Aeronautica - nro reynolds

Life at Low Reynolds Number E.M. Purcell Lyman Laboratory, Harvard University, Cambridge, Mass 02138 June 1976 American Journal of Physics vol 45, pages 3-11, 1977. Editor's note: This is a reprint of a (slightly edited) paper of the same title that appeared in the book Physics and Our World: A Symposium in Honor of Victor F. Weiskopf, published by the American Journal of Physics (1976). Thepersonal tone of the original talk has been preserved in the paper, which was itself a slightly edited transcript of a tape. The figures reproduce transparencies used in the talk. The demonstration involved a tall rectangular transparent vessel of corn syrup, projected by an overhead projector turned on its side. Some essential hand waving could not be reproduced. This is a talk that I would not, I'mafraid, have the nerve to give under any other circumstances. It's a story I've been saving up to tell Viki. Like so many of you here, I've enjoyed from time to time the wonderful experience of exploring with Viki some part of physics, or anything to which we can apply physics. We wander around strictly as amateurs equipped only with some elementary physics even if we don't throw much light on theother subjects. Now this is that kind of a subject, but I have still another reason for wanting to, as it were, needle Viki with it, because I'm going to talk for a while about viscosity. Viscosity in a liquid will be the dominant theme here and you know Viki's program of explaining everything including the height of mountains, with the elementary constants. The viscosity of a liquid is a verytough nut to crack, as he well knows, because when the stuff is cooled by merely 40 degrees, its viscosity can change by a factor of a million. I was really amazed by fluid viscosity in the early days of NMR, when it turned out that glycerin was just what we needed to explore the behavior of spin relaxation. And yet if you were a little bug inside the glycerin looking around, you wouldn't see muchchange in your glycerin as it cooled. Viki will say that he can at least predict the logarithm of the viscosity. And that, of course, is correct because the reason viscosity changes is that it's got one of these activation energy things and what he can predict is the order of magnitude of the exponent. But it's more mysterious than that, Viki, because if you look at the Chemical Rubber Handbooktable you will find that there is almost no liquid with viscosity much lower than that of water. The viscosities have a big range but they stop at the same place. I don't understand that. That's what I'm leaving for him. Now, I'm going to talk about a world which, as physicists, we almost never think about. The physicist hears about viscosity in high school when he's repeating Millikan's oil dropexperiment and he never hears about it again, at least not in what I teach. And Reynolds's number, of course, is something for the engineers. And the low Reynolds's number regime most engineers aren't even interested in--except possibly chemical engineers, in connection with fluidized beds, a fascinating topic I heard about from a chemical engineering friend at MIT. But I want to take you into theworld of very low Reynolds number--a world which is inhabited by the overwhelming majority of the organisms in this room. This world is quite different form the one that we have developed our intuitions in. I might say what got me into this. To introduce something that will come later, I'm going to talk partly about how microorganisms swim. That will not, however, turn out to be the only importantquestion about them. I got into this through the work of a former colleague of mine at Harvard, Howard Berg. Berg got his Ph.D. with Norman Ramsey, working on a hydrogen maser, and then he went back into biology, which had been his early love, and into cellular physiology. He is now at the University of Colorado at Boulder, and has recently participated in what seems to me one of the most...