The Rouse model for dilute polymer solutions undergoing homogeneous flows has been generalized to include the inertia of the beads in the equations of motion. To obtain the correct ‘‘diffusion equation’’ for the probability density distribution function in phase space, we generalize the diffusion equation derived by Murphy and Aguirre [J. Chem. Phys. 57, 2098 (1972)] from Hamilton’s equations of motion for an arbitrary number of interacting Brownian particles at equilibrium. Material functions are found, and the noninertial case is seen to be obtained as the zero mass limit in all steps of the development. In particular, the steady‐state shear results are unaffected by the inclusion of inertia. It is also shown how two assumptions, ‘‘equilibration in momentum space,’’ and the neglect of acceleration, made independently by Curtiss, Bird, and Hassager in their phase‐space kinetic theory, are actually the result of assuming zero mass.

1.
P. E.
Rouse
,
J. Chem. Phys.
21
,
1272
(
1953
).
2.
W.
Kuhn
, and
F.
Grün
,
Kolloid Polym.
101
,
248
(
1942
).
3.
H. R.
Warner
, Jr.
,
Ind. Eng. Chem. Fund.
11
,
379
(
1972
).
4.
R. C.
Armstrong
,
J. Chem. Phys.
60
,
724
,
729
(
1974
).
5.
R. B.
Bird
,
P. J.
Dotson
, and
N. L.
Johnson
,
J. Non‐Newtonian Fluid Mech.
7
,
213
(
1980
).
6.
X. J.
Fan
,
J. Non‐Newtonian Fluid. Mech.
17
,
125
(
1985
).
7.
B. H.
Zimm
,
J. Chem. Phys.
24
,
269
(
1956
).
8.
H. C.
Öttinger
,
J. Chem. Phys.
83
,
6535
(
1985
).
9.
H. C.
Öttinger
,
J. Chem. Phys.
86
,
3731
(
1987
);
H. C.
Öttinger
,
87
,
1460
(E) (
1987
).,
J. Chem. Phys.
10.
H. C.
Öttinger
,
J. Non‐Newtonian Fluid Mech.
26
,
207
(
1987
).
11.
L. E.
Wedgewood
, and
H. C.
Öttinger
,
J. Non‐Newtonian Fluid Mech.
27
,
245
(
1988
).
12.
W.
Kuhn
and
H.
Kuhn
,
Helv. Chim. Acta
28
,
97
(
1945
).
13.
P.
Debye
,
J. Chem. Phys.
14
,
636
(
1946
).
14.
H. A.
Kramers
,
J. Chem. Phys.
14
,
415
(
1946
).
15.
J. G.
Kirkwood
, and
J.
Riseman
,
J. Chem. Phys.
16
,
565
(
1948
).
16.
J. J. Hermans, Polymer Solutins Properties Part II. Hydrodynamics and Light Scattering (Dowden, Hutchins, and Ross, Stroudsburg, PA, 1978).
17.
R. B. Bird, C. F. Curtiss, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids Vol. II: Kinetics Theory, 2nd ed. (Wiley, New York, 1987).
18.
M.
Fixman
,
J. Chem. Phys.
42
,
3831
(
1965
).
19.
C. F.
Curtiss
,
R. B.
Bird
, and
O.
Hassager
,
Adv. Chem. Phys.
35
,
31
(
1976
).
20.
N. N.
Bolgulyubov
,
J. Phys. (Moscow)
10
,
256
,
265
(
1946
).
21.
M.
Born
and
H. S.
Green
,
Proc. R. Soc. London Ser. A
188
,
10
(
1946
).
22.
J. G.
Kirkwood
,
J. Chem. Phys.
14
,
180
(
1946
).
23.
J. Yvon, Statistique des Fluides et l’Équation d’Etat, Actualites Scientifique et Industrielles, No. 203 (Hermann et Cie, Paris, 1935).
24.
T. J.
Murphy
, and
J. L.
Aguirre
,
J. Chem. Phys.
57
,
2098
(
1972
).
25.
O.
Klein
,
Ark. Matem., Astron. Fys.
16
, No.
5
(
1921
).
26.
P. Résibois, and M. DeLeener, Classical Kinetic Theory of Fluids (Wiley, New York, 1977).
27.
J. L.
Lebowitz
, and
E.
Rubin
,
Phys. Rev.
131
,
2381
(
1963
).
28.
J. G.
Kirkwood
,
F. P.
Buff
, and
M. S.
Green
,
J. Chem. Phys.
17
,
988
(
1949
).
29.
L. S.
Ornstein
,
Akad. Wetenschappen Amsterdam
21
,
96
(
1919
).
30.
R.
Zwanzig
,
Adv. Chem. Phys.
15
,
325
(
1969
).
31.
N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North‐Holland, Amsterdam, 1981).
32.
C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences (Springer, Berlin, 1983).
33.
S. C.
Szu
, and
J. J.
Hermans
,
J. Polym. Sci.
12
,
1743
(
1974
).
34.
R. B.
Bird
,
X. J.
Fan
, and
C. F.
Curtiss
,
J. Non‐Newtonian Fluid Mech.
15
,
85
(
1984
).
35.
R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids Vol. I: Fluid Mechanics., 2nd Ed. (Wiley, New York, 1987).
36.
G.
Wilemski
,
J. Stat. Phys.
14
,
153
(
1976
).
37.
R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II. Nonequilibrium Thermodynamics (Springer, New York, 1985).
38.
J. H.
Irving
, and
J. G.
Kirkwood
,
J. Chem. Phys.
18
,
817
(
1950
).
39.
H. C.
Booij
,
J. Rheol.
32
,
47
(
1988
).
This content is only available via PDF.
You do not currently have access to this content.