Similarity Solutions for the Population Balance Equation Describing Particle Fragmentation
Titel:
Similarity Solutions for the Population Balance Equation Describing Particle Fragmentation
Auteur:
Peterson, Thomas W.
Verschenen in:
Aerosol science and technology
Paginering:
Jaargang 5 (1986) nr. 1 pagina's 93-101
Jaar:
1986
Inhoud:
Similarity solutions are obtained to the population balance equation describing particulate systems undergoing fragmentation. The solutions are restricted only by the requirement that the breakage rate of particles of volume v be of the form φ(v) = Avb and the breakage distribution function of the form ω(u, v) = ƒ(v/u)/u, where u is the volume of the fragmenting particle. Under such conditions, the moments of the distribution asymptotically approach the form Ni(t) α t(1-i)/b, and the particle size distribution function is shown to obey a first-order linear ordinary integro-diflerential equation. For the case ƒ(v/u) = γ(v/u)γ-2, analytical solutions to the above equation were obtained. Complete solutions as well as asymptotic behavior are given. The results are potentially applicable to a wide range of particle fragmentation problems, including char/ash fragmentation during pulverized coal combustion, explosively generated aerosol formation, ore comminution, powder crushing and grinding, floe breakage, and crystallization kinetics.
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