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Numerical simulation of a mathematical model for dry/wet-spun nasceni hollow fiber membrane

  • Environmental And Chemical Engineering
  • Published:
Journal of Shanghai University (English Edition)

Abstract

In an effort to find the effect of mass transfer, surface tension and drag forces on the velocity distribution, the mathematical model of the velocity profile of a nascent hollow fiber during membrane formation in the air gap region was numerically simulatec by using the Runge-Kutta method (fourth-order method). The effect of mass transfer on velocity distribution based on the complicatec function (G(C sh )) was presented and the effects of a complicated function were studied in two cases: in the first case, (G(C sh )) was constant; in the second, (G(C sh )) was variable. The latter was done by varying with the concentration of solvent in a nascent hollow fiber through the air-gap region. One empirical equation was used to describe this change and the predicted values had a better agreement with the experimental values. To verify the model hypotheses, hollow fiber membranes were spun from 20:80 polybenzimi dazole/polyetherimide dopes with 25.6 wt% solid in N, N-dimethylacetamide (DMAc) using water as the external and internal coagulants. Based on the experimental results of dry-jet wet-spinning process for the fabrication of hollow fiber membranes, it is found tha the model calculated values were in a good agreement with the experimental values.

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Abbreviations

C sh :

solvent concentration in a nascent hollow fiber (g·cm−3)

f o :

drag coefficient at the external surface of a nascent hollow fiber

F {ie213-1}:

material function defined (Eq. (2))

g :

gravitational function (980 cm·s−2)

G(C sh :

material function defined (Eq. (2))

H o :

the combined reciprocal radii of the curvatures at the outer skin of the nascent hollow fiber (cm−1)

L :

air-gap distance (cm)

R> i :

inner radius of a nascent hollow fiber (cm)

R o :

outer radius of a nascent hollow fiber (cm)

R′ o ,R″ o> :

the first and second order derivatives of R o, with respect to Z, respectively

σ o :

surface tension at air and nascent hollow fiber interface (lO−5 N·cm−1)

{ie213-2}:

strain rate or rate of elongation (s−1)

γ E :

elongation viscosity

γ o :

initial viscosity

{ie213-3}:

average velocity over the cross-section (cm·s−1)

ρ a :

density of ambient air (g·cm−3)

ρ h :

density of nascent hollow fiber (g·cm−3)

τ x,z :

internal stress (10−5 N·cm−2)

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Authors and Affiliations

  1. Chemical Engineering Research Center, East China University of Science and Technology, 200237, Shanghai, P. R. China

    Alsalhy Qusay Fadhel Ph. D. Candidate & Xu Zhen-liang Ph. D. (Prof.)

Authors
  1. Alsalhy Qusay Fadhel Ph. D. Candidate
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  2. Xu Zhen-liang Ph. D.
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Additional information

Project supported by the National Natural Science Foundation of China (Grant No. 20076009), the Science Foundation of Shanghai Priority Academic Disciplines, the Science Foundation of National Key Fundamental Research Development Plan (“973” plan, Grant No. 2003CB615705)

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Fadhel, A.Q., Xu, Zl. Numerical simulation of a mathematical model for dry/wet-spun nasceni hollow fiber membrane. J. of Shanghai Univ. 8, 213–220 (2004). https://doi.org/10.1007/s11741-004-0043-1

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  • DOI: https://doi.org/10.1007/s11741-004-0043-1

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