Karl Weissenberg - The 80th Birthday
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Weissenberg’s Contributions to Rheology
PROFESSOR W. PHILIPPOFF
Newark College of Engineering, Newark, N. J., U.S.A.
Karl Weissenberg’s ideas have had a profound influence on the development of rheology, as the author, who was associated with him in the 1930’s can testify. He was mostly vastly ahead of the accepted science of the time and arrived at his conclusions by an extraordinary intuition of the physical reasons of the phenomena, even if this involved the development of completely new concepts. However, his work is for the most part not widely known, as he published it in journals of limited circulation and further did not bother to put his conclusions into directly provable formulas. An outline of his work in Rheology will be attempted here.
In the first paper1 he introduced the concept of elasticity in the steady flow of liquids to account for the non-Newtonian viscosity of polymer solutions and used an energy balance (triangular diagram) for the flow of “general” liquids: the viscous loss, the potential (elastic) energy and the kinetic energy. The reasoning, as continued through his whole work, was abstract and in terms of continuum mechanics, without discussing how or why elasticity occurs at all in molecular concepts.
In the next papers2,3 the flow of cellulose acetate in dioxane was described and analyzed. The experimental proof of the laminar flow of this material was given and a constant viscosity at low rates of shear was found, both facts contradicting the ideas current at the time. As a side derivation the “Mooney-Rabinowitsch” correction was developed, which was apparently not considered to be important by him at the time, but has been used ever since for the comparison, of capillary and rotational instrument data.
In another paper4 the general theory of the mechanics of deformable bodies was developed, in which the concept of “mechanical equation of state” was introduced, now called “constitutive equation”. He used the generalized Maxwell body (S-body) and Voigt body (P-body) as well as their combinations (SP-body). A series of time derivatives of stress and strain was used, taken up some 20 years later by Oldroyd ref.20. A conclusion of the presence of an elasticity in the liquid was the prediction of the dependence of the viscosity measured in shear vibrations on the frequency. This was subsequently found by Eisenschitz5 and Philippoff6. Now pursuant to the extensive work of J. Ferry and his school the elasticity in vibrational tests is generally accepted, much more so than the one in steady flow.
In another paper7 the general theory was further elaborated, using to some extent extensions of the tensor calculus, without bothering to give a proof. Especially the non-Newtonian viscosity was shown to be the result of a finite angle between the principal stress and principal axis of the deformation velocity. Here also the “Goniometry” was emphasized, the distribution of stresses at a point in space.
The Weissenberg Effect: During the war years the so called “Weissenberg-Effect” (the climbing of a visco-elastic liquid up a rotating rod), was probably first empirically observed; it was his intuition that connected it with elasticity and “normal stresses” in flow. Phenomenologically this was described in papers 10,11,12 but the detailed explanation was given in9 and especially in the more widely known paper12. In this last paper he also introduced the “recoverable shear” in steady flow as an explanation for the effects. Much later this was experimentally proved by the author.
The Weissenberg Postulate: In9 and12 the now often quoted Weissenberg assumption or postulate P22 = P33 was developed for any material in plane stationary laminar flow from completely general symmetry conditions of motion: where there are equal velocity gradients (say zero) there are equal stresses. This is the direct result of his completely general discussion of stresses and strains at a point or “Goniometry”.
The Rheogoniometer: Parallel to the theory, S. M. Freeman9 12 and especially J. E. Roberts14 developed the “Weissenberg Rheogoniometer” to a practically usable instrument, with which Russell8 and Jobling15 together with Roberts conducted extensive tests which proved the logarithmic distribution of pressures along the radius, the validity of the formula for the total force and (Roberts) the equality P22 = P33.14 This proof, though presented as a result in 195316 has unfortunately never been accurately described in a wide circulation publication.
A summary of Weissenberg’s work was presented at a seminar at Columbia University in 196317 but has also a limited distribution. In it his general principles of coordinate transformations, similarity and symmetry are discussed at length, also there is a detailed discussion of the “postulate”. However, this publication does not include all the former developments.
Besides the mentioned publications he has often influenced his collaborators, who published ensuing mathematical developments without expressly stating his authorship. Such cases are the mentioned Rabinowitsch-formula, Jobling’s expression for the total force in the cone-and-plate and also the exact formulation of the recoverable shear and normal-stresses. Only the “Effect”, the “Postulate” and the Rheogoniometer are generally associated with his name in Rheology.
An example of his intuition is that of elasticity: when he introduced it in 1928 nothing was known about its possible origin. Only much later, in the 1950’s, the theory of rubber elasticity was founded through the work of W. Kuhn, Treloar, Guth and James and others. This was more recently, nearly 30 years after the original proposal, adapted to flowing solutions by the author. Due to this unfortunate publication of his ideas and conclusions in not widely accessible periodicals, his work has not exerted its due influence on rheologists in the world. It is partly due to the difficulty in reading his papers that require an exceptional amount of thinking and meditation on the part of the reader: he does not write in an easily understood way.
His work must range with the classical papers in deformational mechanics such as the, equally not widely known, works of E. and F. Cosserat18 and J. Finger,19 that to some extent have been reformulated in more recent developments.
It is to be hoped that now his life’s work should be summarized and published in a widely understood form to achieve its well deserved influence on modern Rheology.
1. Herzog, R. O. and K. Weissenberg, Kolloid-z., 46, 277, 1928.
2. Weissenberg K., Mitt-Staatl. Material p. Asst. Sonderheft V, 1929.
3. Eissenschitz R., B. Rabinowitsch and K. Weissenberg, ibid., IX.
4. Weissenberg K., Abh. Preuss. Akad. Wiss. Heft. 2, 1931.
5. Eisenschitz R. and W. Philippoff, Naturwiss, 21, 145, 1933.
6. Philippoff W., Physik-Z., 35, 884, 900, 1934.
7. Weissenberg K., Arcives Geneve 5, 17, 1, 1935.
Reiner M. and K. Weissenberg, Rheology Leaflet, 1939 Nr. 10, 11.
8. Russell, R. T., Thesis, Imperial College London, 1946.
9. Weissenberg K., Conf. British Rheologist’s Club, 36 1946.
Freeman, S. M., ibid., 68, 1946.
10. Weissenberg K., Nature, 159, 310, 1947.
Weissenberg K., Shirley Inst. Memo. XXI, 203, 1947.
Chadwick G. E., S. E. Shorter and K. Weissenberg, ibid., 223, 1947.
11. Freeman S. M. and K. Weissenberg, Nature, 161, 324 and 162, 320, 1948.
12. Weissenberg K., Proc. 1st Rheology Congress Holland, 1948.
Freeman S. M., ibid.
13. Weissenberg K., Proc. Roy. Soc., 200A, 183, 1950.
Lodge A. and K., Weissenberg Some Recent Dev. Rheol., 129, 1950.
14. Roberts J. E., Ministry of Supply ADE Rep., 13, 1952.
15. Jobling A., Ph.D. Thesis, Univ. Cambridge, 1956.
16. Roberts J. E., Proc. 2nd. Congr. of Rheology, Oxford, 91, 1953.
Weissenberg K., Proc. Faraday Soc., Oxford Meeting, 1959.
17. Weissenberg K., Seminar at Columbia University N.Y., 1963.
18. Cosserat E. and F., Ann. fac. Sci. Toulouse, 10, 1896.
19. Finger J., Akad. Wiss. Wien. Sitzber. Ila, 103, 1073, 1894.
Preface / Acknowledgements / Biographical Notes
Weissenberg’s Influence on Crystallography
Karl Weissenberg and the Development of X-Ray Crystallography
The Isolation of, and the Initial Measurements of the Weissenberg Effect
The Role of Similitude in Continuum Mechanics
The Effect of Molecular Weight and Concentration of Polymers in Solutions on the Normal Stress Coefficient
Elasticity in Incompressible Liquids
The Physical Meaning of Weissenberg's Hypothesis with Regard to the Second Normal-Stress Difference
A Study of Weissenberg's Holistic Approach to Biorheology
The Weissenberg Rheogoniometer Adapted for Biorheological Studies
Dr. Karl Weissenberg, 1922-28
Weissenberg’s Contributions to Rheology
The Early Development of the Rheogoniometer
Some of Weissenberg's More Important Contributions to Rheology: An Appreciation
Publications of Karl Weissenberg and Collaborators / List of Contributors
© Copyright John Harris