Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-18T16:14:24.709Z Has data issue: false hasContentIssue false
  • English
  • Français

A theory of anisotropic fluids

Published online by Cambridge University Press:  28 March 2006

George L. Hand
George L. Hand
Affiliation:
Department of Mechanics, The Johns Hopkins University
Now with the Air Force Cambridge Research Laboratories, Geophysics Research Directorate.
Get access Rights & Permissions [Opens in a new window]

Abstract

A theory is proposed in which the stress tensor is a function of the components of the rate of deformation tensor and a symmetric tensor describing the microscopic structure of a fluid. The expression for the stress tensor can be written in closed form using results from the Hamilton-Cayley theorem. This theory is shown to contain Prager's theory of dumbbell suspensions as a special case. By limiting the type of terms in the constitutive equations, various stress components can be evaluated for simple shear. These exhibit non-Newtonian behaviour typical of certain higher polymer solutions.

Some of the results of the anisotropic fluid theory are compared with experimental measurements of normal stress and apparent viscosity. Certain high polymers in solution show good agreement between theory and experiment, at least for low enough values of the rate of shear.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 13 , Issue 1 , May 1962 , pp. 33 - 46
Copyright
© 1962 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ericksen, J. L. 1959 Anisotropic fluids. Arch. Rat. Mech. Anal., 4, 231–237.Google Scholar
Ericksen, J. L. 1960 Transversely isotropic fluids. Kolloid. Z., 173, 117–122.Google Scholar
Greensmith, H. W. & Rivlin, R. S. 1953 The hydrodynamics of non-Newtonian fluids. III. The normal stress effect in high polymer solutions. Proc. Roy. Soc. A, 245, 399–428.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. Roy. Soc. A, 102, 161–179.Google Scholar
Kotaka, T., Kurata, M. & Tamura, M. 1957 Normal stress effect in polymer solutions. J. Appl. Phys. 30, 1705–1712.Google Scholar
Kuhn, W. & Kuhn, H. 1945 Die Abhängigkeit der Viskosität vom Strömungsgefälle bei hochverdÜnnten Suspensionen und Lösungen. Helv. Chim. Acta, 28, 97–127.Google Scholar
Markovitz, H. & Williamson, R. B. 1957 Normal stress effect in polyisobutylene solutions. I. Measurements in a cone and plate instrument. Trans. Soc. Rheology, 1, 25–36.Google Scholar
Noll, W. 1955 On the continuity of the solid and fluid states. J. Rat. Mech. Anal., 4, 3–81.Google Scholar
Prager, S. 1957 Stress-strain relations in a suspension of dumbbells. Trans. Soc. Rheology, 1, 53–62.Google Scholar
Rivlin, R. S. 1955 Further remarks on the stress-deformation relations for isotropic materials. J. Rat. Mech. Anal., 4, 681–702.Google Scholar