Bubble-induced attrition

Figure 8. Distributor design suggested by Werther and Xi (1993) to separate the jet attrition and bubble-induced attrition.

Modeling ofBubble-Induced Attrition. Merrick and Highley (1974) have modeled bubble-induced attrition as a comminution process. According to Rittinger s law of size reduction by abrasion (cfi, Perry, 1973), the rate of creation of new surface area AS Al is proportional to the rate of energy input Ah. At... 

Vaux (1978), Ulerich et al. (1980) and Vaux and Schruben (1983) proposed a mechanical model of bubble-induced attrition based on the kinetic energy of particles agitated by the bubble motion. Since the bubble velocity increases with bed height due to bubble coalescence, the collision force between particles increases with bed height as well. The authors conclude that the rate of bubble-induced attrition, Rbub, is then proportional to the product of excess gas velocity and bed mass or bed height, respectively,... 

Modeling of Cyclone Attrition. A very simple model of cyclone attrition may be formulated in analogy to the models discussed with respect to jet attrition and bubble-induced attrition (Reppenhagen and Werther, 1997). 

Even though most of the attrition tests presented in the literature deal with bubble-induced attrition, the respective attrition mechanisms are not quite clear yet. There are various theoretical and empirical approaches that can in accordance with Eq. P) be summarized in the following definition of a bubble-induced steady-state attrition rate ... 

Assuming that the particle size dependent rate constant Kl for bubble-induced attrition can—in analogy to the other sources—be written as the product of a particle size independent constant Cb and the surface mean diameter of the bed material d, ... 

For this system, the particle population balance is solved in discretized time steps At. At the beginning of each time step, except the very first one, the fresh material and the material from the return line are fed and mixed with the bed material. It follows the calculation of jet-induced and bubble-induced attrition. Afterwards the particular material mass fractions are determined that are entrained from the bed in the course of this time step. These material fractions are then subjected to the combination of attrition and gas-solid separation inside the cyclone section. Finally, the catch of the cyclone is added to the return line, which in the next time step feeds its excess mass to the bed. At the starting time t = 0, the particle size distributions in both the bed and the return line are identical to that of... 

Aj = rate constant of bubble-induced attrition, defined by Eq. (18), s /m ... 

---