A Simplified Model of Rapid Fluidization

Abstract

The objective of this communication is to interpret the results of Li et al. (1981) in terms of a one-dimensional transport model (Wing, 1962). One refers to this model as the “one-dimensional rod”. Here we use its version presented on page 10 of a book (Wing, 1962), and described by the following two equations:

$$\frac{{du}}{{dz}}(z) = \sigma (z)[F(z) - 1]u(z) + \sigma (z)B(z)v(z)$$

(1)

$$ - \frac{{dv}}{{dz}}(z) = \sigma (z)[F(z) - 1]v(z) + \sigma (z)B(z)u(z)$$

(1)

where u and v are the expected densities of solid lumps at z and moving to the bed bottom or to the bed top, respectively. In the above equations, it is assumed that the bed top is at z = 0, and its bottom at z = a, a > 0. s is called the macroscopic cross section, and should be interpreted here as follows: a solid lump moving a distance D has a probability s • D of happening something to it (for example, a change of direction of moving, a collision with some other lump without happening anything more, a collision with lump splitting or with adhering of lumps to each other, etc.). F and B should be understood as expected lump participations to the direction of lump moving before event and to the opposite direction, respectively.