Karl Weissenberg - The 80th Birthday Celebration Essays
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Some of Weissenberg’s More Important

Contributions to Rheology: An Appreciation

 

 

PROFESSOR HERSHEL MARKOVITZ

Center for Special Studies, Mellon Institute of Science, Carnegie-

Mellon University, Pittsburgh, Pa. 15213. U.S.A.

 

 

The measure of Weissenberg’s contribution to rheology is not simply a matter of counting the number of papers (or pages) published or the number of graduate students trained, or even the number of times his papers have been cited. While a similar statement could be made about almost every scientist, it is especially true in this case for a variety of reasons.

 

One of his most widely used contributions is rarely attributed to Weissenberg these days. Although the record is quite clear and although careful authors indicate the originator correctly (see, for example, Reiner1, and Philippoff2, Lodge8), one of the most frequently employed equations in rheology is usually associated with another name. I refer here to the equation for calculating D(t), without assuming a specific form of the function, from experimental data obtained with a capillary viscometer. Here D(t), a property of the fluid, gives the dependence of the rate of shear D on the shear stress t in steady laminar flow.

 

Admittedly, one can understand why careless authors make an incorrect attribution. Identical derivations were published in two separate articles in 1929. The first to be submitted (March 14, 1929), “Zur Analyse des Formveraenderungswiderstandes” by R . Eisenschitz, B. Rabinowitsch, and K. Weissenberg was published in the Mitteilungen der deutschen Materialspruefungsanstalten.4 Before it appeared, another paper “Ueber die Viskositaet und Elastizitaet von Solen” was sent to the more readily accessible Zeitsschrift fuer physikalische Chemie on August 12, 1929, by B. Rabinowitsch.5 It is this paper that is most frequently cited as the source for this equation. It is perhaps not too surprising then, that it is most often called the “Rabinowitsch equation” despite the fact that the author of the paper makes it quite clear that Weissenberg should be credited. As a footnote to the heading of Subsection III.I, entitled Aligemeine Theorie, which gives the derivation, he notes, “The general theory was developed by K. Weissenberg”. Eisenschitz, the other author involved, in a paper6 published some years later, attempts to clarify the history in a footnote and refers to the equation as “the theory of Weissenberg”. Thus, unequivocally, it is Weissenberg’s name, if anyone’s, that should be associated with this equation.

 

(It is perhaps of interest to note that several other important rheological equations have equally confused histories, for example, the law governing the slow flow of Newtonian fluids through tubes. It was established empirically about 1840 by the independent experimental researches of G. H. L. Hagen and J. L. Poiseuille. Here, I think, the contribution of each of these two men are understood but which of their names is attached to the law varies with the writer. With respect to the derivation of this relation from the general (Napier-Stokes) equation for the Newtonian fluid, there is considerable confusion. Actually, when Stokes7 in 1845 published the formula for the velocity distribution, he had also derived the expression for the rate of discharge but decided not to include it in the paper because “having…. compared the resulting formulae with some of the experiments of Bossut and DuBuat, I found that the formula did not at all agree with experiment.” In 1860, E. Hagenbach8 published his derivation to which reference had been made by Wiedemann9 in 1856. Also in 1860 a derivation appeared in a paper on haemodynamics by H. Jacobson10 (practising doctor from Koenigsburg) but he stated that it was being presented with the permission of Professor Newman who used to give it in his lectures on haemodynamics.)

 

This contribution of Weissenberg came at a critical point in the development of rheology. After a few isolated studies on steady non-Newtonian flow, (Schwedoff11 (1900), Trouton and Andrews12 (1950), W. R. Hess13 (1910)), many colloid chemists followed their colleague Hatscheck’s work in 1913 with studies of their own on the flow of these high molecular weight materials. Most of the publications consisted essentially of presentations of the raw data. During the 1920’s some authors began to interpret the data in terms of various assumed specific relations between the shear stress and rate of shear, such as the power law and plastic body models. However, it became quite clear that colloids followed neither of these equations. Weissenberg’s formula made it possible to procede with the evaluation of data on a rational basis.

 

But Weissenberg4 went deeper than that. He did not consider the rate of shear dependence of the viscosity as an isolated phenomenon. He called attention to the fact that the same fluids also exhibit flow birefrigence, which he took as evidence of an anisotropy in the flowing system. He also noted that the solutions were “elastic” (now referred to as “viscoelastic” by many authors) and discussed this in terms of the Maxwell model of viscoelasticity. Thus, from the start he grasped the important interelated phenomena in the rheology of non-Newton fluids. In fact, he went further. He tried to explain it all on a thermodynamic basis. This programme is not yet complete today.

 

Weissenberg’s name is most often cited by rheologists for the role which he played in the interpretation of the group of phenomena known as the normal stress effects. Unfortunately, in my opinion, too much of this literature concerns itself with controversy over some matters of detail and this has tended to obscure some of his more important contributions. The active study of the normal stress effects began in England during World War II. It was only after that war that this work was declassified and some of it published. Many of the details of these

developments are still not public knowledge.

 

Apparently because of his knowledge of rheology, Weissenberg, then a refugee from Hitler’s Germany, was borrowed from the Cotton Research Institute15 to work with one of a number of groups performing research on flame-thrower materials. A number of unexpected rheological phenomena were observed and investigated :16,17 unusually large inlet effects in flow through tubes, rod-climbing in Conette flow between coaxial cylinders (sometimes referred to as the Mae West effect), and secondary flow between parallel discs.

 

Weissenberg18 devised other experiments which were simple but instructive. In one, a fluid subjected to torsional flow between two discs exerts enough normal force to lift the top disc. With Weissenberg’s advice, R. J. Russell performed a great number of quantitative experiments of various types. Unfortunately they are published only in his dissertation.19 Later, Weissenberg conceived of the rheogoniometer20 which was later refined,21 commercially produced, and is now found in laboratories around the world.

 

Behind and beyond the experiments, Weissenberg had the insight to attribute some of the observed phenomena to the “normal stresses”, that is, to the inequality of the normal stress components in the three natural orthogonal directions. Further, he associated these effects with the viscoelastic behaviour (“recoverable amount of shear”) of these fluids.

 

Perhaps an indication that these concepts are not obvious is the fact that the flow properties of the same type of material were being investigated by competent scientists in the United States and in other countries (probably with less pressure for practical results). Undoubtedly some of them observed phenomena similar to those described above. But, as far as I know, it was only the workers in the U.K., and Weissenberg in particular, that delved into the basic rheological laws behind them. It was this work that played an important role in the development of modern theoretical and experimental continuum mechanics.

 

Weissenberg’s contributions to rheology are thus seen to be many faceted and not simple to document on any numerical basis. He provided germinal ideas, he brought to bear mathematical techniques, he devised experiments and instruments, he aroused the interest of other scientists by his enticing demonstrations, he was an inspiration to many.

 

We are all in his debt.

 

 

REFERENCES

1. Markus Reiner, Physics, 5, 321 (1934).

2. W. Philippoff, “Viskositaet der Kolloide”. Steinkop, Dresden, 1942; reprinted by Edward Brothers, Ann Arbor, 1944.

3. A. S. Lodge, “Elastic Liquids” Academic, New York, 1964.

4. R. Eisenschitz, B. Rabinowitsch, and K. Weissenberg, Mitteil deutsch, Materialspruefungsamt, Sonderheft, 9, 91(1929).

5. B. Rabinowitsch, Z. physik. Chem., A145, 1 (1929).

6. R. Eisenschitz, KoIl Z., 64, 184 (1933).

7. G. G. Stokes, Trans, Cambridge Phil. Soc., 8, (1845); 287 Math. Phys.

Papers I, 75.

8. E. Hagenbach, Ann. Phys. Chem. 109, 385 (1860).

9. G. Wiedmann, Ann. Phys. Chem., 99, 177 (1856).

10. H. Jacobson, Archiv. Physiol., 80. (1860).

11. T. Schwedoff, J. Physique [2.] 9, 34 (1890).

12. F. T. Trouton and E. S. Andrews, Proc. Phys. Soc. (London), 19, 47 (1905).

13. W. R. Hess, Z. klin. Med., 71, 421 (1910).

14. E. Hatschek, KolI Z., 13, 88 (1913).

15. C. H. Landers, J. Inst. Fuel., 19, 1 (1945).

16. F. H. Garner and A. H. Nissan, Nature, 158, 634 (1946).

17. G. F. Wood, A. H. Nissan, and F. H. Garner, J. Inst. Petrol., 33, 71 (1947).

18. K. Weissenberg, Nature, 159, 310 (1947).

19. R. J. Russell, Ph.D. Thesis, University of London, 1946.

20. K. Weissenberg, Proc. Intl. Congress Rheol., Holland, II, 114 (1948).

21. J. E. Roberts ADE report 13/52. Armament Design Establishment, 1952.

 

 


 

Contents

 

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

 

Index

 

 

 

© Copyright John Harris