### 1995 Timoshenko Medal Lecture by Daniel D. Joseph

by Daniel D. Joseph , University of Minnesota

In my instructions about the correct behavior of recipients of the Timoshenko Medal at this dinner, Tom Cruse wrote to me that "While I ask that you consider the hour and the length of the evening in selecting the length of your remarks, the time is yours and we are honored to hear from you at that time." This suggests to me that as a Timoshenko Medalist, I can be indulged but that if I really want to be appreciated, I should keep it short.

I understand that when Jerry Ericksen got this award, he said "thank you" and sat down. I would like to follow this courageous path, but I lack the courage and so I will embellish "thank you" just a little.

Of course, I am pleased and honored to get the Timoshenko Medal and I am especially pleased to be introduced by my teacher and dear friend, Phil Hodge. I got my Ph.D. in 1963 at the Illinois Institute of Technology in Chicago. My advisor was L.N. Tao, but I took a graduate course in continuum mechanics with Phil when I was an undergraduate. It was a very demanding and quite unusual course with an emphasis on mathematical rigor at a level at which beginning students in engineering could understand. The course had a very important and permanent influence on my understanding of the mathematics of mechanics which influences me still.

At the University of Minnesota, Phil and I were running buddies. We even ran some marathons together; that is, we started together, then I saw his backside for a few minutes and three or four hours later, I could find him well rested at the finish. I ran 22 marathons; my best time for all of them was 3:42. In that marathon, Phil did it in 3:16 and was No. 1 in his old age group. My marathon running is like my career; not much talent, but very persistent. It is good for me that the Timoshenko Medal is also given to tortoises.

Applied mechanics was very strong at IIT in the early 1960's. The late Peter Chiarulli and Max Frocht were there then, and Eli Sternberg had been there not so much earlier. Another applied mechanician, Walter Jaunzemis, taught us a very thoughtful course on analytical dynamics which I appreciated greatly. He died as a young man. It is so sad to think of these ghosts of my past. My friend, Ronald Rivlin, who thank God is still alive and feisty, told me on the occasion of my 60th birthday that I was too old to die young. This is actually some comfort. It might interest you that Barenblatt and I are editing a collected works of Rivlin which ought to appear next year.

My relations with the people of applied mechanics developed more strongly at IIT than later. Peter Chiarulli arranged for me to present some work I did about Stokes flow over a porous sphere at an ASME meeting in a session chaired by George Carrier. He introduced me as Dr. Joseph. I wasn't a Dr., but George didn't know it. Later, he told me that he always played it safe. A little later, he saved me from later embarrassment by rejecting that paper. Too many mediocre papers were published in the 1960's and 1970's.

Jim Rice noted already in his acceptance speech of last year that the early 1960's was possi¬bly the best time to get a Ph.D. in mechanics ever. Due to Sputnik, there was lots of money for fel¬lowships, new faculty positions and research. I certainly benefited from this; I got a good job eas¬ily at the University of Minnesota in 1963 and my career advanced very fast. One consequence of the atmosphere of the time was to put a bigger than usual emphasis on foundations at the expense of applications. Many engineers in those days had an exaggerated idea of the power of abstract approaches. Mathematicians, and physicists too, have a good sense of the history of their subject. They know their heroes and who to emulate. We have not this sense of history in engineering and it leaves us rudderless and prey to foreign influences like those which, in the 1960's and 70's, led to the unnatural attempt to axiomatize mechanics.

It is probable that in recent times the pendulum has swung too far against abstract approaches based in mathematics in a kind of over-reaction which generally accompanies the correction of abuses.

My career can also be understood in two phases, the first emphasizing mathematics and the second, engineering. Actually, I could point to a third phase—the sociology phase, which came first. Some of you may know that I got a master's degree in sociology from the University of Chicago in 1950. Even though I have a master's degree in this field, I don't get much respect. The problem is that no matter how well educated you may be in sociology, the man on the street has his own opinion. Engineers are much better off because they get the benefit of the doubt.

Probably only a few of you know why I got this medal. Some years ago, when I had no honors and awards but Jerry Ericksen had many, I noticed that to get them, you needed to be certified. I told Jerry that the best kind of certification is that you have already got some honors and awards from elsewhere. Jerry then noted that "every dog knows where other dogs pee."

Joking aside, I owe so much to the string of superb students who have worked with me in these past years: Luigi Preziosi, KangPing Chen, Howard Hu, Pushpendra Singh, Adam Huang, Runyuan Bai, Jimmy Feng, Todd Hesla, Mike Arney, Joe Liu, Geraldo Ribeiro, Chris Christodoulou, Oliver Riccius, Joe Than, P. Huang and many others. These students worked with me on many projects; here, I will mention two: Hyperbolicity and change of type in the flow of viscoelastic fluids and the water-lubricated pipelining of heavy crudes.

In the 1980's, together with Michael Renardy and Jean Claude Saut, I found that the unsteady vorticity equation for many models of viscoelastic fluid is hyperbolic, giving rise to waves of vorticity. In steady flows, the vorticity field can be of one type here and another there, as in transonic flow. The other variables, stresses and velocities, are neither strictly hyperbolic and/or strictly elliptic. To me, it is surprising that with so much mathematical work coming from rational mechanics in the 1960's, 70's and 80's, that the problem of the mathematical classification of type of the governing PDE's was not joined.

The key quantity in the discussion of hyperbolic waves of vorticity is the speed of shear waves. We invented a device in 1986 to measure the speed of these waves. We must have measured these speeds in 200 different fluids by now. There are over 100 values published in my 1990 book on the Fluid Dynamics of Viscoelastic Liquids. You can compute a relaxation time for these speeds, and usually it is an order of magnitude smaller than what other people get by the devices they use. I think that conventional rheometers have a too slow response, most of the signal has decayed by the time those instruments kick in.

Using speeds measured on my device, I have correlated data from our experiments on delayed die swell, the orientational change of falling bodies, the change in the drag law of air bubbles rising in viscoelastic fluids and other anomalous effects that were reported in experiments, which I interpret as a change of type. If you use the speed we measure, you get a good agreement, but not otherwise.

I must confess that the rheology community, though not hostile, seems largely indifferent to these results which I consider to be so important.

Another topic on which we have worked, which I like greatly, is water-lubricated pipelining of heavy oils. It is a gift of nature that if you put water and oil into a pipeline, and the oil is viscous enough, say, greater than 5 poise, the water will go to the walls of the pipe where it lubricates the flow. You can get drag reductions this way of the order of the viscosity ratio. Crude oils with a viscosity of 1,000 poise are not uncommon. They can't be pushed through pipes at that viscosity, but with water there, they go through easily. You've got drag reductions of the order of thousands. This is a technology which has been used and it will be used more and more.

CNN found out about our work on this and did a short video segment on it which I am going to show you. That week, I had a tooth pulled and my face was swollen. Just my luck to have a swollen face on the road to stardom.

I have been asked many times if the lubrication of one fluid by another can be described by a variational principle. Strictly speaking, it cannot; however there is something in the idea of minimum dissipation which is best expressed in anthropomorphic terms. "High viscosity liquids are lazy. Low viscosity liquids are the victims of the laziness of high viscosity liquids because they are easy to push around."

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