Ciliberto
, “
Experimental study of out-of-equilibrium fluctuations in a colloidal suspension of Laponite using optical traps
,”
J. Stat. Mech. Theory Exp.
2009
,
P04012
.
21.
Khair
,
A. S.
, and
J. F.
Brady
, “
Single particle motion in colloidal dispersions: A simple model for active and nonlinear microrheology
,”
J. Fluid Mech.
557
,
73
117
(
2006
).
22.
Khair
,
A. S.
, and
J. F.
Brady
, “
Microrheology of colloidal dispersions: Shape matters
,”
J. Rheol.
52
,
165
196
(
2008
).
23.
Khan
,
M.
, and
A. K.
Sood
, “
Out-of-equilibrium microrheology using optical tweezers to probe directional viscoelastic properties under shear
,”
Europhys. Lett.
92
,
48001
(
2010
).
24.
Lacasse
,
M. D.
,
G. S.
Grest
,
D.
Levine
,
T. G.
Mason
, and
D. A.
Weitz
, “
Model for the elasticity of compressed emulsions
,”
Phys. Rev. Lett.
76
,
3448
3451
(
1996
).
25.
Lau
,
A. W. C.
,
B. D.
Hoffman
,
A.
Davies
,
J. C.
Crocker
, and
T. C.
Lubensky
, “
Microrheology, stress fluctuations, and active behavior of living cells
,”
Phys. Rev. Lett.
91
,
198101
(
2003
).
26.
Likos
,
C. N.
, “
Soft matter with soft particles
,”
Soft Matter
2
,
478
498
(
2006
).
65.
Liu
,
K. K.
,
D. R.
Williams
, and
B. J.
Briscoe
, “
The large deformation of a single micro-elastomeric sphere
,”
J. Phys. D Appl. Phys.
31
,
294
303
(
1998
).
66.
Lubachevsky
,
B. D.
, and
F. H.
Stillinger
, “
Geometric-Properties of Random Disk Packings
,”
J. Stat. Phys.
60
,
561
583
(
1990
).
27.
Macosko
,
C. W.
, “
Rheology: Principles, measurements, and applications
,”
Advances in Interfacial Engineering Series
(
Wiley-VCH
,
New York
1994
).
28.
Mason
,
T. G.
,
J.
Bibette
, and
D. A.
Weitz
, “
Elasticity of compressed emulsions
,”
Phys. Rev. Lett.
75
,
2051
2054
(
1995
).
29.
Mason
,
T. G.
,
T.
Gisler
,
K.
Kroy
,
E.
Frey
, and
D. A.
Weitz
, “
Rheology of F-actin solutions determined from thermally driven tracer motion
,”
J. Rheol.
44
,
917
928
(
2000
).
30.
Meyer
,
A.
,
A.
Marshall
,
B. G.
Bush
, and
E. M.
Furst
, “
Laser tweezer microrheology of a colloidal suspension
,”
J. Rheol.
50
,
77
92
(
2006
).
31.
Microgel Suspensions: Fundamentals and Applications
, edited by
A.
Fernandez de Las Nieves
,
H.
Wyss
,
J.
Mattson
, and
D. A.
Weitz
(
Wiley-VCH
,
New York
,
2011
).
32.
Microscale Diagnostic Techniques
, edited by
K. S.
Breuer
(
Springer
,
New York
,
2005
).
34.
Mohan
,
L.
, and
R. T.
Bonnecaze
, “
Short-ranged pair distribution function for concentrated suspensions of soft particles
,”
Soft Matter
8
,
4216
4222
(
2012
).
33.
Mohan
,
L.
,
C.
Pellet
,
M.
Cloitre
, and
R.
Bonnecaze
, “
Local mobility and microstructure in periodically sheared soft particle glasses and their connection to macroscopic rheology
,”
J. Rheol.
57
,
1023
1046
(
2013
).
67.
Plimpton
,
S.
, “
Fast Parallel Algorithms for Short-Range Molecular-Dynamics
,”
J. Comput. Phys.
117
,
1
19
(
1995
).
35.
Princen
,
H. M.
, and
A. D.
Kiss
, “
Rheology of foams and highly concentrated emulsions.4. An experimental-study of the shear viscosity and yield stress of concentrated emulsions
,”
J. Colloid Interface Sci.
128
,
176
187
(
1989
).
36.
Ramos
,
L.
, and
L.
Cipelletti
, “
Ultraslow dynamics and stress relaxation in the aging of a soft glassy system
,”
Phys. Rev. Lett.
87
,
245503
(
2001
).
37.
Reichhardt
,
C. J. O.
, and
C.
Reichhardt
, “
Viscous decoupling transitions for individually dragged particles in systems with quenched disorder
,”
Phys. Rev. E
78
,
011402
(
2008
).
38.
Rich
,
J. P.
,
J.
Lammerding
,
G. H.
McKinley
, and
P. S.
Doyle
, “
Nonlinear microrheology of an aging, yield stress fluid using magnetic tweezers
,”
Soft Matter
7
,
9933
9943
(
2011
).
39.
Rogers
,
S. A.
,
B. M.
Erwin
,
D.
Vlassopoulos
, and
M.
Cloitre
, “
A sequence of physical processes determined and quantified in LAOS: Application to a yield stress fluid
,”
J. Rheol.
55
,
435
458
(
2011
).
40.
Schmidt
,
F. G.
,
F.
Ziemann
, and
E.
Sackmann
, “
Shear field mapping in actin networks by using magnetic tweezers
,”
Eur. Biophys. J.
24
,
348
353
(
1996
).
41.
Schnurr
,
B.
,
F.
Gittes
,
F. C.
MacKintosh
, and
C. F.
Schmidt
, “
Determining microscopic viscoelasticity in flexible and semiflexible polymer networks from thermal fluctuations
,”
Macromolecules
30
,
7781
7792
(
1997
).
42.
Segrè
,
P. N.
,
S. P.
Meeker
,
P. N.
Pusey
, and
W. C. K.
Poon
, “
Viscosity and structural relaxation in suspensions of hard-sphere colloids
,”
Phys. Rev. Lett.
75
,
958
962
(
1995
).
43.
Seth
,
J. R.
,
L.
Mohan
,
C.
Locatelli-Champagne
,
M.
Cloitre
, and
R. T.
Bonnecaze
, “
A micromechanical model to predict the flow of soft particle glasses
,”
Nature Mater.
10
,
838
843
(
2011
).
44.
Seth
,
J. R.
,
M.
Cloitre
, and
R. T.
Bonnecaze
, “
Elastic properties of soft particle pastes
,”
J. Rheol.
50
,
353
376
(
2006
).
45.
Squires
,
T. M.
, “
Nonlinear microrheology: Bulk stresses versus direct interactions
,”
Langmuir
24
,
1147
1159
(
2008
).
46.
Squires
,
T. M.
, and
J. F.
Brady
, “
A simple paradigm for active and nonlinear microrheology
,”
Phys. Fluids
17
,
073101
(
2005
).
47.
Squires
,
T. M.
, and
T. G.
Mason
, “
Fluid mechanics of microrheology
,”
Annu. Rev. Fluid Mech.
42
,
413
438
(
2010
).
48.
Sriram
,
I.
,
A.
Meyer
, and
E. M.
Furst
, “
Active microrheology of a colloidal suspension in the direct collision limit
,”
Phys. Fluids
22
,
062003
(
2010
).
49.
Swan
,
J. W.
,
R. N.
Zia
, and
J. F.
Brady
, “
Large amplitude oscillatory micorheology
,”
J. Rheol.
58
,
1
41
(
2014
).
50.
Trepat
,
X.
,
L. H.
Deng
,
S. S.
An
,
D.
Navajas
,
D. J.
Tschumperlin
,
W. T.
Gerthoffer
,
J. P.
Butler
, and
J. J.
Fredberg
, “
Universal physical responses to stretch in the living cell
,”
Nature
447
,
592
595
(
2007
).
51.
Valentine
,
M. T.
,
L. E.
Dewalt
, and
H. D.
OuYang
, “
Forces on a colloidal particle in a polymer solution: A study using optical tweezers
,”
J. Phys. Condens. Matter
8
,
9477
9482
(
1996
).
52.
van der Vaart
,
K.
,
Y.
Rahmani
,
R.
Zargar
,
Z. B.
Hu
,
D.
Bonn
, and
P.
Schall
, “
Rheology of concentrated soft and hard-sphere suspensions
,”
J. Rheol.
57
,
1195
1209
(
2013
).
53.
Velegol
,
D.
, and
F.
Lanni
, “
Cell traction forces on soft biomaterials. I. Microrheology of type I collagen gels
,”
Biophys. J.
81
,
1786
1792
(
2001
).
54.
Waigh
,
T. A.
, “
Microrheology of complex fluids
,”
Rep. Prog. Phys.
68
,
685
742
(
2005
).
55.
Wilking
,
J. N.
, and
T. G.
Mason
, “
Optically driven nonlinear microrheology of gelatin
,”
Phys. Rev. E
77
,
055101
(
2008
).
56.
Williams
,
S. R.
, and
D. J.
Evans
, “
Linear response domain in glassy systems
,”
Phys. Rev. Lett.
96
,
015701
(
2006
).
58.
Wilson
,
L. G.
, and
W. C. K.
Poon
, “
Small-world rheology: An introduction to probe-based active microrheology
,”
Phys. Chem. Chem. Phys.
13
,
10617
10630
(
2011
).
57.
Wilson
,
L. G.
,
A. W.
Harrison
,
A. B.
Schofield
,
J.
Arlt
, and
W. C. K.
Poon
, “
Passive and active microrheology of hard-sphere colloids
,”
J. Phys. Chem. B
113
,
3806
3812
(
2009
).
59.
Winter
,
D.
,
J.
Horbach
,
P.
Virnau
, and
K.
Binder
, “
Active nonlinear microrheology in a glass-forming Yukawa fluid
,”
Phys. Rev. Lett.
108
,
028303
(
2012
).
60.
Wirtz
,
D.
, “
Particle-tracking microrheology of living cells: Principles and applications
,”
Annu. Rev. Biophys.
38
,
301
326
(
2009
).
61.
Yamada
,
S.
,
D.
Wirtz
, and
S. C.
Kuo
, “
Mechanics of living cells measured by laser tracking microrheology
,”
Biophys. J.
78
,
1736
1747
(
2000
).
62.
Zaner
,
K. S.
, and
P. A.
Valberg
, “
Viscoelasticity of F-actin measured with magnetic microparticles
,”
J. Cell Biol.
109
,
2233
2243
(
1989
).
68.
Zia
,
R. N.
, and
J. F.
Brady
, “
Microviscosity, microdiffusivity, and normal stresses in colloidal dispersions
,”
J. Rheol.
56
,
1175
1208
(
2012
).
63.
Zia
,
R. N.
, and
J. F.
Brady
, “
Stress development, relaxation, and memory in colloidal dispersions: Transient nonlinear microrheology
,”
J. Rheol.
57
,
457
492
(
2013
).
64.
Ziemann
,
F.
,
J.
Radler
, and
E.
Sackmann
, “
Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer
,”
Biophys. J.
66
,
2210
2216
(
1994
).
You do not currently have access to this content.