Attrition kinetics

In studying the attrition kinetics of powder compaction through tapping, one of the most convenient ways to organize attrition data is to plot the... 

The attrition index Ai (Equation 32) proposed by Barletta and Barbosa-Canovas (1993a) was found suitable for studying agglomeration and the effects of agglomerate size and water activity on the attrition kinetics of agglomerated coffee and nonfat milk (Yan and Barbosa-Canovas, 2001a). 

Jager, J., de Wolf, S., Kramer, H.J.M. andde Jong, E.J. (1991) Estimation ofnucleation and attrition kinetics from CSD transients in a continuous crystalhzer. Chemical Engineering Research and Design, 69, 53-62. 

Modeling of Jet-Induced Attrition. Werther and Xi (1993) compared the jet attrition of catalysts particles under steady state conditions with a comminution process. They suggested a model which considers the efficiency of such a process by relating the surface energy created by comminution to the kinetic energy that has been spent to produce this surface area. The attrition rate, RaJ, defined as the mass of attrited and elutriated fines per unit time produced by a single jet, is described by... 

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,... 

Size-dependent crystal growth is Included in the model because it can be important to describe diffusion limited growth rates or crystal attrition. As discussed in (6,X), the size reduction by attrition can be modelled by an effective growth rate G (L,t) which is the difference between the kinetic growth rate G, (L,tT and an attrition rate G (L,t) ... 

The method of lines and system identification are not restricted in their applicability. System identification is preferred because the order of the resulting state space model is significantly lower. Another advantage of system Identification is that it can directly be applied on experimental data without complicated analysis to determine the kinetic parameters. Furthermore, no model assumptions are required with respect to the form of the kinetic expressions, attrition, agglomeration, the occurence of growth rate dispersion, etc. 

The term fa) is the volume-averaged dissipation function for the energy dissipated by the viscous force, which is irreversible dissipation of mechanical work into thermal energy or heat. For the solid-particle phase, the kinetic energy loss by attrition or inelastic collision may be included in this term. 

The fluidized bed reactor can also handle fast, complex reactions, with mixing and temperature control being especially good when stirring is provided. Unfortunately, the extent of back mixing is difficult to assess so that the residence time distribution of the reactants in the reactor is uncertain. In addition, only small catalyst particles can be used, and attrition, with the consequent breakdown and loss of catalyst, is a problem. Finally, a catalyst bed is adequately fluidized over only a comparatively narrow range of flow rates. More information about kinetic reactors can be found in reviews [33,34,50], Applications of the basket-type mixed reactor to liquid-solid systems are discussed by Suzuki and Kawazo [62] and by Teshima and Ohashi [63], and the development of a laminar flow, liquid-solid reactor by Schmalzer et al. [64], In the latter reactor the wall is coated with a catalyst layer. 

In the kinetic theory, attrition is focused on the event of bond fracture and the latter is described in terms of chemical rate theory. The mechanical stress on the bond (normally the result of an applied load) modifies the free energy barrier that must be crossed if the bond is to change from an unbroken to a broken state. Figure 2 illustrates the situaticm. 

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