The existence and stability of quasi-steady periodic voidage waves in a fluidized bed

摘要: Using the Hopf bifurcation theorem we are able to show existence of a one-parameter family quasi-steady periodic solutions nonlinear equations motion governing one-dimensional flow in fluidized bed at rates for which uniformly state is unstable. We then obtain valid expansions these close point using method multiple scales, and extend results by numerical integrations certain values parameters. The also identifies rateE *such that less thanE *the supercritical while greater thanE *it subcritical. Having established can exist, discuss temporal stability voidage waves considering weakly evolution slowly varying wave train critical stability. For lower find stable only such uniform unstable provided their wavelength λ<λ*. upper find, as well there being wavelength $$\overline \lambda $$ if $$\lambda< \overline , further parameterγ u with conditionγ ≧1 needed