Abstract
One-dimensional unsteady models of a fluidized suspension based on modeling the forces that the fluid exerts on the particles are considered. Four different theories are discussed. The first, by Foscolo and Gibilaro [1984, 1987], gives a criterion for the loss of stability of uniform fluidization. A second theory by Joseph [1990] which appears to carry the Foscolo-Gibilaro theory to a logical conclusion with the addition of a term proportional to the particle velocity gradient, leads always to instability. A third theory by G.K. Batchelor [1988] is formally similar to the one by Foscolo-Gibilaro, but is more generally derived. A fourth theory which takes into account the finite size of particles and can be used in any of the other three theories is derived here. We show that the finite size of particles is a regularizer of the short wave instability of uniform fluidization which occurs when the particle phase pressure is neglected. We introduce the problem of losing range. If the fluids and solids fractions are both intitially in the interval (0, 1), will they stay on that interval as they evolve? An answer is given.
This research was supported under grants from the US Army Research Office, Mathematics, the Department of Energy and the National Science Foundation.
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© 1990 Springer-Verlag New York Inc.
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Singh, P., Joseph, D.D. (1990). One-Dimensional, Particle Bed Models of Fluidized Suspensions. In: Joseph, D.D., Schaeffer, D.G. (eds) Two Phase Flows and Waves. The IMA Volumes in Mathematics and Its Applications, vol 26. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9022-0_10
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DOI: https://doi.org/10.1007/978-1-4613-9022-0_10
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