It is a significant feature of most gas-fluidized beds that they contain rising ‘bubbles’ of almost clear gas. The purpose of this paper is to account plausibly for this remarkable property first by supposing that primary and secondary instabilities of the fluidized bed generate compact regions of above-average or below-average particle concentration, and second by invoking a mechanism for the expulsion of particles from a buoyant compact blob of smaller particle concentration. We postulate that the rising of such an incipient bubble generates a toroidal circulation of the gas in the bubble, roughly like that in a drop of liquid rising through a second liquid of larger density, and that particles in the blob carried round by the fluid move on trajectories which ultimately cross the bubble boundary. Numerical calculations of particle trajectories for practical values of the relevant parameters show that a large percentage of particles, of such small concentration that they move independently, are expelled from a bubble in the time taken by it to rise through a distance of several bubble diameters.Similar calculations for a liquid-fluidized bed show that the expulsion mechanism is much weaker, as a consequence of the larger density and viscosity of a liquid, which is consistent with the absence of observations of relatively empty bubbles in liquid-fluidized beds.It is found to be possible, with the help of the Richardson-Zaki correlation, to adjust the results of these calculations so as to allow approximately for the effect of interaction of particles in a bubble in either a gas- or a liquid-fluidized bed. The interaction of particles at volume fractions of 20 or 30 % lengthens the expulsion times, although without changing the qualitative conclusions.
Measuring particle concentration of multimodal synthetic reference materials and extracellular vesicles with orthogonal techniques: Who is up to the challenge?
