Based upon findings with respect to the viability of the expression jv=ρDvv̂ hypothesized to represent the constitutive equation for the diffusive volume flux in ideal binary mixtures (ρ=mass density, v̂=1/ρ=specific volume, and Dv=volume diffusion coefficient), implicit evidence is offered in support of the recently developed theory of bivelocity continuum hydrodynamics for mixtures. Present findings for the case of mixtures add to existing evidence already available for the single-component case, thus supporting the viability of bivelocity hydrodynamic theory in general.

1.
S. R.
de Groot
and
P.
Mazur
,
Non-Equilibrium Thermodynamics
(
North-Holland
,
Amsterdam
,
1962
).
2.
R.
Haase
,
Thermodynamics of Irreversible Processes
(
Dover
,
New York
,
1990
).
3.
S.
Chapman
and
T. G.
Cowling
,
The Mathematical Theory of Non-Uniform Gases
, 3rd ed. (
Cambridge University Press
,
Cambridge
,
1970
).
4.
J. H.
Ferziger
and
H. G.
Kaper
,
Mathematical Theory of Transport Processes in Gases
(
North-Holland
,
Amsterdam
,
1972
).
5.
Y.
Sone
,
Kinetic Theory and Fluid Dynamics
(
Birkhäuser
,
Boston
,
2002
).
7.
8.
10.
H.
Brenner
, “
A critical test of bi-velocity hydrodynamics for mixtures
,”
Phys. Rev. E
(submitted).
11.
R. B.
Bird
,
W. E.
Stewart
, and
E. N.
Lightfoot
,
Transport Phenomena
, 2nd ed. (
Wiley
,
New York
,
2002
).
12.
H.
Brenner
,
Physica A
349
,
10
(
2005
).
13.
G. D. C.
Kuiken
,
Thermodynamics of Irreversible Processes: Applications to Diffusion and Rheology
(
Wiley
,
New York
,
1994
).
14.
J. G.
Kirkwood
and
I.
Oppenheim
,
Chemical Thermodynamics
(
McGraw-Hill
,
New York
,
1961
).
15.
K.
Denbigh
,
The Principles of Chemical Equilibrium
(
Cambridge University Press
,
London
,
1955
).
16.
M. Sh.
Shavaliyev
,
Fluid Dyn.
9
,
96
(
1974
).
17.
B. K.
Annis
,
Phys. Fluids
14
,
269
(
1971
).
18.
D. E.
Rosner
,
Transport Processes in Chemically Reacting Flow Systems
(
Academic
,
New York
,
1980
).
19.
The zero value of the thermal diffusivity owes to Shavaliyev’s (Ref. 16) assumption of a spherically symmetric intermolecular potential.
20.
Yu. L.
Klimontovich
,
Statistical Theory of Open Systems Volume 1: A Unified Approach to Kinetic Descriptions of Processes in Active Systems
(
Kluwer
,
Dordrecht
,
1995
), pp.
223
238
;
Yu. L.
Klimontovich
,
Theor. Math. Phys.
92
,
909
(
1992
);
Yu. L.
Klimontovich
,
Theor. Math. Phys.
96
,
1035
(
1993
).
21.
H.
Brenner
, “
Onsager reciprocity as a consequence of Maxwell reciprocity
,”
Phys. Fluids
(submitted).
22.
H. B.
Callen
,
Thermodynamics and an Introduction to Thermostatics
, 2nd ed. (
Wiley
,
New York
,
1985
).
H. B. G.
Casimir
,
Rev. Mod. Phys.
17
,
343
(
1945
).
24.
D. G.
Miller
,
Chem. Rev. (Washington, D.C.)
60
,
15
(
1960
).
25.
C.
Truesdell
and
R. G.
Muncaster
,
Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas
(
Academic
,
New York
,
1980
).
26.
D.
Burnett
,
Proc. London Math. Soc.
s2-39
,
385
(
1935
);
D.
Burnett
,
Proc. London Math. Soc.
s2-40
,
382
(
1936
).
27.
H.
Struchtrup
,
Macroscopic Transport Equations for Rarefied Gas Flows
(
Springer
,
New York
,
2005
).
28.
Table I provides experimental values of the Prandtl and Lewis numbers for a variety of pure gases, wherein the diffusivity D refers to the self-diffusivity of the pure gas. The tabulated Prandtl numbers are noted to accord with the theoretical value (Ref. 1) of Pr=2/3 for monatomic gases based upon the Boltzmann equation. The corresponding Prandtl number for a BGK-model gas (Ref. 29) is, however, noted to be (Ref. 27) Pr=1, a result more in harmony with our present calculations.
29.
P. L.
Bhatnagar
,
E. P.
Gross
, and
M.
Krook
,
Phys. Rev.
94
,
511
(
1954
).
30.
J. O.
Hirschfelder
,
C. F.
Curtiss
, and
R. B.
Bird
,
Molecular Theory of Gases and Liquids
(
Wiley
,
New York
,
1954
).
You do not currently have access to this content.