We study isothermal transport of a binary fluid mixture, which lies in the homogeneous phase near the demixing critical point, through a capillary tube. A short-range interaction is assumed between each mixture component and the tube's wall surface, which usually attracts one component more than the other. The resulting preferential adsorption becomes significant owing to large osmotic susceptibility. The mixture flowing out of the tube is rich in the preferred component when flow is driven by the pressure difference between the reservoirs. When flow is driven by the mass-fraction difference, the total mass flow occurs in the presence of the preferential adsorption. These phenomena can be regarded as cross-effects linked by the reciprocal relation. The latter implies that diffusioosmosis arises from the free energy of the bulk of the mixture not involving the surface potential, unlike usual diffusioosmosis far from the critical point. We also study these phenomena numerically by using the hydrodynamics based on the coarse-grained free-energy functional, which was previously obtained to reveal near-critical static properties, and using material constants that were previously obtained in some experimental studies. Influence of the critical enhancement of the transport coefficients is found to be negligible because of off-critical composition in the tube. It is also shown that the conductance, or the total mass flow rate under a given mass-fraction difference, can change non-monotonically with the temperature. The change is well expected to be large enough to be detected experimentally.
References
1.
J. W.
Cahn
, “Critical point wetting
,” J. Chem. Phys.
66
, 3667
(1977
).2.
D.
Beysens
and D.
Estève
, “Adsorption phenomena at the surface of silica spheres in a binary liquid mixture
,” Phys. Rev. Lett.
54
, 2123
(1985
).3.
D.
Beysens
and S.
Leibler
, “Observation of an anomalous adsorption in a critical binary mixture
,” J. Phys. Lett.
43
, 133
–136
(1982
).4.
D.
Bonn
and D.
Ross
, “Wetting transitions
,” Rep. Prog. Phys.
64
, 1085
–1163
(2001
).5.
M. N.
Binder
, “Critical behavior at surfaces
,” in Phase Transitions and Critical Phenomena VIII
(Academic
, London
, 1983
).6.
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
).7.
A.
Furukawa
, A.
Gambassi
, S.
Dietrich
, and H.
Tanaka
, “Nonequilibrium critical Casimir effect in binary fluids
,” Phys. Rev. Lett.
111
, 055701
(2013
).8.
A.
Onuki
, Phase Transition Dynamics
(Cambridge University Press
, 2002
), Chap. 6.1.2.9.
K.
Kawasaki
, “Kinetic equations and time correlation functions of critical fluctuations
,” Ann. Phys. (N.Y.)
61
(1
), 1
(1970
).10.
T.
Ohta
, “Selfconsistent calculation of dynamic critical exponents for classical liquid
,” Prog. Theor. Phys.
54
, 1566
(1975
).11.
M. E.
Fisher
and H.
Au-Yang
, “Critical wall perturbations and a local free energy functional
,” Phys. A
101
, 255
(1980
).12.
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
).13.
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
).14.
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
(2015
).15.
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
).16.
S. R.
de Groot
and G.
Mazur
, Non-Equilibrium Thermodynamics
(Dover
, New York
, 1984
), Chap. XV, Sec. IV.17.
S.
Samin
and R.
van Roij
, “Interplay between adsorption and hydrodynamics in nanomechanics: Towards tunable membranes
,” Phys. Rev. Lett.
118
, 014502
(2017
).18.
P. G.
Wolynes
, “Osmotic effects near the critical point
,” J. Phys. Chem.
80
, 1570
–1572
(1976
).19.
X.
Xu
and T.
Qian
, “Generalized Lorentz reciprocal theorem in complex fluids and in nonisothermal systems
,” J. Phys.: Condens. Matter
31
, 475101
(2019
).20.
Y.
Uematsu
and T.
Araki
, “Electro-osmotic flow of semidilute polyelectrolyte solutions
,” J. Chem. Phys.
139
, 094901
(2013
).21.
C.
Lee
, C.
Cottin-Bizonne
, A.-L.
Biance
, P.
Joseph
, L.
Bocquet
, and C.
Ybert
, “Osmotic flow through fully permeable nanochannels
,” Phys. Rev. Lett.
112
, 244501
(2014
).22.
H. J.
Keh
, “Diffusiophoresis of charged particles and diffusioosmosis of electrolyte solutions
,” Curr. Opin. Colloid Interface Sci.
24
, 13
–22
(2016
).23.
M.
Atlas
, R. U.
Haq
, and T.
Mekkaoui
, “Active and zero flux of nanoparticles between a squeezing channel with thermal radiation effects
,” J. Mol. Liq.
223
, 289
(2016
).24.
D.
Velegol
, A.
Garg
, R.
Gusha
, A.
Kar
, and M.
Kumar
, “Origins of concentration gradients for diffusiophoresis
,” Soft Matter
12
, 4686
(2016
).25.
M.
Hamid
, M.
Usman
, Z. H.
Khan
, R. U.
Haq
, and W.
Wang
, “Numerical study of unsteady MHD flow of Williamson nanofluid in a permeable channel with heat source/sink and thermal radiation
,” Eur. Phys. J. Plus
133
, 527
(2018
).26.
S.
Marbach
and L.
Bocquet
, “Osmosis, from molecular insights to large-scale applications
,” Chem. Soc. Rev.
48
, 3102
–3144
(2019
).27.
S.
Shin
, “Diffusiophoretic separation of colloids in microfluidic flows
,” Phys. Fluids
32
, 101302
(2020
).28.
B. L.
Werkhoven
and R.
van Roij
, “Coupled water, charge and salt transport in heterogeneous nano-fluidic systems
,” Soft Matter
16
, 1527
–1537
(2020
).29.
V. S.
Sivasankar
, S. A.
Etha
, H. S.
Sachar
, and S.
Das
, “Ionic diffusioosmotic transport in nanochannels grafted with pH-responsive polyelectrolyte brushes modeled using augmented strong stretching theory
,” Phys. Fluids
32
, 042003
(2020
).30.
S.
Ramírez-Hinestrosa
and D.
Frenkel
, “Challenges in modelling diffusiophoretic transport
,” Eur. Phys. J. B
94
, 199
(2021
).31.
C.
Sun
, R.
Zhou
, Z.
Zhao
, and B.
Bai
, “Extending the classical continuum theory to describe water flow through two-dimensional nanopores
,” Langmuir
37
, 6158
–6167
(2021
).32.
B. V.
Derjaguin
, S. S.
Dukhin
, and V. V.
Koptelova
, “Capillary osmosis through porous partitions and properties of boundary layers of solutions
,” J. Colloid Interface Sci.
38
, 584
–595
(1972
).33.
J. L.
Anderson
, “Colloid transport by interfacial forces
,” Ann. Rev. Fluid Mech.
21
, 61
–99
(1989
).34.
Y.
Fujitani
, “Diffusiophoresis in a near-critical binary fluid mixture
,” Phys. Fluids
34
, 041701
(2022
).35.
L.
Onsager
, “Reciprocal relations in irreversible processes. I
,” Phys. Rev.
37
, 405
(1931
).36.
L.
Onsager
, “Reciprocal relations in irreversible processes. II
,” Phys. Rev.
38
, 2265
(1931
).37.
A. J.
Bray
and M. A.
Moore
, “Critical behaviour of semi-infinite systems
,” J. Phys. A: Math. Gen.
10
, 1927
–1962
(1977
).38.
H. W.
Diehl
, “Phase transition and critical phenomena X
,” in Field Theoretical Approach to Critical Behavior at Surfaces
(Academic
, London
, 1986
).39.
H. W.
Diehl
, “The theory of boundary critical phenomena
,” Int. J. Mod. Phys. B
11
, 3503
–3523
(1997
).40.
R.
Okamoto
and A.
Onuki
, “Attractive interaction and bridging transition between neutral colloidal particles due to preferential adsorption in a near-critical binary mixture
,” Phys. Rev. E
88
, 022309
(2013
).41.
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
).42.
A.
Pelisetto
and E.
Vicari
, “Critical phenomena and renormalization-group theory
,” Phys. Rep.
368
, 549
(2002
).43.
I.
Iwanowski
, K.
Leluk
, M.
Rudowski
, and U.
Kaatze
, “Critical dynamics of the binary system nitroethane/3-methylpentane: Relaxation rate and scaling function
,” J. Phys. Chem. A
110
, 4313
(2006
).44.
R. F.
Berg
and M. R.
Moldover
, “Critical exponent for the viscosity of four binary liquids
,” J. Chem. Phys.
89
, 3694
–3704
(1988
).45.
R. F.
Berg
and M. R.
Moldover
, “Critical exponent for viscosity
,” Phys. Rev. A
42
, 7183
–7187
(1990
).46.
J. V.
Sengers
, “Transport properties near critical points
,” Int. J. Thermophys.
6
, 203
–232
(1985
).47.
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
).48.
A.
Stein
, S. J.
Davidson
, J. C.
Allegra
, and G. F.
Allen
, “Tracer diffusion and shear viscosity for the system 2,6-lutidine-water near the lower critical point
,” J. Chem. Phys.
56
, 6164
(1972
).49.
C. A.
Grattoni
, R. A.
Dawe
, C. Y.
Seah
, and J. D.
Gray
, “Lower critical solution coexistence curve and physical properties (density, viscosity, surface tension, and interfacial tension) of 2,6-lutidine + water
,” Chem. Eng. Data
38
, 516
–519
(1993
).50.
Y.
Jayalakshmi
, J. S.
Van Duijneveldt
, and D.
Beysens
, “Behavior of density and refractive index in mixtures of 2,6-lutidine and water
,” J. Chem. Phys.
100
, 604
–609
(1994
).51.
H. M.
Leister
, J. C.
Allegra
, and G. F.
Allen
, “Tracer diffusion and shear viscosity in the liquid–liquid critical region
,” J. Chem. Phys.
51
, 3701
(1969
).52.
J.
Reeder
, T. E.
Block
, and C. M.
Knobler
, “Excess volumes of nitroethane + 3-methylpentane
,” J. Chem. Thermodyn.
8
, 133
(1976
).53.
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
).54.
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
).55.
K.
Miyazaki
, D.
Bedeaux
, and K.
Kitahara
, “Nonequilibrium thermodynamics of multicomponent systems
,” Physica A
230
, 600
(1996
).56.
57.
S.
Yabunaka
, R.
Okamoto
, and A.
Onuki
, “Phase separation in a binary mixture confined between symmetric parallel plates: Capillary condensation transition near the bulk critical point
,” Phys. Rev. E
87
, 032405
(2013
).58.
Y.
Tsori
and L.
Leibler
, “Phase-separation in ion-containing mixtures in electric fields
,” Proc. Natl. Acad. Sci. U. S. A.
104
, 7348
–7350
(2007
).59.
S.
Samin
and Y.
Tsori
, “Attraction between like-charge surfaces in polar mixtures
,” Europhys. Lett.
95
, 36002
(2011
).60.
S.
Samin
and Y.
Tsori
, “Reversible pore-gating in aqueous mixtures via external potential
,” Colloid Interface Sci. Commun.
12
, 9
(2016
).61.
R.
Okamoto
and A.
Onuki
, “Precipitation in aqueous mixtures with addition of a strongly hydrophilic or hydrophobic solute
,” Phys. Rev. E
82
, 051501
(2010
).62.
R.
Okamoto
and A.
Onuki
, “Charged colloids in an aqueous mixture with a salt
,” Phys. Rev. E
84
, 051401
(2011
).63.
H. W.
Diehl
and H. K.
Janssen
, “Boundary conditions for field theory of dynamic critical behavior in semi-infinite systems with conserved order parameter
,” Phys. Rev. A
45
, 7145
(1992
).64.
Y.
Fujitani
, “Effective viscosity of a near-critical binary fluid mixture with colloidal particles dispersed dilutely under weak shear
,” J. Phys. Soc. Jpn.
83
, 084401
(2014
).65.
Y.
Fujitani
, “Relaxation rate of the shape fluctuation of a fluid membrane immersed in a near-critical binary fluid mixture
,” Eur. Phys. J. E
39
, 31
(2016
).66.
K.
To
, “Coexistence curve exponent of a binary mixture with a high molecular weight polymer
,” Phys. Rev. E
63
, 026108
(2001
).67.
A. M.
Wims
, D.
Mcintyre
, and F.
Hynne
, “Coexistence curve for 3-methylpentane-nitroethane near the critical point
,” J. Chem. Phys.
50
, 616
(1969
).68.
M. E.
Fisher
and P. G.
de Gennes
, “Phénomènes aux parois dans un mélange binaire critique
,” C. R. Acad. Sci. Paris B
287
, 207
(1978
).69.
E. D.
Siggia
, P. C.
Hohenberg
, and B. I.
Halperin
, “Renormalization-group treatment of the critical dynamics of the binary-fluid and gas-liquid transitions
,” Phys. Rev. B
13
, 2110
–2123
(1976
).70.
R.
Folk
and G.
Moser
, “Critical dynamics: A field-theoretical approach
,” J. Phys. A: Math. Gen.
39
, R207
–R313
(2006
).71.
A.
Onuki
and K.
Kawasaki
, “Nonequilibrium steady state of critical fluids under shear flow: A renormalization group approach
,” Ann. Phys.
121
, 456
–528
(1979
).72.
T.
Ohta
, “Multiplicative renormalization of the anomalous shear viscosity in classical liquids
,” J. Phys. C: Solid State Phys.
10
, 791
(1977
).73.
J. K.
Bhattacharjee
, R. A.
Ferrell
, R. S.
Basu
, and J. V.
Sengers
, “Crossover function for the critical viscosity of a classical fluid
,” Phys. Rev. A
24
, 1469
(1981
).74.
B. C.
Tsai
and D.
McIntyre
, “Shear viscosity of nitroethane-3-methylpentane in the critical region
,” J. Chem. Phys.
60
, 937
(1974
).75.
A.
Onuki
, “Phase transitions of fluids in shear flow
,” J. Phys.: Condens. Matter
9
, 6119
–6157
(1997
).76.
D.
Beysens
, “Brownian motion in strongly fluctuating liquid
,” Thermodyn. Interfaces Fluid Mech.
3
, 1
–8
(2019
).77.
Y.
Fujitani
, “Suppression of viscosity enhancement around a Brownian particle in a near-critical binary fluid mixture
,” J. Fluid Mech.
907
, A21
(2021
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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