(361d) Solution for the Speed of Decompression Waves in Fluidization

We consider the decompression wave in fluidization, as described by Wallis, et al. [Int. J. Multiphase Flow,19, 839--874, 1993], and give the analytic solution for the one--dimensional wave speed. In its simplest form, the decompression wave is a concentration wave moving upward into a close--packed region. The wave structure is such that this wave connects the close--packed region with a nonpacked, expanding, region that is in local equilibrium the the hydrostatic pressure gradient. The solution is general; hence it is valid for beds of solid grains fluidized by either gas or liquid, sedimentation, and for small gas bubbles rising in a liquid. Averaged two--body forces are the main physical effects that determine the wave speed. The hyperbolic model equations developed by Kashiwa & Rauenzahn [Proc. 3rd Int. Symp. on Two--Phase Flow Modeling and Exp., Edizioni ETS, 2004] supply the general framework; data from experiments by DiFelice [in Wallis, et al. 1993] provide an undetermined coefficient associated with the viscous part two--body force. The solution is shown to be capable of predicting the onset of bubbling in the fluidization of solid grains, by comparison with the data of Rietema [Chem. Eng. Sci., 37, 1125--1150, 1982].