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Unformatted text preview: The ultimate website for understanding granular flows Wednesday, September 07, 2005 - 10:49:05 AM All I wanna know bout Viscous Stress (but I never dare to ask !) Good Afternoon! You will find the basic facts about viscous phenomenon - no details -. If you wanna know more just email me or feel free to ask in the Discussion Forum . I purposely erased all the bibliographical references and detailed equations to keep the text simple and easy to read. If you need an official reference for the content of this website, please, use: Dartevelle, S., Numerical and granulometric approaches to geophysical granular flows, Ph.D. thesis, Michigan Technological University, Department of Geological and Mining Engineering , Houghton, Michigan, July 2003. You will find herewith: I. Introduction: Have you said viscosity? II. Stress view of viscosity III. Granular kinetic view of viscosity IV. Viscosity and Tensors V. Bulk viscosity, Shear viscosity and Second coefficient of viscosity VI. The concept of viscosity within rigid-plastic granular flows Please, dont forget to sign our Granular Volcano Guest Book . Done and updated by Sbastien Dartevelle, The WebMaster, Saturday November 22 2003. I. Introduction: Have you said viscosity? After all, what is viscosity? Hmmmm, there are many different ways to answer to this question. When I was a High-School student, my science teacher said that viscosity is a property that owns any fluid and makes it somehow resistant to the flowing process. When I was Bachelor student, I got another picture of the viscosity. I was told that the viscosity is the tendencies towards uniformity of mass-velocity (momentum) throughout the flow. Such tendencies are explained by kinetic theory which attributes this phenomenon to the motion of molecules or grains from point to point. I have been long a wee bit confused about those two views or explanations of the phenomenon of viscosity because I could not reconcile what was for me two different stories. But believe me, it is the same story but seen from a different point of view. The "resistance to flow" point of view is a global macroscopic force balance view, while the "mass-velocity uniformity" is a molecular-granular microscopic view of the viscosity phenomenon. Herewith, I will only consider the viscosity concept for granular materials, and since granular theory has evolved from gas-kinetic theory, the following paragraphs also apply to the gas viscosity concept. Page 1 of 14 All I wanna know about Viscous Stress 9/7/2005 http://www.granular-volcano-group.org/viscous_stress.html [ Back to Top ] II. Stress view of viscosity A moving fluid exhibit evidences of internal friction ( friction is a good word, it gives us somehow the feeling of resistance), called viscosity. To see this, lets consider a moving fluid where the velocity is minimal at the bottom and tend to be higher towards the top of the fluid: [Figure 1a: the Y axis is perpendicular to your screen, hence the XY plane is parallel to your table and the ZX plane is nothing but...
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This note was uploaded on 02/11/2012 for the course MET 4305 taught by Professor Lazarus during the Fall '09 term at FIT.
- Fall '09