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Inertia effects in rheometrical flow systems

Part 1: The orthogonal rheometer

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Summary

The flow field of a linear viscoelastic material in the orthogonal rheometer, taking fluid inertia into account, has been studied theoretically and an exact solution is given. The flow field of a Newtonian liquid is included in this solution as a special case. The forces on the plates are readily deduced from this solution. The paper concludes with an energy consideration.

Zusammenfassung

Das Strömungsfeld eines linear-viskoelastischen Stoffes im Orthogonal-Rheometer wurde unter Berücksichtigung der Flüssigkeitsträgheit theoretisch untersucht und eine exakte Lösung dafür angegeben. Das Strömungsfeld einer newtonschen Flüssigkeit ergibt sich als Sonderfall dieser Lösung. Die auf die Platten ausgeübten Kräfte lassen sich in einfacher Weise aus dieser Lösung ableiten. Abschließend wird eine Energiebetrachtung angestellt.

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Abbreviations

a :

distance between axis of upper and lower plate

c * = c′ + ic″:

complex velocity of propagation of shear waves

h :

distance between the plates

i :

\(i = \sqrt { - 1} \)

k * = k′ − ik″:

complex wave number

k = (ρω/2η)1/2 :

complex wave number

k e :

wave number in a Hookean material

n = 0, 1, 2, ⋯:

wave number in a Hookean material

t :

time

x, y, z :

Cartesian coordinates

A :

area of a plate

A + :

displacement amplitude of shear wave in +z direction

A − :

displacement amplitude of shear wave in−z direction

E :

kinetic energy

F :

force on lower plate

G * = G′ + iG″:

complex shear modulus

R :

radius of the plates

ΔW :

energy dissipated in the sample during one cycle

δ :

loss angle

Γ :

propagation factor

λ :

wave length

ω :

angular velocity

η :

viscosity

ρ :

density

τ :

shear stress

ξ :

particle displacement

References

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Authors and Affiliations

  1. Department of Applied Physics, Twente University of Technology, Enschede, The Netherlands

    H. A. Waterman

Authors
  1. H. A. Waterman
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With 6 figures

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Waterman, H.A. Inertia effects in rheometrical flow systems. Rheol Acta 15, 444–453 (1976). https://doi.org/10.1007/BF01530347

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  • DOI: https://doi.org/10.1007/BF01530347

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