Karl Weissenberg - The 80th Birthday Celebration Essays
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The Early Development of the Rheogoniometer




Defence Research and Development Staff,

British Defence Staff, Washington, U.S.A.




In the early 1 940s it was becoming increasingly important to determine the true parameters of materials which exhibited both the properties of elasticity and viscosity. At this time, Merrington1 had demonstrated that thickened hydrocarbons exhibited recoverable strain when ejected from a nozzle, whilst Russell and the author had (independently) experimentally shown that jets of high viscosity also possessed elastic properties.


The real complexity of the materials and their possible further analysis was not appreciated at this time. It was not until Weissenberg, who was at that time Director of Physics Research at the Shirley Institute, agreed to act as consultant to the Petroleum Warfare Establishment, that the process of formulating and conducting experiments was co-ordinated.


Weissenberg had indeed shown in two outstanding papers2,3 his grasp of the theoretical principles involved, and it became clearer as preliminary experiments were made by Rosin, Fehling, Russell, Gardner, Nissan, Wood and Freeman and the author, that new and better instrumentation was required. Among Weissenberg’s many abilities were those of clearly stating his theories and encouraging in others, the desire to master the problems presented in understanding all of the facets of complex materials. Indeed, it is now difficult to imagine gaining control of the phenomena governing flow without goniometric experiments, as whenever the mechanical quantity to be measured is anisotropic, shearing components in the deformation will ensure different values in stress in different directions with all except isotropic fluids, (Note that thixotropic fluids are sometimes isotropic also). These are of course special cases of a general fluid. We can possibly define, therefore, the goniometry of flow as the measurement of the distribution of stresses and strains within the flowing material at every instant in time and at every point in space around the full solid angle.




Before Weissenberg’s concept of measuring the properties of fluid-like materials in a goniometric pattern, the analysis of flowing materials had been limited to the relationship of tangential or shear stresses to the displacement. He pointed out that in materials of a general nature, additional forces were generated and in his theoretical approach, the application of three fundamental principles were required and that goniometry was of importance to each of these principles.


Although his theoretical approach is covered by other authors, these principles are basic to the instrument and are:

(a) the dynamic equilibrium of forces at every point in the flowing material,

(b) the maintenance of continuity, and

(c) the stress/strain relation.


These principles were clearly established in the mid-forties, when the team dispersed, but Weissenberg,4,5 Freeman6 and Russell7 reported preliminary development of an instrument which approximated to the ideal at least in a phenomological way. At the first Rheological Congress in 1948, Weissenberg named the instrument Rheogoniometer8 (it had previously been named in 1946) and it was shown that normal and shear stress were present when liquids were sheared. It was also shown in shear vibrations that normal stresses were small or negligible for small vibrations but the frequency of normal stress was double that of the shearing stress for large vibrations. A modified form for the study of the properties of molten plastics was devised by Pollet9,10 and Cross.


Although this instrument did not in fact achieve Weissenberg’s goal of measurement of all the stresses and strains, it was obvious that he would continue until the good was reached. It was unfortunate Freeman left his work at the Shirley Institute as his experience and expertise would have greatly aided development. However, Thomas appreciated fully that further understanding of viscoelastic materials could not be achieved until adequate instrumentation was available and contracts were placed with Huger and Watts and with Thomas Keatings who with the design aid of Richmond, Wylde and the author made one type of instrument whilst in-house work produced others. These designs and patents were made available to Farol Research11.


At the same time Schulman advised a small team comprising Weissenberg, Jobling,12 Grossman and Egan, and experiments on more defined materials were made. Shaw and Pilpel also examined various visco-elastic materials with the instruments. Weissenberg from his studies, evolved a series of experiments which were designed to simplify the mathematical analysis. One of Weissenberg’s theories was that planes which have suffered the same normal displacement would suffer the same normal stresses. That is, that in a simple continuous shearing action, the normal stresses of P22 and P33 would be, in a first approximation, equal. The author13,14 with Weissenberg’s help, eventually evolved experiments with minimal assumptions. With this advance, the instrument could be simplified and Jobling, Pilpel and Kotaka15-18 conducted extensive experiments on a variety of materials.


Weissenberg19 continued his work and one of the many workers who was influenced, was Lammiman. Lammiman20 appreciated that bitumens were of viscoelastic nature and was determined to make meaningful measurements of them. Consequently, he and the author designed an instrument of far wider which Rheogoniometer was this veisatility, which was largely built by King, of Farol Research.


This instrument was designed to subject materials to either unidirectional laminar shear of vibrational shear or both in various frequencies and amplitudes in varying amounts, at the same time measuring normal and shear components. The advantages of quick response of stress measurement with very small strains enabled high viscosity materials to be investigated without undue changes due to viscous heating of the material under test. Materials could also be subjected to relaxation experiments. The method of measurement of normal stresses and compensating forces had always been desired by Weissenberg and this was at last achieved by a servo mechanism.


The requirements of determining the properties of bitumen over a wide range of rates of shear and temperature ensured that the instrument could be used for a wide variety of other materials enabling Lammiman to measure the mechanical properties of polymers above their melting points. Fracture was also observed in flowing materials giving new criteria for break up.


It is not always appreciated that Weissenberg21 was keenly interested in the break-up of materials and in fact that he had in mind another type of Rheogoniometer. All who have attended his classic lectures will know of his marking of rubber sheets and deforming these to demonstrate various mechanical deformations. He appreciated that the ink or paint was subjected to the deformations and that if material was sandwiched between two such deformable membranes that new types of controlled deformation would be possible.


As we all know, “simple shear” is a most complex mechanical action. Weissenberg’s concept encouraged the author, Grossman22,23 and Jobling14-26 to devise such an instrument so that the stresses, strains and their derivatives would be co-axial, thus simplifying the mathematical analysis. Before the break-up of our team, preliminary experiments were made showing again that the apparent shear thinning of viscoelastic fluid was mostly due to a change in the comparative direction of stress and strain velocity, tensors as Weissenberg predicted.


One can easily sum up Weissenberg’s contribution in that he has changed the whole concept of mechanical testing of real materials and one can only wonder how he achieved so much with insufficient funds for his great abilities. Perhaps it was because he is not only a man of great scientific ability, but one whom everyone respects because of his human qualities, anyone can approach him and receive wise counsel with courtesy and all who worked with him are proud of their association.




1. Merrington, A. G. (1943), Nature, 152, 663.

2. Weissenberg, K. (1931), Abhadl. preuss. Akad. Wiss. Math, nature R.I. no2.

3. Weissenber, K. (1934), Arch. sci. Phys. et nat., 17, 1.

4. Weissenberg, K. and Freeman, S. M. (1948/49), Proc. 1st Intern. Rheol. Cong. Holland, 11-12.

5. Weissenberg, K. (1949), Proc. 1st Intern. Cong. Holland, 11-14.

6. Weissenberg, K. and Freeman, S. M. (1948), Nature, 161, 334.

7. Russell, R. J. (1946), Ph.D. thesis London University..

8. Weissenberg, K. (1948/9), Proc. 1st Intern. Rheol. Cong. Holland, 1-29.

9. Pollett, W. F. O. and Cross, A. H. (1950), .J. Sci. Inst., 227, 209.

10. Pollett, W. F. O. (1953/4), Proc. 2nd Intern. Rheol. Cong. Oxford, 85.

11. Roberts, J. E. and Weissenberg, K. (1900), Brit. Pat. Appn., 20583/53.

12. Jobling, A. and Roberts, J. E. (1959), J., Polymer, Sci., 36, 421.

13. Roberts, J. E. (1952), Ministry of Supply, ADE, 13/52.

14. Roberts, J. E. (1953), Proc., 2nd. Intern., Cong., Oxford, 91.

15. Jobling, A. and Roberts, J. E. (1959), J. Polymer., Sci., 36, 433.

16. Pilpel, N. (1954), Trans., Faraday. Soc., 50, 1369.

17. Pilpel, N. (1955), Trans., Faraday, Soc., 51, 1307.

18. Kotaka, T. (1960), Thesis, Kyoto Univ., 1960.

19. Weissenberg, K. (1960), Proc., Roy., Soc. (London), A200, 183.

20. Lammiman, K. and J. E. Roberts (1961), Lab., Pract., Vol., 10, 11.

21. Weissenberg, K. (1955), Bull., Brit., Soc., Rheol., no, 43, 6.

22. Grossman, P. U. A. (1958), J., Sci., Instrum., 35, 131.

23. Grossman, P. U. A. (1961), CoIl., Zeit., 174, 98.

24. Jobling, A. and Roberts, J. E. (1958), Brit., J., Appl., Phys., 9, 235.

25. Jobling, A. and Roberts, J. E. (1959), Rheology of Disperse Systems Pergamon Press.

26. Jobling A. and Roberts, J. E. (1958), in Eirich, F. R. (Ed.) Rheology Theory and Applications, 11-503.




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