טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentHila Nachlieli
SubjectDescription of Granular Flow
DepartmentDepartment of Physics
Supervisor Full Professor Levine Dov


Abstract

     Granular materials are ubiquitous: sugar and salt in the kitchen, sand and marbles in the playground, powders in medicines and explosives are all examples of granular matter. Yet, while water is well described as a Newtonian fluid, there is no such simple description for the behavior of granular materials. In this thesis we try to close this gap, by proposing two continuum models describing the connections between the stress and the rate of strain tensors in granular flow. The models focus on slow flow near the static-flow transition.

     The first model assumes that granular matter flows when the shear stress acting on some plane in the granular matter is larger than the friction which is proportional to the normal stress. When granular matter flows, the flow is assumed to be Newtonian-like, where the shear stress is replaced by shear stress minus friction.

      The second model assumes, as suggested by simulations, that the pressure in the flowing granular matter is isotropic. Flow exists when an invariant function of the stress tensor is bigger than the friction times the isotropic pressure. In the flowing granular matter the deviatoric stress tensor is proportional to the rate of strain tensor.

      Both models are accompanied by flow profile predictions for some examples of two and three dimensional systems. Experiments done in the last decade are based on new technologies, such as x-ray detection and NMR, that enable velocity measurement in the middle of the flowing granular matter without influencing it. These experiments contain too few grain layers to be analyzed by a continuum model. Larger scale experiments will determine which of our models gives a better description of granular flow, and will show us which of our assumptions needs to be replaced or fine-tuned.