We consider placing a rigid spherical particle into a binary fluid mixture in the homogeneous phase near the demixing critical point. The particle surface is assumed to have a short-range interaction with each mixture component and to attract one component more than the other. Owing to large osmotic susceptibility, the adsorption layer, where the preferred component is more concentrated, can be of significant thickness. This causes a particle motion under an imposed composition gradient. Thus, diffusiophoresis emerges from a mechanism which has not been considered so far. We calculate how the mobility depends on the temperature and particle size.
References
1.
B. V.
Derjaguin
, S. S.
Dukhin
, and V. V.
Koptelova
, “Capillary osmosis through porous partitions and properties of boundary layers of solutions
,” J. Coll. Interface Sci.
38
, 584
–595
(1972
).2.
J. L.
Anderson
, M. E.
Lowell
, and D. C.
Prieve
, “Motion of a particle generated by chemical gradients part 1. Non-electrolytes
,” J. Fluid Mech.
117
, 107
–121
(1982
).3.
J. L.
Anderson
and D. C.
Prieve
, “Diffusiophoresis: Migration of colloidal particles in gradients of solute concentration
,” Sep. Purif. Methods
13
, 67
–103
(1984
).4.
D. C.
Prieve
and R.
Roman
, “Diffusiophoresis of a rigid sphere through a viscous electrolyte solution
,” J. Chem. Soc., Faraday Trans. 2
83
, 1287
–1306
(1987
).5.
J. L.
Anderson
, “Colloid transport by interfacial forces
,” Ann. Rev. Fluid Mech.
21
, 61
–99
(1989
).6.
P. O.
Staffeld
and J. A.
Quinn
, “Diffusion-induced banding of colloid particles via diffusiophoresis: 2. Non-electrolyte
,” J. Coll. Interface Sci.
130
, 88
–100
(1989
).7.
B.
Abécassis
, C.
Cottin-Bizonne
, C.
Ybert
, A.
Adjari
, and L.
Bocquet
, “Osmotic manipulation of particles for microfluidic applications
,” New J. Phys.
11
, 075022
(2009
).8.
G.
Volpe
, I.
Buttinoni
, D.
Vogt
, H.-J.
Kümmerer
, and C.
Bechinger
, “Microswimmers in patterned environments
,” Soft Matter
7
, 8810
(2011
).9.
C.
Lee
, C.
Cottin-Bizonne
, A.-L.
Biance
, P.
Jpseph
, L.
Bocquet
, and C.
Ybert
, “Osmotic flow through fully permeable nanochannels
,” Phys. Rev. Lett.
112
, 244501
(2014
).10.
A.
Kar
, T.-Y.
Chang
, I. O.
Riviera
, A.
Sen
, and D.
Velegol
, “Enhanced transport into and out of dead-end pores
,” ACS Nano
9
, 746
–753
(2015
).11.
S.
Shin
, E.
Urn
, B.
Sabass
, J. T.
Auit
, M.
Rahimi
, P. B.
Warren
, and H. A.
Stone
, “Size-dependent control of colloid transport via solute gradients in dead-end channels
,” Proc. Natl. Acad. Sci. U. S. A.
113
, 257
–261
(2016
).12.
H. J.
Keh
, “Diffusiophoresis of charged particles and diffusioosmosis of electrolyte solutions
,” Curr. Opin. Colloid Interface Sci.
24
, 13
–22
(2016
).13.
D.
Velegol
, A.
Garg
, R.
Gusha
, A.
Kar
, and M.
Kumar
, “Origins of concentration gradients for diffusiophoresis
,” Soft Matter
12
, 4686
–4703
(2016
).14.
S.
Marbach
and L.
Bocquet
, “Osmosis, from molecular insights to large-scale applications
,” Chem. Soc. Rev.
48
, 3102
–3144
(2019
).15.
S.
Shin
, “Diffusiophoretic separation of colloids in microfluidic flows
,” Phys. Fluids
32
, 101302
(2020
).16.
S.
Ramírez-Hinestrosa
and D.
Frenkel
, “Challenges in modelling diffusiophoretic transport
,” Eur. Phys. J. B
94
, 199
(2021
).17.
P. M.
Vinze
, A.
Choudhary
, and S.
Pushpavanam
, “Motion of an active particle in a linear concentration gradient
,” Phys. Fluids
33
, 032011
(2021
).18.
R.
Okamoto
, Y.
Fujitani
, and S.
Komura
, “Drag coefficient of a rigid spherical particle in a near-critical binary fluid mixture
,” J. Phys. Soc. Jpn.
82
, 084003
(2013
).19.
A.
Furukawa
, A.
Gambassi
, S.
Dietrich
, and H.
Tanaka
, “Nonequilibrium critical Casimir effect in binary fluids
,” Phys. Rev. Lett.
111
, 055701
(2013
).20.
J. W.
Cahn
, “Critical point wetting
,” J. Chem. Phys.
66
, 3667
–3672
(1977
).21.
D.
Beysens
and S.
Leibler
, “Observation of an anomalous adsorption in a critical binary mixture
,” J. Phys. Lett.
43
, 133
–136
(1982
).22.
M. N.
Binder
, “Critical behavior at surfaces
,” in Phase Transitions and Critical Phenomena VIII
, edited by C.
Domb
and J.
Lebowitz
(Academic
, London
, 1983
).23.
D.
Beysens
and D.
Estève
, “Adsorption phenomena at the surface of silica spheres in a binary liquid mixture
,” Phys. Rev. Lett.
54
, 2123
–2126
(1985
).24.
R.
Holyst
and A.
Poniewierski
, “Wetting on a spherical surface
,” Phys. Rev. B
36
, 5628
–5630
(1987
).25.
H. W.
Diehl
, “The theory of boundary critical phenomena
,” Int. J. Mod. Phys. B
11
, 3503
–3523
(1997
).26.
D.
Beysens
, “Brownian motion in strongly fluctuating liquid
,” Thermodyn. Interface Fluid Mech.
3
, 1
–8
(2019
).27.
Y.
Fujitani
, “Suppression of viscosity enhancement around a Brownian particle in a near-critical binary fluid mixture
,” J. Fluid Mech.
907
, A21
(2021
).28.
S.
Yabunaka
and Y.
Fujitani
, “Drag coefficient of a rigid spherical particle in a near-critical binary fluid mixture, beyond the regime of the Gaussian model
,” J. Fluid Mech.
886
, A2
(2020
).29.
M. E.
Fisher
and H.
Au-Yang
, “Critical wall perturbations and a local free energy functional
,” Physica A
101
, 255
–264
(1980
).30.
R.
Okamoto
and A.
Onuki
, “Casimir amplitude and capillary condensation of near-critical binary fluids between parallel plates: Renormalized local functional theory
,” J. Chem. Phys.
136
, 114704
(2012
).31.
S.
Yabunaka
and A.
Onuki
, “Critical adsorption profiles around a sphere and a cylinder in a fluid at criticality: Local functional theory
,” Phys. Rev. E
96
, 032127
(2017
).32.
S.
Yabunaka
, R.
Okamoto
, and A.
Onuki
, “Hydrodynamics in bridging and aggregation of two colloidal particles in a near-critical binary mixture
,” Soft Matter
11
, 5738
–5747
(2015
).33.
Y.
Fujitani
, “Undulation amplitude of a fluid membrane in a near-critical binary fluid mixture calculated beyond the Gaussian model supposing weak preferential attraction
,” J. Phys. Soc. Jpn.
86
, 044602
(2017
).34.
A.
Pelisetto
and E.
Vicari
, “Critical phenomena and renormalization-group theory
,” Phys. Rep.
368
, 549
–727
(2002
).35.
S.
Yabunaka
and Y.
Fujitani
, “Isothermal transport of a near-critical binary fluid mixture through a capillary tube with the preferential adsorption
,” arXiv:2105.00466.36.
P. C.
Hohenberg
and B. I.
Halperin
, “Theory of dynamic critical phenomena
,” Rev. Mod. Phys.
49
, 435
–479
(1977
).37.
A.
Onuki
, Phase Transition Dynamics
(Cambridge University Press
, Cambridge
, 2002
), Chap. VI A.38.
A.
Onuki
, “Dynamic equations and bulk viscosity near the gas-liquid critical point
,” Phys. Rev. E
55
, 403
–420
(1997
).39.
K.
Kawasaki
, “Kinetic equations and time correlation functions of critical fluctuations
,” Ann. Phys.
61
, 1
–56
(1970
).40.
J. V.
Sengers
, “Transport properties near critical points
,” Int. J. Thermophys.
6
, 203
–232
(1985
).41.
G. G.
Stokes
, “On the effect of the internal friction of fluid on the motion of pendulums
,” Trans. Cambridge Philos. Soc.
9
, 8
–93
(1851
).42.
W.
Sutherland
, “A dynamical theory of diffusion for nonelectrolytes and the molecular mass of albumin
,” Philos. Mag.
9
, 781
–785
(1905
).43.
A.
Einstein
, “Über die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen
,” Ann. Phys.
322
, 549
–560
(1905
).44.
Y.
Fujitani
, “Connection of fields across the interface in the fluid particle dynamics method for colloidal dispersion
,” J. Phys. Soc. Jpn.
76
, 064401
(2007
).45.
S. Z.
Mirzaev
, R.
Behrends
, T.
Heimburg
, J.
Haller
, and U.
Kaatze
, “Critical behavior of 2,6-dimethylpyridine-water: Measurements of specific heat, dynamic light scattering, and shear viscosity
,” J. Chem. Phys.
124
, 144517
(2006
).46.
H. L.
Swinney
and D. L.
Henry
, “Dynamics of fluids near the critical point: Decay rate of order-parameter fluctuations
,” Phys. Rev. A
8
, 2586
–2617
(1973
).47.
N.
Sharifi-Mood
, J.
Koplik
, and C.
Maldarelli
, “Molecular dynamics simulation of the motion of colloidal nanoparticles in a solute concentration gradient and a comparison to the continuum limit
,” Phys. Rev. Lett.
111
, 184501
(2013
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
