Kostoglou M, Karabelas A J
Chemical Process Engineering Research Institute, P.O. Box 1517, 54006 Thessaloniki, Greece.
J Colloid Interface Sci. 2005 Apr 15;284(2):571-81. doi: 10.1016/j.jcis.2004.10.029.
It is well known that the fragmentation equation admits self-similar solutions for evolving particle-size distributions (PSD); i.e., if the shape of PSD is independent of time after an initial transient period. Although an analytical derivations of the self-similar PSD cases have been studied extensively, results for cases requiring numerical solutions are rare. The aim of the present work is to fill this gap for the case of homogeneous breakage functions. The known analytical and approximate solutions for the self-similar PSD are reviewed and a general algorithm for the numerical solution is proposed. Results for a broad range of breakage functions (kernel and rate) are presented. Further, the work is focused on the sensitivity of the relation between self-similar PSD and breakage kernel and its influence on the inverse breakage problem, i.e., that of estimating the breakage kernel from experimental self-similar PSDs. Useful suggestions are made for tackling the inverse problem.
众所周知，破碎方程对于不断演化的粒度分布（PSD）允许自相似解；也就是说，如果在初始瞬态期之后PSD的形状与时间无关。尽管自相似PSD情况的解析推导已得到广泛研究，但需要数值解的情况的结果却很少见。本工作的目的是填补均匀破碎函数情况下的这一空白。回顾了自相似PSD的已知解析解和近似解，并提出了一种数值解的通用算法。给出了广泛的破碎函数（核和速率）的结果。此外，这项工作关注自相似PSD与破碎核之间关系的敏感性及其对逆破碎问题的影响，即从实验自相似PSD估计破碎核的问题。针对解决逆问题提出了有用的建议。
