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An analysis of flow induced formation of long fibers

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Summary

An engineering model of fiber growth from a flowing solution is presented. Attention is focussed on three main issues: the fluid mechanics, the molecular structure of the fluid, coupled with the thermodynamics, and the crystal growth itself. Although because of existing uncertainties order of magnitude analyses had to be adopted it was possible to obtain quantitative predictions about the growth process.

Zusammenfassung

Es wird ein einfaches Modell des Faserwachstums aus einer strömenden Lösung vorgestellt. Dabei werden vor allem drei wesentliche Aspekte betrachtet: die Strömungsmechanik, die molekulare Struktur und Thermodynamik der Flüssigkeit, sowie das Kristallwachstum selbst. Obgleich wegen der noch bestehenden Unsicherheiten nur größenordnungsmäßige Abschätzungen in Ansatz gebracht werden konnten, war es dennoch möglich, quantitative Aussagen über den Wachstumsvorgang zu erhalten.

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Abbreviations

b :

surface layer thickness

C :

constant

c :

concentration

d :

rate of strain tensor

F :

free energy

F K :

kink energy

F V :

free energy far from the fiber

G :

growth rate constant

H :

enthalpy

K :

ratio between tube diameter and fiber diameter

L :

filament length

l :

length of the critical nucleus

Q :

flow rate

R :

fiber diameter

R * :

gas constant

r :

radial coordinate

S :

entropy

S f :

internal entropy in the fluid phase

S s :

internal entropy in the solid phase

T :

temperature

T m,d :

melting or dissolution temperature

T d :

dissolution temperature

t :

time

u :

axial fluid velocity

V :

difference between draw velocity and maximal fluid velocity

V D :

draw velocity

V F :

maximal fluid velocity without fiber

V G :

fiber grow velocity

v :

velocity vector

Z u :

length of the “entrance length” upstream of the fiber tip

z :

axial coordinate

α :

constant, depending on the nucleation model

Γ :

total stretch

γ :

activity coefficient

\(\dot \Gamma \) :

shear rate or stretch rate

δ :

boundary layer thickness

ζ :

characteristic length

η :

viscosity

η el :

elongational viscosity

η sh :

shear viscosity

θ :

relative temperature difference

Λ :

time constant

µ :

driving force

ρ :

density

σ′ :

tensile strength of the fiber

σ :

lateral surface free energy

σ e :

fold surface free energy

τ :

excess stress tensor co-ordinated to the polymer molecules

χ :

lattice restriction constant

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Authors and Affiliations

  1. Laboratorium voor Fysische Technologie, Delft University of Technology, Prins Bernhardlaan 6, Delft, The Netherlands

    L. P. B. M. Janssen & R. Janssen-van Rosmalen

Authors
  1. L. P. B. M. Janssen
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  2. R. Janssen-van Rosmalen
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Additional information

On leave from the Laboratory for Physical Technology Delft University of Technology, Delft (The Netherlands).

On leave from the RIM Laboratory for Solid State Physics, Catholic University Nijmegen (The Netherlands).

With 6 figures

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Janssen, L.P.B.M., Janssen-van Rosmalen, R. An analysis of flow induced formation of long fibers. Rheol Acta 17, 578–588 (1978). https://doi.org/10.1007/BF01522030

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  • DOI: https://doi.org/10.1007/BF01522030

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