Granular Hydrodynamics
Sand flowing through the constriction of an hourglass or jumping on a vibrating plate is fluidized in the sense that it moves analogously to a fluid. Dense flows of grains driven by gravity down inclines occur in nature and in industrial processes. Natura
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Abstract Sand flowing through the constriction of an hourglass or jumping on a vibrating plate is fluidized in the sense that it moves analogously to a fluid. Dense flows of grains driven by gravity down inclines occur in nature and in industrial processes. Natural examples include rock avalanches and landslides. Applications are found in the chemical, pharmaceutical and petroleum industry. Grain flow can be modeled as a fluid-mechanical phenomenon. However, granular fluids teach us about an astounding complexity that emerges from simple, macroscopic particles. For example, starting from an homogenous fluidized system, structures evolve and a dilute granular fluid co-exists with much denser solid-like clusters. Another example is the so-called Brazil nut effect, whereby larger and heavier particles placed into an agitated granular bed rise to the top. We present an outlook of the hydrodynamic description of granular materials. Our purpose is to outline a theory of grain flow which is based upon the description of continuous matter fields derived from the kinetic theory for dense gases, as is usually encountered in fluid dynamics. L. Trujillo L. D. G. Sigalotti Instituto Venezolano de Investigaciones Científicas, IVIC, Centro de Física, Apartado Postal 20632 Caracas, 1020-A, Venezuela e-mail: [email protected] L. Trujillo (&) The Abdus Salam, International Centre for Theoretical Physics, ICTP, Trieste, Italy e-mail: [email protected] J. Klapp Instituto Nacional de Investigaciones Nucleares ININ, Carretera Mexico- Toluca Km 36.5, La Marquesa, 52750 Estado de Mexico, Mexico e-mail: [email protected] J. Klapp Departamento de Matemáticas, Cinvestav del I.P.N., San Pedro Zacatenco, 07360 Mexico D.F., Mexico
J. Klapp et al. (eds.), Fluid Dynamics in Physics, Engineering and Environmental Applications, Environmental Science and Engineering, DOI: 10.1007/978-3-642-27723-8_11, Springer-Verlag Berlin Heidelberg 2013
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1 Introduction Granular materials consist of a collection of discrete macroscopic solid particles interacting via short-range repulsive contact forces. Classical examples are sand, powders, sugar, salt, and gravel. No limitation is imposed on the size of the particles, which may range from nanometer scale, as in pigments or aerosols, to the scale of mined or quarried materials and rocks. Their physical behavior involves complex nonlinear phenomena, including non-equilibrium static configurations, energy dissipation, nonlinear elastic response, and peculiar flow dynamics (Jaeger et al. 1996). Why are granular materials interesting? A new state of matter.—Beyond their practical importance, granular materials interest physicists because they are an unusual form of matter with interesting properties that are still not yet fully understood. Interdisciplinary effort.—Investigations in granular materials gather teams from civil, chemical and mechanical engineers, food technologists, powder metallurgists, materials scientists, pharmaceutical scientists, appli
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