We develop and characterize a wide angle static and dynamic light scattering under shear setup. The apparatus is suitable for the study of the structure and the dynamics of soft materials systems with a sub-micron characteristic length scale. The shear device consists in two parallel plates, and the optical setup allows us to perform light scattering measurements in any plane that contains the gradient of the velocity field direction. We demonstrate several capabilities of our apparatus: a measurement of the evolution with shear of the first peak of the structure factor of a concentrated suspension of spherical particles, both in the compression and extension quadrants of the shear flow, and the measurement of the velocity profile in dynamic light scattering. We present a theoretical treatment of light scattering under flow that takes into account the Gaussian character of the illumination and detection optical paths, in the case where the scattering volume extension is smaller than the gap of the flow cell, and compare with experimental measurements.
REFERENCES
1.
G.
Szamel
, “Nonequilibrium structure and rheology of concentrated colloidal suspensions: Linear response
,” J. Chem. Phys.
114
, 8708
–8717
(2001
).2.
F.
Westermeier
, D.
Pennicard
, H.
Hirsemann
, U. H.
Wagner
, C.
Rau
, H.
Graafsma
, P.
Schall
, M.
Paul Lettinga
, and B.
Struth
, “Connecting structure, dynamics and viscosity in sheared soft colloidal liquids: A medley of anisotropic fluctuations
,” Soft Matter
12
, 171
–180
(2016
).3.
M.
Rubinstein
and R. H.
Colby
, Polymer Physics
, 1st ed. (Oxford University Press
, Oxford
, 2003
).4.
B. J.
Bentley
and L. G.
Leal
, “An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows
,” J. Fluid Mech.
167
, 241
–283
(1986
).5.
S. V.
Kao
and S. G.
Mason
, “Dispersion of particles by shear
,” Nature
253
, 619
–621
(1975
).6.
P. T.
Callaghan
, “Rheo-NMR: Nuclear magnetic resonance and the rheology of complex fluids
,” Rep. Prog. Phys.
62
, 599
(1999
).7.
S.
Manneville
, L.
Bécu
, and A.
Colin
, “High-frequency ultrasonic speckle velocimetry in sheared complex fluids
,” Eur. Phys. J.: Appl. Phys.
28
, 361
–373
(2004
).8.
R.
Besseling
, L.
Isa
, E. R.
Weeks
, and W. C. K.
Poon
, “Quantitative imaging of colloidal flows
,” Adv. Colloid Interface Sci.
146
, 1
–17
(2009
).9.
R.
Besseling
, E. R.
Weeks
, A. B.
Schofield
, and W. C. K.
Poon
, “Three-dimensional imaging of colloidal glasses under steady shear
,” Phys. Rev. Lett.
99
, 028301
(2007
).10.
I.
Cohen
, T. G.
Mason
, and D. A.
Weitz
, “Shear-induced configurations of confined colloidal suspensions
,” Phys. Rev. Lett.
93
, 046001
(2004
).11.
D.
Derks
, H.
Wisman
, A. V.
Blaaderen
, and A.
Imhof
, “Confocal microscopy of colloidal dispersions in shear flow using a counter-rotating cone–plate shear cell
,” J. Phys.: Condens. Matter
16
, S3917
(2004
).12.
D.
Lootens
, H.
van Damme
, Y.
Hemar
, and P.
Hébraud
, “Dilatant flow of concentrated suspensions of rough particles
,” Phys. Rev. Lett.
95
, 268302
(2005
).13.
N. Y. C.
Lin
, J. H.
McCoy
, X.
Cheng
, B.
Leahy
, J. N.
Israelachvili
, and I.
Cohen
, “A multi-axis confocal rheoscope for studying shear flow of structured fluids
,” Rev. Sci. Instrum.
85
, 033905
(2014
).14.
P.
Schall
, I.
Cohen
, D. A.
Weitz
, and F.
Spaepen
, “Visualization of dislocation dynamics in colloidal crystals
,” Science
305
, 1944
–1948
(2004
).15.
P.
Schall
, D. A.
Weitz
, and F.
Spaepen
, “Structural rearrangements that govern flow in colloidal glasses
,” Science
318
, 1895
–1899
(2007
).16.
Y. L.
Wu
, J. H. J.
Brand
, J. L. A.
van Gemert
, J.
Verkerk
, H.
Wisman
, A.
van Blaaderen
, and A.
Imhof
, “A new parallel plate shear cell for in situ real-space measurements of complex fluids under shear flow
,” Rev. Sci. Instrum.
78
, 103902
(2007
).17.
T. A.
Klar
and S. W.
Hell
, “Subdiffraction resolution in far-field fluorescence microscopy
,” Opt. Lett.
24
, 954
(1999
).18.
V.
Prasad
, D.
Semwogerere
, and E. R.
Weeks
, “Confocal microscopy of colloids
,” J. Phys.: Condens. Matter
19
, 113102
(2007
).19.
S. J.
Johnson
, C. G.
de Kruif
, and R. P.
May
, “Structure factor distortion for hard-sphere dispersions subjected to weak shear flow: Small-angle neutron scattering in the flow-vorticity plane
,” J. Chem. Phys.
89
, 5909
–5921
(1988
).20.
C. G.
de Kruif
, J. C.
van der Werff
, S. J.
Johnson
, and R. P.
May
, “Small-angle neutron scattering of sheared concentrated dispersions: Microstructure along principal flow axes
,” Phys. Fluids A
2
, 1545
–1556
(1990
).21.
A. P. R.
Eberle
and L.
Porcar
, “Flow-SANS and Rheo-SANS applied to soft matter
,” Curr. Opin. Colloid Interface Sci.
17
, 33
–43
(2012
).22.
C. P.
Amann
, D.
Denisov
, M. T.
Dang
, B.
Struth
, P.
Schall
, and M.
Fuchs
, “Shear-induced breaking of cages in colloidal glasses: Scattering experiments and mode coupling theory
,” J. Chem. Phys.
143
, 034505
(2015
).23.
R. L.
Leheny
, M. C.
Rogers
, K.
Chen
, S.
Narayanan
, and J. L.
Harden
, “Rheo-XPCS
,” Curr. Opin. Colloid Interface Sci.
20
, 261
–271
(2015
).24.
M. C.
Rogers
, K.
Chen
, L.
Andrzejewski
, S.
Narayanan
, S.
Ramakrishnan
, R. L.
Leheny
, and J. L.
Harden
, “Echoes in x-ray speckles track nanometer-scale plastic events in colloidal gels under shear
,” Phys. Rev. E
90
, 062310
(2014
). 25.
D.
Denisov
, M. T.
Dang
, B.
Struth
, G.
Wegdam
, and P.
Schall
, “Resolving structural modifications of colloidal glasses by combining x-ray scattering and rheology
,” Sci. Rep.
3
, 1631
(2013
).26.
D. V.
Denisov
, M. T.
Dang
, B.
Struth
, A.
Zaccone
, G. H.
Wegdam
, and P.
Schall
, “Sharp symmetry-change marks the mechanical failure transition of glasses
,” Sci. Rep.
5
, 14359
(2015
).27.
T.
Narayanan
, R.
Dattani
, J.
Möller
, and P.
Kwaśniewski
, “A microvolume shear cell for combined rheology and x-ray scattering experiments
,” Rev. Sci. Instrum.
91
, 085102
(2020
).28.
X.-L.
Wu
, D. J.
Pine
, P. M.
Chaikin
, J. S.
Huang
, and D. A.
Weitz
, “Diffusing-wave spectroscopy in a shear flow
,” J. Opt. Soc. Am. B
7
, 15
(1990
).29.
F.
Ozon
, T.
Narita
, A.
Knaebel
, G.
Debrégeas
, P.
Hébraud
, and J.-P.
Munch
, “Partial rejuvenation of a colloidal glass
,” Phys. Rev. E
68
, 032401
(2003
).30.
A. D.
Gopal
and D. J.
Durian
, “Nonlinear bubble dynamics in a slowly driven foam
,” Phys. Rev. Lett.
75
, 2610
–2613
(1995
).31.
R.
Höhler
, S.
Cohen-Addad
, and H.
Hoballah
, “Periodic nonlinear bubble motion in aqueous foam under oscillating shear strain
,” Phys. Rev. Lett.
79
, 1154
–1157
(1997
).32.
P.
Hébraud
, F.
Lequeux
, J. P.
Munch
, and D. J.
Pine
, “Yielding and rearrangements in disordered emulsions
,” Phys. Rev. Lett.
78
, 4657
–4660
(1997
).33.
G.
Petekidis
, A.
Moussaïd
, and P. N.
Pusey
, “Rearrangements in hard-sphere glasses under oscillatory shear strain
,” Phys. Rev. E
66
, 051402
(2002
).34.
M.
Erpelding
, A.
Amon
, and J.
Crassous
, “Diffusive wave spectroscopy applied to the spatially resolved deformation of a solid
,” Phys. Rev. E
78
, 046104
(2008
).35.
B. J.
Ackerson
, J.
van der Werff
, and C. G.
de Kruif
, “Hard-sphere dispersions: Small-wave-vector structure-factor measurements in a linear shear flow
,” Phys. Rev. A
37
, 4819
–4827
(1988
).36.
L.
Cipelletti
and D. A.
Weitz
, “Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator
,” Rev. Sci. Instrum.
70
, 3214
–3221
(1999
).37.
S.
Aime
, L.
Ramos
, J. M.
Fromental
, G.
Prévot
, R.
Jelinek
, and L.
Cipelletti
, “A stress-controlled shear cell for small-angle light scattering and microscopy
,” Rev. Sci. Instrum.
87
, 123907
(2016
).38.
S.
Aime
and L.
Cipelletti
, “Probing shear-induced rearrangements in Fourier space. I. Dynamic light scattering
,” Soft Matter
15
, 200
–212
(2019
).39.
J.
Läuger
and W.
Gronski
, “A melt rheometer with integrated small angle light scattering
,” Rheol. Acta
34
, 70
–79
(1995
).40.
J.-B.
Salmon
, S.
Manneville
, A.
Colin
, and B.
Pouligny
, “An optical fiber based interferometer to measure velocity profiles in sheared complex fluids
,” Eur. Phys. J.: Appl. Phys.
22
, 143
–154
(2003
).41.
B. J.
Ackerson
, C. G.
De Kruif
, N. J.
Wagner
, and W. B.
Russel
, “Comparison of small shear flow rate-small wave vector static structure factor data with theory
,” J. Chem. Phys.
90
, 3250
–3253
(1989
).42.
A.
Pommella
, A.-M.
Philippe
, T.
Phou
, L.
Ramos
, and L.
Cipelletti
, “Coupling space-resolved dynamic light scattering and rheometry to investigate heterogeneous flow and nonaffine dynamics in glassy and jammed soft matter
,” Phys. Rev. Appl.
11
, 034073
(2019
).43.
J. F.
Schwarzl
and S.
Hess
, “Shear-flow-induced distortion of the structure of a fluid: Application of a simple kinetic equation
,” Phys. Rev. A
33
, 4277
–4283
(1986
).44.
E.
Guyon
, J.-P.
Hulin
, L.
Petit
, and C. D.
Mitescu
, Physical Hydrodynamics
, 2nd ed. (Oxford University Press
, Oxford
, 2015
).45.
B. J.
Maranzano
and N. J.
Wagner
, “Flow-small angle neutron scattering measurements of colloidal dispersion microstructure evolution through the shear thickening transition
,” J. Chem. Phys.
117
, 10291
–10302
(2002
).46.
R.
Seto
, G. G.
Giusteri
, and A.
Martiniello
, “Microstructure and thickening of dense suspensions under extensional and shear flows
,” J. Fluid Mech.
825
, R3
(2017
). 47.
N. S.
Martys
, M.
Khalil
, W. L.
George
, D.
Lootens
, and P.
Hébraud
, “Stress propagation in a concentrated colloidal suspension under shear
,” Eur. Phys. J. E
35
, 1
–7
(2012
).48.
K. N.
Pham
, A. M.
Puertas
, J.
Bergenholtz
, S. U.
Egelhaaf
, A.
MoussaId
, P. N.
Pusey
, A. B.
Schofield
, M. E.
Cates
, M.
Fuchs
, and W. C. K.
Poon
, “Multiple glassy states in a simple model system
,” Science
296
, 104
–106
(2002
).49.
P. J.
Lu
, E.
Zaccarelli
, F.
Ciulla
, A. B.
Schofield
, F.
Sciortino
, and D. A.
Weitz
, “Gelation of particles with short-range attraction
,” Nature
453
, 499
–503
(2008
).50.
T.
Eckert
and E.
Bartsch
, “Re-entrant glass transition in a colloid-polymer mixture with depletion attractions
,” Phys. Rev. Lett.
89
, 125701
(2002
).51.
J.
Schneider
, M.
Wiemann
, A.
Rabe
, and E.
Bartsch
, “On tuning microgel character and softness of cross-linked polystyrene particles
,” Soft Matter
13
, 445
–457
(2017
).52.
N.
Koumakis
, A.
Pamvouxoglou
, A. S.
Poulos
, and G.
Petekidis
, “Direct comparison of the rheology of model hard and soft particle glasses
,” Soft Matter
8
, 4271
–4284
(2012
).53.
C. P.
Royall
, W. C. K.
Poon
, and E. R.
Weeks
, “In search of colloidal hard spheres
,” Soft Matter
9
, 17
–27
(2013
).54.
I. M.
Krieger
and T. J.
Dougherty
, “A mechanism for non-Newtonian flow in suspensions of rigid spheres
,” Trans. Soc. Rheol.
3
, 137
–152
(1959
).55.
W. B.
Russel
and A. P.
Gast
, “Nonequilibrium statistical mechanics of concentrated colloidal dispersions: Hard spheres in weak flows
,” J. Chem. Phys.
84
, 1815
–1826
(1986
).56.
B. J.
Ackerson
and P. N.
Pusey
, “Shear-induced order in suspensions of hard spheres
,” Phys. Rev. Lett.
61
, 1033
–1036
(1988
).57.
J. K.
Percus
and G. J.
Yevick
, “Analysis of classical statistical mechanics by means of collective coordinates
,” Phys. Rev.
110
, 1
–13
(1958
).58.
B. J.
Ackerson
and N. A.
Clark
, “Dynamic light scattering at low rates of shear
,” J. Phys.
42
, 929
–936
(1981
).59.
The angle ϕ between the scattering vector q = kout − k0 and the velocity direction, ux, is . corresponds to the extension quadrants and to the compression quadrants.
60.
E.
Born
and M.
Wolf
, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light
(Cambridge University Press
, 1999
).61.
62.
63.
M.
Adhikari
and S.
Sastry
, “Memory formation in cyclically deformed amorphous solids and sphere assemblies
,” Eur. Phys. J. E
41
, 105
(2018
).64.
V.
Viasnoff
and F.
Lequeux
, “Rejuvenation and overaging in a colloidal glass under shear
,” Phys. Rev. Lett.
89
, 065701
(2002
).65.
S.
Kaloun
, M.
Skouri
, A.
Knaebel
, J.-P.
Münch
, and P.
Hébraud
, “Aging of a colloidal glass under a periodic shear
,” Phys. Rev. E
72
, 011401
(2005
).66.
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