Abstract
We develop a model to describe the velocity variance and particulate pressure in fluidized beds, and also in one-dimensional disperse flows. These quantities involve contributions caused by 1) short-scale pseudoturbulent fluctuations of particles in the dense phase of a fluidized bed, and 2) long-scale fluctuations due to macroscopic flow patterns, such as rising bubbles that are practically devoid of particles. Energy comes to the pseudoturbulent fluctuations from the relative motion of the ambient fluid as it interacts with random fluctuations of the dispersion concentration, and also from gravity working at density fluctuations. Inter-particle exchange by momentum and energy is assumed to be carried out by particle collisions, in which case the particles may be approximately treated as statistically independent, and their fluctuations can be regarded as nearly isotropic. The long-scale contributions to velocity variance and particulate pressure are evaluated on the basis of a simple dimensionality consideration. In some dispersion flows, the gas slip velocity may greatly exceed the particle terminal velocity, and consequently, the pseudoturbulent particulate pressure turns out to be much larger than that in a fluidized bed of the same particles at the same concentration. The theoretical conclusions are proven to be in good keeping with all experimental data for fluidized beds available to date.