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An analysis of apparent slip flow of polymer solutions

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Abstract

Theapparent slip flow phenomenon of polymer solutions in capillary tubes is analyzed by a thermodynamic diffusion model. An approximate solution of the developing concentration profiles shows a significant decrease in the polymer wall concentration. The approximate concentration profiles are coupled with the concentration-dependent viscosity for aqueous polyacrylamide solutions to provide a priori predictions of the magnitude of the effective slip velocity at the wall. The results are in a reasonable agreement with the available apparent slip data for 1% and 0.5% solutions of partially hydrolyzed polyacrylamide.

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Abbreviations

b :

parameter defined in eq. (12)

C :

polymer mass concentration

C p :

polymer concentration in weight percent

d :

parameter defined in eq. (13)

D :

tube diameter

D 12 :

phenomenological diffusion coefficient for a polymer in a solvent

D :

polymer mass diffusivity in polymer solution; eq. (9)

f :

entropic potential; eqs. (5) and (17)

J (2) :

diffusion flux of polymer

k, k 0 :

power law parameter (consistency index) at the local and initial concentrations, respectively

k m :

empirical relaxation time parameter: eq. (35)

L :

tube length

m :

empirical parameter; eq. (35)

n, n 0 :

power-law parameter (flow-behavior index) at the local and initial concentrations

N WS :

Weissenberg number; eq. (21)

N pec :

Peclet number; eq. (15)

p :

pressure

Q :

total flow rate

Q s :

flow rate increase due toapparent slip

r :

radial position

\(\bar r\) :

dimensionless radial position

R :

tube radius

R c :

universal gas constant

T :

temperature

v :

velocity

V s :

effective slip velocity

〈V z 〉:

average axial velocity

\(\bar V_z \) :

dimensionless axial velocity

〈V z 〉 NS :

average axial velocity in the absence of apparent slip effects

V r :

radial velocity

z :

axial position

z * :

dimensionless axial position

\(\dot \gamma \) :

shear rate

\(\dot \gamma \) :

wall shear rate corrected for apparent slip effects

θ :

fluid relaxation time

θ NS :

relaxation time in the absence of apparent slip at\(\dot \gamma = \dot \gamma _{NS} \)

τ :

shear stress

τ w :

wall shear stress

η :

local viscosity

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Authors and Affiliations

  1. Department of Chemical Engineering, University of California, Los Angeles, 90024, Los Angeles, CA, USA

    Y. Cohen

  2. Department of Chemical Engineering, University of Delaware, 19716, Newark, Del., USA

    A. B. Metzner

Authors
  1. Y. Cohen
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  2. A. B. Metzner
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Cohen, Y., Metzner, A.B. An analysis of apparent slip flow of polymer solutions. Rheol Acta 25, 28–35 (1986). https://doi.org/10.1007/BF01369977

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