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EFFECT OF TEMPERATURE ON POLYMER MIGRATION II : CONCENTRATION EQUATION
Korean Journal of Chemical Engineering, July 1994, 11(3), 145-152(8), 10.1007/BF02697459
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Abstract
Polymer migration is a generally well-known phenomenon in a flow field, and it has been verified that the sources of such phenomena are nonhomogeneity of the flow, concentration effects and hydrodynamic interactions between the polymer molecules. In addition, temperature effects were found to be another source of polymer migration. The Langevin equation for a polymer molecule was first derived from single chain dynamics using a kinetic theory for the bead-spring elastic harmonic dumbbell model, as described in part I (reference[1]). In this paper the diffusion equation and concentration profile of the polymer molecules induced by a temperature gradient are obtained from the Fokker-Planck equation. A new differential operator is also introduced to calculate the concentration profile. From the concentration equation obtained in the general flow geometry, we find that in dilute polymer solution there are significant effects on the polymer migration not only due to the nonhomogeneity of the flow field but also due to temperature gradients.
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Shafer RH, Laiken N, zimm BH, Biophys. Chem., 2, 180 (1974)
Aubert JH, Tirrell M, J. Chem. Phys., 72(4), 2694 (1980)
Aubert JH, Prager S, Tirrell M, J. Chem. Phys., 73(8), 4103 (1980)
Sekhon G, Armstrong RC, Jhon MS, J. Polym. Sci. B: Polym. Phys., 20, 947 (1982)
Crone RM, Jhon MS, Choi HJ, J. Mol. Liquids, 59, 115 (1994)
Choi HJ, Jhon MS, "Theoretical and Applied Rheology," Moldenaers, P. and Keunings, R. ed, Elsevier Science, Amsterdam, The Netherlands, p. 464 (1992)
Brunn PO, Int. J. Multiph. Flow, 9(2), 187 (1983)
Doi M, Edwards SF, "The Theory of Polymer Dynamics," Oxford Univ. Press, Oxford (1986)
Edwards SF, Freed KF, J. Chem. Phys., 61, 1189 (1974)
Freed KF, Edwards SF, J. Chem. Phys., 61, 3626 (1974)
Freed KF, Muthukumar M, J. Chem. Phys., 68, 2088 (1978)
Freed KF, "Progress in Liquid Physics," Croxton, C.A. ed., Wiley, New York, p. 343 (1978)
Jhon MS, Sekhon G, Armstrong R, "Advances in Chemical Physics," Prigogine, I. and Rice, S.A. ed., Wiley, N.Y., p. 66 (1987)
Freed KF, Perico A, Macromolecules, 14, 1290 (1981)
Denn MM, "Process Fluid Mechanics," Prentice-Hall, New Jersey, p. 235 (1980)
Tanner RI, "Engineering Rheology," Oxford Univ. Press, Oxford, p. 177 (1985)
Larson RG, "Constitutive Equations for Polymer Melts and Solutions," Butterworths, Boston, p. 41 (1988)
