*Karl Weissenberg - The 80th Birthday
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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, Reiner^{1}, and Philippoff^{2},
Lodge^{8}), 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

(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 Stokes^{7}
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. Hagenbach^{8} published his derivation to
which reference had been made by Wiedemann^{9} in 1856. Also in 1860 a
derivation appeared in a paper on haemodynamics by H. Jacobson^{10}
(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, (Schwedoff^{11} (1900),
Trouton and Andrews^{12} (1950), W. R. Hess^{13} (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 Weissenberg^{4}
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 Institute^{15} 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.

Weissenberg^{18}
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
rheogoniometer^{20} 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.

**
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**

**
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**

**
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**