论文标题
合并溶液用于广义电动核聚集
Combinatorial solutions to generalized electrorheological kernel aggregation
论文作者
论文摘要
在本文中，我们研究了具有真实功率的广义电学（ER）内核下凝结颗粒系统的时间演变，$ k \ left（i，j \ right）= \ left（\ frac {1} {i} {i} {i}+\ frac+\ frac {1}} {1} {j} {j} \ right）我们使用了一个组合框架，其中时间和群集大小是离散的，二进制聚合控制了系统的时间演变。我们修改了恒定内核的先前已知的解决方案，以覆盖广义的ER内核，并在框架中使用它，以获取群集大小分布的确切表达式（给定尺寸的平均粒子数）和标准偏差。我们的理论解决方案是通过与$α$的几个值的数值模拟结果以及与聚苯乙烯颗粒的实验数据进行比较来验证的。在聚合过程的任何时间和$α$的范围内，理论预测都是准确的。
For this paper, we studied the time evolution of a system of coagulating particles under a generalized electrorheological (ER) kernel with real power, $K\left(i,j\right) = \left( \frac{1}{i}+\frac{1}{j} \right)^α$, and monodisperse initial conditions. We used a combinatorial framework in which time and cluster sizes were discrete and the binary aggregation governed the time evolution of the system. We modified a previously-known solution for the constant kernel to cover the generalized ER kernel and used it in the framework to obtain the exact expression for the cluster size distribution (the average number of particles of a given size) and the standard deviation. Our theoretical solution is validated by a comparison to numerically simulated results for several values of $α$ and to the experimental data of coagulating polystyrene particles. Theoretical predictions were accurate for any time of the aggregation process and for a wide range of $α$.
