Vigil R Dennis, Vermeersch Isaac, Fox Rodney O
Department of Chemical & Biological Engineering, 2114 Sweeney Hall, Iowa State University, Ames, IA 50011-2230, USA.
J Colloid Interface Sci. 2006 Oct 1;302(1):149-58. doi: 10.1016/j.jcis.2006.05.066. Epub 2006 Jun 8.
Mean-field population balance equations are used to describe the evolution of particle size distributions in a wide variety of systems undergoing simultaneous aggregation and breakage. In this paper we develop a population balance that includes aggregation combined with collision-induced particle breakage for arbitrary fragment distribution functions, provided that this distribution function depends only on the total mass of the particles undergoing a collision. We then develop a specific distribution function for arbitrary two-body collisions by postulating that each collision produces a transition-state aggregate having the morphology of a linear polymer. The behavior of the resulting equation is then analyzed for the case in which the collision kernel is a constant, and partial analytical solutions are derived and compared to corresponding Monte-Carlo simulation results. The computer simulations are then used to validate a proposed scaling law for the steady-state particle size distribution. Lastly, the behavior of the aggregation with collision-induced-breakage population balance equation is compared and contrasted with the behavior of an analogous aggregation with linear-breakage population balance equation.
平均场群体平衡方程用于描述在同时经历聚集和破碎的各种系统中颗粒尺寸分布的演变。在本文中，我们建立了一个群体平衡模型，该模型包括聚集以及结合了碰撞诱导颗粒破碎的过程，适用于任意碎片分布函数，前提是该分布函数仅取决于发生碰撞的颗粒的总质量。然后，我们通过假设每次碰撞都会产生具有线性聚合物形态的过渡态聚集体，为任意两体碰撞开发了一个特定的分布函数。接着，针对碰撞核为常数的情况分析所得方程的行为，推导部分解析解并与相应的蒙特卡罗模拟结果进行比较。然后利用计算机模拟来验证所提出的稳态颗粒尺寸分布的标度律。最后，将具有碰撞诱导破碎的聚集群体平衡方程的行为与类似的具有线性破碎的聚集群体平衡方程的行为进行比较和对比。
