Rheologica Acta

, Volume 14, Issue 11, pp 959–962 | Cite as

On a classification scheme for flow fields

  • R. I. Tanner
  • R. R. Huilgol
Article
First Online:
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Summary

There are some flows in which certain strain components grow exponentially in time, while there are other flows in which the components depend otherwise on the time. In this paper the former type are called strong flows and the latter weak. An examination of theJordan form of the matrix of the velocity gradient of a steady, homogeneous, isochoric flow is made, along with the eigenvalues of such a matrix, to discover when such a flow is strong or weak. It is shown that if the eigenvalues are all zero or if one is zero and the other two purely imaginary, then the flow is weak, with the remaining cases leading to strong flows.

Keywords

Polymer Flow Field Classification Scheme Velocity Gradient Isochoric Flow 
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Zusammenfassung

Es gibt Strömungen, in denen gewisse Deformationskomponenten exponentiell mit der Zeit anwachsen, und es gibt solche, in denen die Zeitabhängigkeit der Deformationskomponenten eine andere mathematische Form aufweist. In dieser Abhandlung sind die ersteren alsstarke Strömungen und die letztgenannten alsschwache Strömungen bezeichnet. Eine Untersuchung derJordanschen Form der Matrix des Geschwindigkeitsgradienten einer stationären, homogenen Strömung, zusammen mit den Eigenwerten einer solchen Matrix, erlaubt zu bestimmen, ob die Strömung stark oder schwach ist. Es wird gezeigt, daß die Strömung schwach ist, wenn entweder alle Eigenwerte verschwinden oder aber wenn ein Eigenwert verschwindet und die beiden anderen rein imaginär sind. Alle übrigbleibenden Fälle entsprechen starken Strömungen.

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Copyright information

© Dr. Dietrich Steinkopff Verlag 1975

Authors and Affiliations

  • R. I. Tanner
    • 1
    • 2
    • 3
  • R. R. Huilgol
    • 1
    • 2
    • 4
  1. 1.Division of EngineeringBrown UniversityProvidenceUSA
  2. 2.Department of Mechanics and Mechanical and Aerospace EngineeringIllinois Institute of TechnologyChicagoUSA
  3. 3.Dept. of Mechanical EngineeringUniversity of SydneySydneyAustralia
  4. 4.School of Mathematical SciencesFlinders UniversityBedford ParkAustralia

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