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Effect of temperature on polymer migration II: Concentration equation

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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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Abbreviations

a:

radius of bead

A:

arbitrary quantity A+ =(A1+A2)/2 (A=V, ζ and β) A- =A2-A1 (A = V, ζ and β)

C:

local dumbbell concentration

H:

spring constant

k:

Boltzmann’s constant

r:

position vector

ri :

position vector of ith bead

rc :

center of mass, = (r1 + r2)/2

R:

internal configuration coordinate, = r2 - r1

t:

time

T:

absolute temperature

v:

fluid velocity

vc :

fluid velocity at the center of mass

v0 :

fluid velocity at the origin

ζ:

friction coefficient

η:

viscosity

v:

1/ζ

ζ:

kT/ζ

Ψ :

probability function

φ:

probability function (normalized with respect to internal coordinates)

Δ:

polymer migration velocity

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Author notes

  1. Yong Woo Inn

    Present address: Dept. of Macromolecular Science, Case Western Reserve Univ., 44106, Cleveland, OH, USA

Authors and Affiliations

  1. Dept. of Polymer Science and Engineering, Inha University, Inchon, Korea

    Hyoung Jin Choi, Yong Woo Inn & Myung S. Jhon

  2. Dept. of Chem. Eng., Carnegie Mellon University, 15213, Pittsburgh, PA, USA

    Myung S. Jhon

Authors
  1. Hyoung Jin Choi
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  2. Yong Woo Inn
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  3. Myung S. Jhon
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Choi, H.J., Inn, Y.W. & Jhon, M.S. Effect of temperature on polymer migration II: Concentration equation. Korean J. Chem. Eng. 11, 145–152 (1994). https://doi.org/10.1007/BF02697459

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  • DOI: https://doi.org/10.1007/BF02697459

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