Abstract
A mathematical model for gas-fluidized beds is examined which treats both the particles and gas as continua by volume averaging. The system is then considered as two interlocking one-phase fluids. For small perturbations to the uniform state, these equations have been shown by Crighton (1991) to reduce to the Burgers-KdV equation and under certain criteria, we have instability. We consider the unstable situation when the amplification effects are a perturbation to the KdV equation and take an initial condition of a single KdV soliton. The growth of this soliton is followed through several regions in which the unstable Burgers-KdV equation is no longer appropriate, but KdV remains the leading order equation. Eventually, there is a fundamental change in the solution and the new governing equations are fully nonlinear and O(1). These admit a solitary wave solution which matches back onto the KdV soliton. Thus, we can follow the formation of a bubble from a small amplitude perturbation to the uniform state.
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References
Crighton D.G., In Nonlinear Waves in real fluids (ed. A.Kluwick).-Wien, New York.: Springer-Verlag, 1991. p.83–90.
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Additional information
University of Cambridge, Cambridge, United Kingdom. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 8, pp. 797–800, August, 1993.
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Harris, S.E. Nonlinear waves in gas-fluidized beds. Radiophys Quantum Electron 36, 540–542 (1993). https://doi.org/10.1007/BF01038430
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DOI: https://doi.org/10.1007/BF01038430