Vibrated beds of powders: A new mathematical formulation |
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| Affiliation: | 1. Department of Radiotherapy, Lucien Neuwirth Cancer Institute, 108 bis, Avenue Albert Raimond, BP 60008, 42271 Saint-Priest en Jarez, France;2. Laboratoire de Radiobiologie Cellulaire et Moléculaire, CNRS UMR 5822, Institut de Physique Nucléaire de Lyon, IPNL, 69622 Villeurbanne, France;3. Department of Radiotherapy, Sichuan Cancer Hospital, 55 Renmin Nan Lu, Sect 4. Wuhou District, Chengdu, 610041, China;4. Department of Radiotherapy, Institut Gustave Roussy, 114, Rue Edouard Vaillant, 94805 Villejuif, France;5. Institut de Recherche Biomédicale des Armées, D19, 91220 Brétigny sur Orge, France;6. French Military Health Services Academy, Ecole du Val-de-Grâce, Paris, France;1. School of Fundamental Sciences, Massey University, New Zealand;2. School of Food and Advanced Technology, Massey University, New Zealand;1. Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia;2. Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong;1. Institute of Fundamental Sciences, Massey University, Palmerston North Campus, Private Bag 11222, Palmerston North 4442, New Zealand;2. School of Engineering and Advanced Technology, Massey University, Palmerston North Campus, Private Bag 11222, Palmerston North 4442, New Zealand |
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| Abstract: | A new mathematical formulation was made to deal with the compressible gas model that represents the vibrated particle bed. A novel boundary condition, which incorporates the equation of motion of the bed and the equation of continuity in the air gap between the bed and the vessel base, was introduced. This made it possible to reduce three differential equations, hitherto treated as governing equations that characterize the vibrated particle bed, to a single partial differential equation with pertinent initial and boundary conditions. Experiments were also conducted to assess the validity of the model. Satisfactory agreements between the predicted and measured values have been observed within limited parameter ranges. |
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