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Rheological Measurement pp 211–245Cite as

Elongational Rheometers

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Abstract

The study of the elongational or extensional flow of polymeric fluids has been the subject of intense research for most of the last two decades. Continuing interest in this area stems from the fact that several industrially important polymer processing operations such as fibre spinning, blow moulding, flat film extrusion and film blowing involve a predominantly extensional mode of deformation. This flow field is also highly effective in orienting polymer molecules in the flow direction, and the high deformation rates which typically occur in industrial operations, albeit for a short duration, result in the presence of unusually large fluid stresses; the theoretical prediction of these stresses is an unsolved issue which represents an intellectual challenge to every rheologist.

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Abbreviations

A 0 :

cross-sectional area of nozzle exit in eqns (8.18) and (8.19)

a 1 to a 5 :

constants in eqn (8.17)

D :

diameter

F :

force (used with various subscripts)

g :

acceleration due to gravity

l :

sample length

L :

capillary length

L 0 :

initial length in eqn (8.7)

l, l 0 :

sample length at time t and t = 0

n :

power law index

P Ent :

entrance pressure drop

P 0, P x :

pressures in viscometer before and after stretching in eqns (8.20) and (8.21)

Q :

volumetric flow rate

Q 0,Q 1 :

volumetric flow rate without stretching and with stretching in eqns (8.20) and (8.21) r radius

R :

capillary radius

T r :

Trouton ratio

v 1,v 2, v 3 :

flow velocity components

V 0 :

average flow velocity at nozzle exit in eqn (8.19)

x 1, x 2, x 3 :

coordinate directions, with flow in x x direction

γ :

surface tension

γ̇ A :

apparent shear rate

ε̇ :

tensile strain rate

ε̇ E :

net average extension rate

η E :

tensile viscosity

η + E :

tensile stress growth coefficient

η :

shear viscosity

ρ :

polymer density

σ :

total stress tensor

σ 11 :

total stress at x

σ E :

net average extensional stress

τ :

extra stress tensor

τ 22 — τ 22 :

first normal stress difference

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Author information

Authors and Affiliations

  1. Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, New York, USA

    R. K. Gupta

  2. Department of Chemical Engineering, Monash University, Clayton, Victoria, Australia

    T. Sridhar

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  1. R. K. Gupta
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  2. T. Sridhar
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Editor information

Editors and Affiliations

  1. Department of Applied Physics, Sheffield City Polytechnic, Sheffield, UK

    A. A. Collyer

  2. Department of Metallurgy and Materials Science, University of Nottingham, Nottingham, UK

    D. W. Clegg

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Gupta, R.K., Sridhar, T. (1993). Elongational Rheometers. In: Collyer, A.A., Clegg, D.W. (eds) Rheological Measurement. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2898-0_8

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  • DOI: https://doi.org/10.1007/978-94-017-2898-0_8

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