Breakage kernel local

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 ... 

However, in other cases the model predictions deviate much more from each other and were in poor agreement the experimental data considering the measurable quantities like phase velocities, gas volume fractions and bubble size distributions. An obvious reason for this discrepancy is that the breakage and coalescence kernels rely on ad-hoc empiricism determining the particle-particle and particle-turbulence interaction phenomena. The existing param-eterizations developed for turbulent flows are high order functions of the local... 

Venneker et al [118] made an off-line simulation of the underlying flow and the local gas fractions and bubble size distributions for turbulent gas dispersions in a stirred vessel. The transport of bubbles throughout the vessel was estimated from a single-phase steady-state flow fleld, whereas literature kernels for coalescence and breakage were adopted to close the population balance equation predicting the gas fractions and bubble size distributions. 

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