Breakage kernel constant

Analytical solutions are available for some particular cases for a constant breakage kernel, a( ) = do. For example, in the case of symmetric fragmentation with daughter distribution... 

We have shown how this set of differential equations is closed in some simple cases (i.e. for nucleation at zero size, with constant growth rate, and constant aggregation and breakage kernels). In general, when the system is not closed, closure must be sought through a stable numerical method. 

As an example, consider a monodisperse population of particles characterized by mass as internal coordinate and moments m = mjt(O) = 1 with k = 0,..., 2N 1. This population of particles is continuously fed to a system wherein particles undergo aggregation and symmetric binary breakage with constant kernels. The equations describing the evolution of the moments are... 

For this specific example, consider the case of constant aggregation and breakage kernels, namelyPa,y,s,[Pg.326]

Empirical parameter in breakage kernel closure (—) Equihbrium constant for reaction i Reaction rate constant for reaction i Overall liquid-side mass transfer coeflhcient (m/s)... 

A general expression can be found by combining these two cases (Melis et al., 1999). In these expressions, kB is the Boltzmann constant, T is the fluid temperature (Kelvin), ji is the fluid viscosity, y is the local shear rate, and a is an efficiency factor. For shear-induced breakage, the kernel is usually fit to experimental data (Wang et al., 2005a,b). A typical form is (Pandya and Spielman, 1983) as follows ... 

As for the univariate case for constant kernels and symmetric breakage (see Eq. (7.92)), under the assumption of additive internal coordinates for breakage,... 

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