We examine the impact of confinement on the structure, dynamics, and rheology of spherically confined macromolecular suspensions, with a focus on the role played by entropic forces, by comparing the limits of strong hydrodynamics and no hydrodynamics. We present novel measurements of the osmotic pressure, intrinsic viscosity, and long-time self-diffusivity in spherical confinement and find confinement induces strong structural correlations and restrictions on configurational entropy that drive up osmotic pressure and viscosity and drive down self-diffusion. Even in the absence of hydrodynamics, confinement produces distinct short-time and long-time self-diffusion regimes. This finding revises the previous understanding that short-time self-diffusion is a purely hydrodynamic quantity. The entropic short-time self-diffusion is proportional to an entropic mobility, a direct analog to the hydrodynamic mobility. A caging plateau following the short-time regime is stronger and more durable without hydrodynamics, and entropic drift—a gradient in volume fraction—drives particles out of their cages. The distinct long-time regime emerges when an entropic mobility gradient arising from heterogeneous distribution of particle volume drives particles out of local cages. We conclude that entropic mobility gradients produce a distinct long-time dynamical regime in confinement and that hydrodynamic interactions weaken this effect. From a statistical physics perspective, confinement restricts configurational entropy, driving up confined osmotic pressure, viscosity, and (inverse) long-time dynamics as confinement tightens. We support this claim by rescaling the volume fraction as the distance from confinement-dependent maximum packing, which collapses the data for each rheological measure onto a single curve.
REFERENCES
1.
Tolić-Nørrelykke
, I. M.
, E. L.
Munteanu
, G.
Thon
, L.
Oddershede
, and K.
Berg-Sørensen
, “Anomalous diffusion in living yeast cells
,” Phys. Rev. Lett.
93
, 078102
(2004
).2.
Banks
, D. S.
, and C.
Fradin
, “Anomalous diffusion of proteins due to molecular crowding
,” Biophys. J.
89
, 2960
–2971
(2005
). 3.
Weber
, S. C.
, A. J.
Spakowitz
, and J. A.
Theriot
, “Bacterial chromosomal loci move subdiffusively through a viscoelastic cytoplasm
,” Phys. Rev. Lett.
104
, 238102
(2010
).4.
Guo
, M.
, A. J.
Ehrlicher
, M. H.
Jensen
, M.
Renz
, J. R.
Moore
, R. D.
Goldman
, J.
Lippincott-Schwartz
, F. C.
Mackintosh
, and D. A.
Weitz
, “Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy
,” Cell
158
, 822
–832
(2014
). 5.
Stylianidou
, S.
, N. J.
Kuwada
, and P. A.
Wiggins
, “Cytoplasmic dynamics reveals two modes of nucleoid-dependent mobility
,” Biophys. J.
107
, 2684
–2692
(2015
). 6.
Reverey
, J. F.
, J. H.
Jeon
, H.
Bao
, M.
Leippe
, R.
Metzler
, and C.
Selhuber-Unkel
, “Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic Acanthamoeba castellanii
,” Sci. Rep.
5
, 1
–14
(2015
). 7.
Sabri
, A.
, X.
Xu
, D.
Krapf
, and M.
Weiss
, “Elucidating the origin of heterogeneous anomalous diffusion in the cytoplasm of mammalian cells
,” Phys. Rev. Lett.
125
, 058101
(2020
). 8.
Maheshwari
, A. J.
, A. M.
Sunol
, E.
Gonzalez
, D.
Endy
, and R. N.
Zia
, “Colloidal hydrodynamics of biological cells: A frontier spanning two fields
,” Phys. Rev. Fluids
4
, 1
–26
(2019
). 9.
Maheshwari
, A. J.
, A. M.
Sunol
, E.
Gonzalez
, D.
Endy
, and R. N.
Zia
, “Colloidal physics modeling reveals how per-ribosome productivity increases with growth rate in Escherichia coli
,” mBio (2022). 10.
Perham
, R. N.
, “Self-assembly of biological macromolecules
,” Philos. Trans. R. Soc. London, Ser. B
272
, 123
–136
(1975
).11.
Gao
, Y.
, J.
Shi
, D.
Yuan
, and B.
Xu
, “Imaging enzyme-triggered self-assembly of small molecules inside live cells
,” Nat. Commun.
3
, 1033
(2012
). 12.
Marsh
, J. A.
, and S. A.
Teichmann
, “Structure, dynamics, assembly, and evolution of protein complexes
,” Annu. Rev. Biochem.
84
, 551
–575
(2015
). 13.
Hyman
, A. A.
, C. A.
Weber
, and F.
Jülicher
, “Liquid-liquid phase separation in biology
,” Annu. Rev. Cell Dev. Biol.
30
, 39
–58
(2014
). 14.
Brangwynne
, C. P.
, P.
Tompa
, and R. V.
Pappu
, “Polymer physics of intracellular phase transitions
,” Nat. Phys.
11
, 899
–904
(2015
). 15.
Konopka
, M. C.
, I. A.
Shkel
, S.
Cayley
, M. T.
Record
, and J. C.
Weisshaar
, “Crowding and confinement effects on protein diffusion in vivo
,” J. Bacteriol.
188
, 6115
–6123
(2006
). 16.
Pinot
, M.
, F.
Chesnel
, J. Z.
Kubiak
, I.
Arnal
, F. J.
Nedelec
, and Z.
Gueroui
, “Effects of confinement on the self-organization of microtubules and motors
,” Curr. Biol.
19
, 954
–960
(2009
). 17.
Mika
, J. T.
, and B.
Poolman
, “Macromolecule diffusion and confinement in prokaryotic cells
,” Curr. Opin. Biotechnol.
22
, 117
–126
(2011
). 18.
Guo
, M.
, A. F.
Pegoraro
, A.
Mao
, E. H.
Zhou
, P. R.
Arany
, Y.
Han
, D. T.
Burnette
, M. H.
Jensen
, K. E.
Kasza
, J. R.
Moore
, F. C.
Mackintosh
, J. J.
Fredberg
, D. J.
Mooney
, J.
Lippincott-Schwartz
, and D. A.
Weitz
, “Cell volume change through water efflux impacts cell stiffness and stem cell fate
,” Proc. Natl. Acad. Sci. U.S.A.
114
, E8618
–E8627
(2017
).19.
Yang
, Y. S. S.
, K. D.
Moynihan
, A.
Bekdemir
, T. M.
Dichwalkar
, M. M.
Noh
, N.
Watson
, M.
Melo
, J.
Ingram
, H.
Suh
, H.
Ploegh
, F. R.
Stellacci
, and D. J.
Irvine
, “Targeting small molecule drugs to T cells with antibody-directed cell-penetrating gold nanoparticles
,” Biomater. Sci.
7
, 113
–124
(2019
). 20.
Li
, W.
, L.
Zhang
, X.
Ge
, B.
Xu
, W.
Zhang
, L.
Qu
, C. H.
Choi
, J.
Xu
, A.
Zhang
, H.
Lee
, and D. A.
Weitz
, “Microfluidic fabrication of microparticles for biomedical applications
,” Chem. Soc. Rev.
47
, 5646
–5683
(2018
). 21.
Schieferstein
, J. M.
, P.
Reichert
, C. N.
Narasimhan
, X.
Yang
, and P. S.
Doyle
, “Hydrogel microsphere encapsulation enhances the flow properties of monoclonal antibody crystal formulations
,” Adv. Ther.
4
, 2000216
(2021
).22.
Vaughan
, E.
, J.
DeGiulio
, and D.
Dean
, “Intracellular trafficking of plasmids for gene therapy: Mechanisms of cytoplasmic movement and nuclear import
,” Curr. Gene Ther.
6
, 671
–681
(2006
). 23.
Lenshof
, A.
, and T.
Laurell
, “Continuous separation of cells and particles in microfluidic systems
,” Chem. Soc. Rev.
39
, 1203
–1217
(2010
). 24.
Galliker
, P.
, J.
Schneider
, H.
Eghlidi
, S.
Kress
, V.
Sandoghdar
, and D.
Poulikakos
, “Direct printing of nanostructures by electrostatic autofocussing of ink nanodroplets
,” Nat. Commun.
3
, 890
(2012
). 25.
Bansal
, L.
, S.
Basu
, and S.
Chakraborty
, “Confinement suppresses instabilities in particle-laden droplets
,” Sci. Rep.
7
, 1
–8
(2017
).26.
Shang
, L.
, Y.
Cheng
, and Y.
Zhao
, “Emerging droplet microfluidics
,” Chem. Rev.
117
, 7964
–8040
(2017
). 27.
Zhu
, P.
, and L.
Wang
, “Passive and active droplet generation with microfluidics: A review
,” Lab Chip
17
, 34
–75
(2017
). 28.
Cusola
, O.
, S.
Kivistö
, S.
Vierros
, P.
Batys
, M.
Ago
, B. L.
Tardy
, L. G.
Greca
, M. B.
Roncero
, M.
Sammalkorpi
, and O. J.
Rojas
, “Particulate coatings via evaporation-induced self-assembly of polydisperse colloidal lignin on solid interfaces
,” Langmuir
34
, 5759
–5771
(2018
). 29.
Kaewpetch
, T.
, and J. F.
Gilchrist
, “Chemical versus mechanical microstructure evolution in drying colloid and polymer coatings
,” Sci. Rep.
10
, 1
–10
(2020
). 30.
Georgiev
, R. N.
, S. O.
Toscano
, W. E.
Uspal
, B.
Bet
, S.
Samin
, R.
van Roij
, and H. B.
Eral
, “Universal motion of mirror-symmetric microparticles in confined stokes flow
,” Proc. Natl. Acad. Sci. U.S.A.
117
, 21865
–21872
(2020
). 31.
Mackay
, M. E.
, “The importance of rheological behavior in the additive manufacturing technique material extrusion
,” J. Rheol.
62
, 1549
–1561
(2018
). 32.
Corker
, A.
, H. C.
Ng
, R. J.
Poole
, and E.
García-Tuǹón
, “3D printing with 2D colloids: Designing rheology protocols to predict ‘printability’ of soft-materials
,” Soft Matter
15
, 1444
–1456
(2019
). 33.
Pfeiffer
, C.
, C.
Rehbock
, D.
Hühn
, C.
Carrillo-Carrion
, D. J. D.
Aberasturi
, V.
Merk
, S.
Barcikowski
, and W. J.
Parak
, “Interaction of colloidal nanoparticles with their local environment: The (ionic) nanoenvironment around nanoparticles is different from bulk and determines the physico-chemical properties of the nanoparticles
,” J. R. Soc. Interface
11
, 20130931
(2014
). 34.
Varoqui
, R.
, and P.
Dejardin
, “Hydrodynamic thickness of adsorbed polymers
,” J. Chem. Phys.
66
, 4395
–4399
(1977
). 35.
Russel
, W. B.
, “The huggins coefficient as a means for characterizing suspended particles
,” J. Chem. Soc., Faraday Trans. 2
80
, 31
–41
(1984
). 36.
Riese
, D. O.
, G. H.
Wegdam
, W. L.
Vos
, R.
Sprik
, D.
Fenistein
, J. H.
Bongaerts
, and G.
Grübel
, “Effective screening of hydrodynamic interactions in charged colloidal suspensions
,” Phys. Rev. Lett.
85
, 5460
–5463
(2000
). 37.
Hoh
, N. J.
, and R. N.
Zia
, “Force-induced diffusion in suspensions of hydrodynamically interacting colloids
,” J. Fluid Mech.
795
, 739
–783
(2016
). 38.
Beenakker
, C. W.
, “The effective viscosity of a concentrated suspension of spheres (and its relation to diffusion)
,” Physica A
128
, 48
–81
(1984
). 39.
Medina-Noyola
, M.
, “Long-time self-diffusion in concentrated colloidal dispersions
,” Phys. Rev. Lett.
60
, 2705
–2708
(1988
). 40.
Selim
, M. S.
, M. A.
Al-Naafa
, and M. C.
Jones
, “Brownian diffusion of hard spheres at finite concentrations
,” AIChE J.
39
, 3
–16
(1993
). 41.
Brady
, J. F.
, “The long-time self-diffusivity in concentrated colloidal dispersions
,” J. Fluid Mech.
272
, 109
–133
(1994
). 42.
Parry
, B. R.
, I. V.
Surovtsev
, M. T.
Cabeen
, C. S.
O’Hern
, E. R.
Dufresne
, and C.
Jacobs-Wagner
, “The bacterial cytoplasm has glass-like properties and is fluidized by metabolic activity
,” Cell
156
, 183
–194
(2014
). 43.
Cayley
, S.
, B. A.
Lewis
, H. J.
Guttman
, and M. T.
Record
, “Characterization of the cytoplasm of Escherichia coli k-12 as a function of external osmolarity. Implications for protein-dna interactions in vivo
,” J. Mol. Biol.
222
, 281
–300
(1991
). 44.
Pusey
, P. N.
, and W. V.
Megen
, “Phase behaviour of concentrated suspensions of nearly hard colloidal spheres
,” Nature
320
, 340
–342
(1986
). 45.
van Megen
, W.
, and S. M.
Underwood
, “Glass transition in colloidal hard spheres: Measurement and mode-coupling-theory analysis of the coherent intermediate scattering function
,” Phys. Rev. E
49
, 4206
–4220
(1994
). 46.
Pusey
, P. N.
, E.
Zaccarelli
, C.
Valeriani
, E.
Sanz
, W. C.
Poon
, and M. E.
Cates
, “Hard spheres: Crystallization and glass formation
,” Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci.
367
, 4993
–5011
(2009
). 47.
Zaccarelli
, E.
, S. M.
Liddle
, and W. C.
Poon
, “On polydispersity and the hard sphere glass transition
,” Soft Matter
11
, 324
–330
(2015
). 48.
Weeks
, E. R.
, “Introduction to the colloidal glass transition
,” ACS Macro Lett.
6
, 27
–34
(2017
). 49.
Aponte-Rivera
, C.
, and R. N.
Zia
, “Simulation of hydrodynamically interacting particles confined by a spherical cavity
,” Phys. Rev. Fluids
1
, 023301
(2016
). 50.
Aponte-Rivera
, C.
, Y.
Su
, and R. N.
Zia
, “Equilibrium structure and diffusion in concentrated hydrodynamically interacting suspensions confined by a spherical cavity
,” J. Fluid Mech.
836
, 413
–450
(2018
). 51.
Gonzalez
, E.
, C.
Aponte-Rivera
, and R. N.
Zia
, “Impact of polydispersity and confinement on diffusion in hydrodynamically interacting colloidal suspensions
,” J. Fluid Mech.
925
, A35
(2021
). 52.
Aponte-Rivera
, C.
, and R. N.
Zia
, “The confined generalized Stokes–Einstein relation and its consequence on intracellular two-point microrheology,” J. Colloid Interface Sci.
609, 423–433 (2022). 53.
Holmqvist
, P.
, J. K.
Dhont
, and P. R.
Lang
, “Anisotropy of Brownian motion caused only by hydrodynamic interaction with a wall
,” Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys.
74
, 021402
(2006
). 54.
Holmqvist
, P.
, J. K.
Dhont
, and P. R.
Lang
, “Colloidal dynamics near a wall studied by evanescent wave light scattering: Experimental and theoretical improvements and methodological limitations
,” J. Chem. Phys.
126
, 044707
(2007
). 55.
Swan
, J. W.
, and J. F.
Brady
, “Simulation of hydrodynamically interacting particles near a no-slip boundary
,” Phys. Fluids
19
, 113306
(2007
). 56.
Michailidou
, V. N.
, G.
Petekidis
, J. W.
Swan
, and J. F.
Brady
, “Dynamics of concentrated hard-sphere colloids near a wall
,” Phys. Rev. Lett.
102
, 068302
(2009
). 57.
Swan
, J. W.
, and J. F.
Brady
, “Particle motion between parallel walls: Hydrodynamics and simulation
,” Phys. Fluids
22
, 103301
(2010
). 58.
Swan
, J. W.
, and J. F.
Brady
, “The hydrodynamics of confined dispersions
,” J. Fluid Mech.
687
, 254
–299
(2011
). 59.
Lele
, P. P.
, J. W.
Swan
, J. F.
Brady
, N. J.
Wagner
, and E. M.
Furst
, “Colloidal diffusion and hydrodynamic screening near boundaries
,” Soft Matter
7
, 6844
–6852
(2011
). 60.
Edmond
, K. V.
, C. R.
Nugent
, and E. R.
Weeks
, “Influence of confinement on dynamical heterogeneities in dense colloidal samples
,” Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys.
85
, 041401
(2012
). 61.
Mittal
, J.
, J. R.
Errington
, and T. M.
Truskett
, “Thermodynamics predicts how confinement modifies the dynamics of the equilibrium hard-sphere fluid
,” Phys. Rev. Lett.
96
, 177804
(2006
). 62.
Mittal
, J.
, J. R.
Errington
, and T. M.
Truskett
, “Does confining the hard-sphere fluid between hard walls change its average properties?
,” J. Chem. Phys.
126
, 244708
(2007
). 63.
Mittal
, J.
, T. M.
Truskett
, J. R.
Errington
, and G.
Hummer
, “Layering and position-dependent diffusive dynamics of confined fluids
,” Phys. Rev. Lett.
100
, 145901
(2008
). 64.
Goel
, G.
, W. P.
Krekelberg
, M. J.
Pond
, J.
Mittal
, V. K.
Shen
, J. R.
Errington
, and T. M.
Truskett
, “Available states and available space: Static properties that predict self-diffusivity of confined fluids
,” J. Stat. Mech.: Theory Exp.
2009
, P04006
(2009
). 65.
Weiss
, M.
, M.
Elsner
, F.
Kartberg
, and T.
Nilsson
, “Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells
,” Biophys. J.
87
, 3518
–3524
(2004
). 66.
McGuffee
, S. R.
, and A. H.
Elcock
, “Diffusion, crowding & protein stability in a dynamic molecular model of the bacterial cytoplasm
,” PLoS Comput. Biol.
6
, e1000694
(2010
). 67.
Ando
, T.
, and J.
Skolnick
, “Crowding and hydrodynamic interactions likely dominate in vivo macromolecular motion
,” Proc. Natl. Acad. Sci.
107
, 18457
–18462
(2010
). 68.
Weber
, S. C.
, J. A.
Theriot
, and A. J.
Spakowitz
, “Subdiffusive motion of a polymer composed of subdiffusive monomers
,” Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys.
82
, 011913
(2010
).69.
Shinar
, T.
, M.
Mana
, F.
Piano
, and M. J.
Shelley
, “A model of cytoplasmically driven microtubule-based motion in the single-celled Caenorhabditis elegans embryo
,” Proc. Natl. Acad. Sci.
108
, 10508
–10513
(2011
). 70.
Shelley
, M. J.
, “The dynamics of microtubule/motor-protein assemblies in biology and physics
,” Annu. Rev. Fluid Mech.
48
, 487
–506
(2016
). 71.
Chow
, E.
, and J.
Skolnick
, “Effects of confinement on models of intracellular macromolecular dynamics
,” Proc. Natl. Acad. Sci.
112
, 14846
–14851
(2015
). 72.
Foster
, P. J.
, S.
Furthauer
, M. J.
Shelley
, and D. J.
Needleman
, “Active contraction of microtubule networks
,” eLife
4
, 1
–21
(2015
). 73.
Nazockdast
, E.
, A.
Rahimian
, D.
Needleman
, and M.
Shelley
, “Cytoplasmic flows as signatures for the mechanics of mitotic positioning
,” Mol. Biol. Cell
28
, 3261
–3270
(2017
). 74.
Saintillan
, D.
, M. J.
Shelley
, and A.
Zidovska
, “Extensile motor activity drives coherent motions in a model of interphase chromatin
,” Proc. Natl. Acad. Sci. U.S.A.
115
, 11442
–11447
(2018
). 75.
Li
, J.
, X.
Jiang
, A.
Singh
, O. G.
Heinonen
, J. P.
Hernández-Ortiz
, and J. J.
de Pablo
, “Structure and dynamics of hydrodynamically interacting finite-size Brownian particles in a spherical cavity: Spheres and cylinders
,” J. Chem. Phys.
152
, 204109
(2020
). 76.
Chong
, J. S.
, E. B.
Christiansen
, and A. D.
Baer
, “Rheology of concentrated suspensions
,” J. Appl. Polym. Sci.
15
, 2007
–2021
(1971
). 77.
Poslinski
, A. J.
, M. E.
Ryan
, R. K.
Gupta
, S. G.
Seshadri
, and F. J.
Frechette
, “Rheological behavior of filled polymeric systems II. The effect of a bimodal size distribution of particulates
,” J. Rheol.
32
, 751
–771
(1988
). 78.
Rodriguez
, B. E.
, E. W.
Kaler
, and M. S.
Wolfe
, “Binary mixtures of monodisperse latex dispersions. 2. Viscosity
,” Langmuir
8
, 2382
–2389
(1992
). 79.
Yang
, X.
, C.
Liu
, Y.
Li
, F.
Marchesoni
, P.
Hänggi
, and H. P.
Zhang
, “Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels
,” Proc. Natl. Acad. Sci. U.S.A.
114
, 9564
–9569
(2017
). 80.
Einstein
, A.
, “On the movement of small particles suspended in stationary liquids required by the molecular-kinetic theory of heat
,” Ann. Phys.
322
, 549
–560
(1905
). 81.
Sutherland
, W.
, “LXXV. A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin
,” London Edinburgh Dublin Philos. Mag. J. Sci.
9
, 781
–785
(1905
). 82.
Einstein
, A.
, “On the theory of Brownian movement
,” Ann. Phys.
19
, 371
–381
(1906
). 83.
Einstein
, A.
, “A new determination of molecular dimensions
,” Ann. Phys.
324
, 289
–306
(1906
). 84.
Einstein
, A.
, “Theoretical observations on the Brownian motion
,” Z. Elektrochem.
13
, 41
–42
(1907
). 85.
Einstein
, A.
, “The elementary theory of Brownian motion
,” Z. Elektrochem.
14
, 235
–239
(1908
). 86.
Batchelor
, G. K.
, “Brownian diffusion of particles with hydrodynamic interaction
,” J. Fluid Mech.
74
, 1
–29
(1976
). 87.
Batchelor
, G. K.
, “The effect of Brownian motion on the bulk stress in a suspension of spherical particles
,” J. Fluid Mech.
83
, 97
–117
(1977
). 88.
Batchelor
, G. K.
, “Diffusion in a dilute polydisperse system of interacting spheres
,” J. Fluid Mech.
131
, 155
–175
(1983
). 89.
Rallison
, J. M.
, and E. J.
Hinch
, “The effect of particle interactions on dynamic light scattering from a dilute suspension
,” J. Fluid Mech.
167
, 131
–168
(1986
). 90.
Johari
, C. P.
, and M.
Goidstein
, “Viscous liquids and the glass transition. II. Secondary relaxations in glasses of rigid molecules
,” J. Chem. Phys.
53
, 2372
–2388
(1970
). 91.
Weeks
, E. R.
, J. C.
Crocker
, A. C.
Levitt
, A.
Schofield
, and D. A.
Weitz
, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition
,” Science
287
, 627
–631
(2000
). 92.
Peng
, X.
, J. G.
Wang
, Q.
Li
, D.
Chen
, R. N.
Zia
, and G. B.
McKenna
, “Exploring the validity of time-concentration superposition in glassy colloids: Experiments and simulations
,” Phys. Rev. E
98
, 062602
(2018
).93.
Wang
, J. G.
, Q.
Li
, X.
Peng
, G. B.
McKenna
, and R. N.
Zia
, “‘Dense diffusion’ in colloidal glasses: Short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics
,” Soft Matter
16
, 7370
–7389
(2020
). 94.
Wang
, J. G.
, and R. N.
Zia
, “Vitrification is a spontaneous non-equilibrium transition driven by osmotic pressure
,” J. Phys.: Condens. Matter
33
, 184002
(2021
).95.
Dolata
, B. E.
, and R. N.
Zia
, “Non-equilibrium pair interactions in colloidal dispersions
,” J. Fluid Mech.
836
, 694
–739
(2018
). 96.
Gillespie
, T.
, “Application of the hydrodynamic-structural theory of non-Newtonian flow to suspensions which exhibit moderate shear thickening with particular reference to ‘dilatant’ vinyl plastisols
,” J. Colloid Interface Sci.
22
, 554
–562
(1966
). 97.
Strivens
, T. A.
, “The shear thickening effect in concentrated dispersion systems
,” J. Colloid Interface Sci.
57
, 476
–487
(1976
). 98.
Russel
, W. B.
, “Review of the role of colloidal forces in the rheology of suspensions
,” J. Rheol.
24
, 287
–317
(1980
). 99.
Woodcock
, L. V.
, “Origins of shear dilatancy and shear thickening phenomena
,” Chem. Phys. Lett.
111
, 455
–461
(1984
). 100.
Heyes
, D. M.
, “Shear thinning of dense suspensions modelled by Brownian dynamics
,” Phys. Lett. A
132
, 399
–402
(1988
). 101.
Bossis
, G.
, and J. F.
Brady
, “The rheology of Brownian suspensions
,” J. Chem. Phys.
91
, 1866
–1874
(1989
). 102.
Foss
, D. R.
, and J. F.
Brady
, “Brownian dynamics simulation of hard-sphere colloidal dispersions
,” J. Rheol.
44
, 629
–651
(2000
). 103.
Foss
, D. R.
, and J. F.
Brady
, “Structure, diffusion and rheology of Brownian suspensions by Stokesian dynamics simulation
,” J. Fluid Mech.
407
, 167
–200
(2000
). 104.
Carpen
, I. C.
, and J. F.
Brady
, “Microrheology of colloidal dispersions by Brownian dynamics simulations
,” J. Rheol.
49
, 1483
–1502
(2005
). 105.
Squires
, T. M.
, and J. F.
Brady
, “A simple paradigm for active and nonlinear microrheology
,” Phys. Fluids
17
, 1
–21
(2005
). 106.
Zia
, R. N.
, and J. F.
Brady
, “Single-particle motion in colloids: Force-induced diffusion
,” J. Fluid Mech.
658
, 188
–210
(2010
). 107.
Zia
, R. N.
, and J. F.
Brady
, “Microviscosity, microdiffusivity, and normal stresses in colloidal dispersions
,” J. Rheol.
56
, 1175
–1208
(2012
). 108.
Chu
, H. C. W.
, and R. N.
Zia
, “Active microrheology of hydrodynamically interacting colloids: Normal stresses and entropic energy density
,” J. Rheol.
60
, 755
–781
(2016
). 109.
Chu
, H. C. W.
, and R. N.
Zia
, “The non-Newtonian rheology of hydrodynamically interacting colloids via active, nonlinear microrheology
,” J. Rheol.
61
, 551
–574
(2017
). 110.
Chu
, H. C.
, and R. N.
Zia
, “Toward a nonequilibrium Stokes–Einstein relation via active microrheology of hydrodynamically interacting colloidal dispersions
,” J. Colloid Interface Sci.
539
, 388
–399
(2019
). 111.
Huang
, D. E.
, and R. N.
Zia
, “Sticky, active microrheology: Part 1. Linear-response
,” J. Colloid Interface Sci.
554
, 580
–591
(2019
). 112.
Huang
, D. E.
, and R. N.
Zia
, “Sticky-probe active microrheology: Part 2. The influence of attractions on non-Newtonian flow
,” J. Colloid Interface Sci.
562
, 293
–306
(2020
). 113.
Mason
, T. G.
, and D. A.
Weitz
, “Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids
,” Phys. Rev. Lett.
74
, 1250
–1253
(1995
). 114.
Nägele
, G.
, and J.
Bergenholtz
, “Linear viscoelasticity of colloidal mixtures
,” J. Chem. Phys.
108
, 9893
–9904
(1998
).115.
Banchio
, A. J.
, G.
Nägele
, and J.
Bergenholtz
, “Viscoelasticity and generalized Stokes–Einstein relations of colloidal dispersions
,” J. Chem. Phys.
111
, 8721
–8740
(1999
). 116.
Squires
, T. M.
, and T. G.
Mason
, “Fluid mechanics of microrheology
,” Annu. Rev. Fluid Mech.
42
, 413
–438
(2010
). 117.
Khair
, A. S.
, and J. F.
Brady
, “Microrheology of colloidal dispersions: Shape matters
,” J. Rheol.
52
, 165
–196
(2008
). 118.
Zia
, R. N.
, and J. F.
Brady
, “Stress development, relaxation, and memory in colloidal dispersions: Transient nonlinear microrheology
,” J. Rheol.
57
, 457
–492
(2013
). 119.
Zia
, R. N.
, “Active and passive microrheology: Theory and simulation
,” Annu. Rev. Fluid Mech.
50
, 371
–405
(2018
). 120.
Ma
, Y.
, X.
Wang
, H.
Liu
, L.
Wei
, and L.
Xiao
, “Recent advances in optical microscopic methods for single-particle tracking in biological samples
,” Anal. Bioanal. Chem.
411
, 4445
–4463
(2019
). 121.
Tough
, R. J. A.
, and C. B. D.
Broeck
, “Diffusion within a sphere; a non-Gaussian statistical model for particle displacements in a dense colloidal suspension
,” Physica A
157
, 769
–796
(1989
). 122.
Saintillan
, D.
, M. J.
Shelley
, and A.
Zidovska
, “Extensile motor activity drives coherent motions in a model of interphase chromatin
,” Proc. Natl. Acad. Sci.
115
, 11442
–11447
(2018
). 123.
MacPherson
, Q.
, B.
Beltran
, and A. J.
Spakowitz
, “Bottom–up modeling of chromatin segregation due to epigenetic modifications
,” Proc. Natl. Acad. Sci. U.S.A.
115
, 12739
–12744
(2018
). 124.
Heyes
, D. M.
, and J. R.
Melrose
, “Brownian dynamics simulations of model hard-sphere suspensions
,” J. Non-Newtonian Fluid Mech.
46
, 1
–28
(1993
). 125.
Schaertl
, W.
, and H.
Sillescu
, “Brownian dynamics of polydisperse colloidal hard spheres: Equilibrium structures and random close packings
,” J. Stat. Phys.
77
, 1007
–1025
(1994
). 126.
Németh
, Z. T.
, and H.
Löwen
, “Freezing and glass transition of hard spheres in cavities
,” Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top.
59
, 6824
–6829
(1999
).127.
Zhang
, D. Z.
, and A.
Prosperetti
, “Ensemble phase-averaged equations for bubbly flows
,” Phys. Fluids
6
, 2956
–2970
(1994
). 128.
Man
, W.
, A.
Donev
, F. H.
Stillinger
, M. T.
Sullivan
, W. B.
Russel
, D.
Heeger
, S.
Inati
, S.
Torquato
, and P. M.
Chaikin
, “Experiments on random packings of ellipsoids
,” Phys. Rev. Lett.
94
, 1
–4
(2005
). 129.
Dolata
, B. E.
, and R. N.
Zia
, “Heterogeneous dispersions as microcontinuum fluids
,” J. Fluid Mech.
888
, A28
(2020
). 130.
Zia
, R. N.
, B. J.
Landrum
, and W. B.
Russel
, “A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski’s ratchet
,” J. Rheol.
58
, 1121
–1157
(2014
). 131.
Johnson
, L. C.
, R. N.
Zia
, E.
Moghimi
, and G.
Petekidis
, “Influence of structure on the linear response rheology of colloidal gels
,” J. Rheol.
63
, 583
–608
(2019
). 132.
Ryu
, B. K.
, S. M.
Fenton
, T. T. D.
Nguyen
, M.
Helgeson
, and R. N.
Zia
, “Modeling colloidal interactions that predict equilibrium and non-equilibrium states
,” J. Chem. Phys.
156
, 224101
(2022
). 133.
Hofmann
, J. L.
, T. S.
Yang
, A. M.
Sunol
, and R. N.
Zia
, “Protein-protein interaction valency regulates prokaryotic protein synthesis via colloidal-scale transport” (unpublished).134.
Langevin
, P.
, “Sur la théorie du mouvement brownien
,” C.R. Acad. Sci.
146
, 530
–533
(1908
).135.
Milatz
, J. M.
, and L. S.
Ornstein
, “Properties of the fortuitous force in the Einstein–Langevin equation
,” Physica
7
, 793
–801
(1940
). 136.
Bixon
, M.
, and R.
Zwanzig
, “Boltzmann-langevin equation and hydrodynamic fluctuations
,” Phys. Rev.
187
, 267
–272
(1969
). 137.
Ermak
, D. L.
, and J. A.
McCammon
, “Brownian dynamics with hydrodynamic interactions
,” J. Chem. Phys.
69
, 1352
–1360
(1978
). 138.
Rintoul
, M. D.
, and S.
Torquato
, “Computer simulations of dense hard-sphere systems
,” J. Chem. Phys.
105
, 9258
–9265
(1996
). 139.
Peng
, Y.
, W.
Chen
, T. M.
Fischer
, D. A.
Weitz
, and P.
Tong
, “Short-time self-diffusion of nearly hard spheres at an oil-water interface
,” J. Fluid Mech.
618
, 243
–261
(2009
). 140.
Kämmerer
, S.
, W.
Kob
, and R.
Schilling
, “Dynamics of the rotational degrees of freedom in a supercooled liquid of diatomic molecules
,” Phys. Rev. E: Stat., Phys., Plasmas, Fluids, Relat. Interdiscip. Top.
56
, 5450
–5461
(1997
).141.
Michele
, C. D.
, and D.
Leporini
, “Viscous flow and jump dynamics in molecular supercooled liquids. II. Rotations
,” Phys. Rev. E
63
, 036702
(2001
).142.
Hunter
, G. L.
, K. V.
Edmond
, M. T.
Elsesser
, and E. R.
Weeks
, “Tracking rotational diffusion of colloidal clusters
,” Opt. Express
19
, 17189
(2011
). 143.
Brady
, J. F.
, “Brownian motion, hydrodynamics, and the osmotic pressure
,” J. Chem. Phys.
98
, 3335
–3341
(1993
). 144.
Strating
, P.
, “The stress tensor in colloidal suspensions
,” J. Chem. Phys.
103
, 10226
–10237
(1995
). 145.
Batchelor
, G. K.
, “The stress system in a suspension of force-free particles
,” J. Fluid Mech.
41
, 545
–570
(1970
). 146.
Sierou
, A.
, and J. F.
Brady
, “Accelerated Stokesian dynamics simulations
,” J. Fluid Mech.
448
, 115
–146
(2001
). 147.
Banchio
, A. J.
, and J. F.
Brady
, “Accelerated Stokesian dynamics: Brownian motion
,” J. Chem. Phys.
118
, 10323
–10332
(2003
). 148.
Percus
, J. K.
, and G. J.
Yevick
, “Analysis of classical statistical mechanics by means of collective coordinates
,” Phys. Rev.
110
, 1
–13
(1958
). 149.
Kirkwood
, J. G.
, “The general theory of irreversible processes in solutions of macromolecules
,” J. Polym. Sci.
XII
, 1
–14
(1954
). 150.
Doi
, M.
, “Variational principle for the kirkwood theory for the dynamics of polymer solutions and suspensions
,” J. Chem. Phys.
79
, 5080
–5087
(1983
). 151.
Hofmann
, J. L.
, A. J.
Maheshwari
, A. M.
Sunol
, D.
Endy
, and R. N.
Zia
, “Ultra-weak protein-protein interactions can modulate proteome-wide searching and binding,” bioRxiv (2022).152.
Elowitz
, M. B.
, M. G.
Surette
, P.-E.
Wolf
, J. B.
Stock
, and S.
Leibler
, “Protein mobility in the cytoplasm of Escherichia coli
,” J. Bacteriol.
181
, 197
–203
(1999
). 153.
Green
, M. S.
, “Markoff random processes and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids
,” J. Chem. Phys.
22
, 398
–413
(1954
).154.
Kubo
, R.
, “Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems
,” J. Phys. Soc. Jpn.
12
, 570
–586
(1957
). 155.
Bergenholtz
, J.
, J. F.
Brady
, and M.
Vicic
, “The non-Newtonian rheology of dilute colloidal suspensions
,” J. Fluid Mech.
456
, 239
–275
(2002
). 156.
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
). 157.
Cichocki
, B.
, and B. U.
Felderhof
, “Linear viscoelasticity of semidilute hard-sphere suspensions
,” Phys. Rev. A
43
, 5405
–5411
(1991
). 158.
Brady
, J. F.
, “The rheological behavior of concentrated colloidal dispersions
,” J. Chem. Phys.
99
, 567
–581
(1993
). 159.
Foss
, D. R.
, “Rheological behavior of colloidal suspensions: The effects of hydrodynamic interactions
” Ph.D. thesis, California Institute of Technology, 1999. 160.
Swaroop
, M.
, “The bulk viscosity of suspensions
,” Ph.D. thesis, California Institute of Technology, 2010. 161.
Oseen
, C. W.
, Neuere Methoden und Ergebnisse in der Hydrodynamik
(Akademische Verlagsgesellschaft
, Leipzig, Germany
, 1927
).162.
Urrutia
, I.
, “Two hard spheres in a spherical pore: Exact analytic results in two and three dimensions
,” J. Stat. Phys.
131
, 597
–611
(2008
). 163.
Urrutia
, I.
, and L.
Szybisz
, “Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in d dimension
,” J. Math. Phys.
51
, 033303
(2010
). 164.
Urrutia
, I.
, “Two hard spheres in a pore: Exact statistical mechanics for different shaped cavities
,” J. Chem. Phys.
133
, 104503
(2010
). 165.
Zhang
, B.
, and X.
Cheng
, “Structures and dynamics of glass-forming colloidal liquids under spherical confinement
,” Phys. Rev. Lett.
116
, 098302
(2016
).166.
Chen
, D.
, and G. B.
McKenna
, “Deep glassy state dynamic data challenge glass models: Configurational entropy models
,” J. Non-Cryst. Solids
566
, 120871
(2021
). 167.
Furnas
, C. C.
, “Mathematical relations for beds of broken solids of maximum density
,” Ind. Eng. Chem.
23
, 1052
–1058
(1931
). 168.
Wang
, M.
, and J. F.
Brady
, “Constant stress and pressure rheology of colloidal suspensions
,” Phys. Rev. Lett.
115
, 158301
(2015
).169.
Desmond
, K. W.
, and E. R.
Weeks
, “Random close packing of disks and spheres in confined geometries
,” Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys.
80
, 051305
(2009
). 170.
Bremer
, H.
, and P. P.
Dennis
, “Modulation of chemical composition and other parameters of the cell at different exponential growth rates
,” EcoSal Plus
3
, ecosal.5.2.3
(2008
). 171.
Amiad-Pavlov
, D.
, D.
Lorber
, G.
Bajpai
, A.
Reuveny
, F.
Roncato
, R.
Alon
, S.
Safran
, and T.
Volk
, “Live imaging of chromatin distribution reveals novel principles of nuclear architecture and chromatin compartmentalization
,” Sci. Adv.
7
, 6251
–6253
(2021
). 172.
Lang
, F.
, “Mechanisms and significance of cell volume regulation
,” J. Am. Coll. Nutr.
26
, 613S
–623S
(2007
). 173.
Adar
, R. M.
, and S. A.
Safran
, “Active volume regulation in adhered cells
,” Proc. Natl. Acad. Sci.
117
, 5604
–5609
(2020
). 174.
Yan
, G.
, S.
Monnier
, M.
Mouelhi
, and T.
Dehoux
, “Probing molecular crowding in compressed tissues with brillouin light scattering
,” Proc. Natl. Acad. Sci.
119
, e2113614119
(2022
). 175.
Hunter
, G. L.
, K. V.
Edmond
, and E. R.
Weeks
, “Boundary mobility controls glassiness in confined colloidal liquids
,” Phys. Rev. Lett.
112
, 218302
(2014
). 176.
Crocker
, J. C.
, M. T.
Valentine
, E. R.
Weeks
, T.
Gisler
, P. D.
Kaplan
, A. G.
Yodh
, and D. A.
Weitz
, “Two-point microrheology of inhomogeneous soft materials
,” Phys. Rev. Lett.
85
, 888
–891
(2000
). 177.
Crocker
, J. C.
, and B. D.
Hoffman
, “Multiple-particle tracking and two-point microrheology in cells
,” Methods Cell Biol.
83
, 141
–178
(2007
).178.
Williams
, I.
, E. C.
Oğuz
, P.
Bartlett
, H.
Löwen
, and C. P.
Royall
, “Direct measurement of osmotic pressure via adaptive confinement of quasi hard disc colloids
,” Nat. Commun.
4
, 2555
(2013
).179.
Jeffrey
, D. J.
, and Y.
Onishi
, “Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow
,” J. Fluid Mech.
139
, 261
–290 (1984
). 180.
Zia
, R. N.
, J. W.
Swan
, and Y.
Su
, “Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Force, torque, translation, and rotation
,” J. Chem. Phys.
143
, 224901
(2015
). 181.
Dolata
, B. E.
, “ Micromechanical modeling of heterogeneous dispersions
,” Ph.D. thesis, Cornell University, 2019. 182.
See supplementary material at https://www.scitation.org/doi/suppl/10.1122/8.0000520 for the supplementary figures discussed throughout the paper.
© 2023 The Society of Rheology.
2023
The Society of Rheology
You do not currently have access to this content.