Pierce F, Sorensen C M, Chakrabarti A
Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Aug;74(2 Pt 1):021411. doi: 10.1103/PhysRevE.74.021411. Epub 2006 Aug 25.
The motion of particles, dispersed in a medium, between collisions with each other can, in limiting situations, be either ballistic (straight line) or diffusive (random walker). The diffusive regime can be divided into two distinct subregimes. The "continuum regime" exhibits Stokes-Einstein-type diffusion (no-slip surface boundary condition) with a frictional coefficient proportional to the particle size (linear dimension). The "Epstein regime," as we shall refer to it, is characterized by a frictional coefficient proportional to the particle cross-sectional area, hence an Epstein-type diffusion (slip surface). The purpose of the current study is to illuminate the dynamics of dilute-limit aggregation in the Epstein regime. We present results from low volume fraction Monte Carlo simulations of cluster-cluster aggregation in the Epstein regime with the particle motion based on each particle's cross-sectional area. Our findings indicate that aggregates grown under Epstein conditions have a fractal dimension of approximately 1.8, similar to that of diffusion-limited cluster-cluster aggregates (DLCA) in the continuum regime. The kinetic exponent z in the Epstein regime is found to be z approximately 0.8, lower than its value for both the continuum regime DLCA (z = 1) and for the ballistic cluster aggregation regime (z approximately 2). Cluster size distribution data for Epstein systems are found to scale at large cluster sizes with exponents consistent with the kinetic data. A scaling argument for predicting the kinetic exponent and kernel homogeneity based on the mass or size dependence of the particle velocity and collision cross section is presented and is seen to give accurate results for dilute and intermediate values of particle volume fractions not only for the current study, but also for work done by other researchers with various choices for the aggregation kernel.
分散在介质中的粒子在相互碰撞之间的运动，在极限情况下，要么是弹道式的（直线运动），要么是扩散式的（随机游走）。扩散 regime 可分为两个不同的子 regime。“连续 regime”表现出斯托克斯 - 爱因斯坦型扩散（无滑移表面边界条件），其摩擦系数与粒子大小（线性尺寸）成正比。我们将其称为“爱泼斯坦 regime”，其特征是摩擦系数与粒子横截面积成正比，因此是爱泼斯坦型扩散（滑移表面）。本研究的目的是阐明爱泼斯坦 regime 中稀溶液极限聚集的动力学。我们展示了基于每个粒子横截面积的粒子运动，对爱泼斯坦 regime 中团簇 - 团簇聚集进行低体积分数蒙特卡罗模拟的结果。我们的研究结果表明，在爱泼斯坦条件下生长的聚集体的分形维数约为1.8，与连续 regime 中的扩散限制团簇 - 团簇聚集体（DLCA）相似。发现爱泼斯坦 regime 中的动力学指数z约为0.8，低于连续 regime DLCA（z = 1）和弹道团簇聚集 regime（z约为2）的值。发现爱泼斯坦系统的团簇大小分布数据在大团簇尺寸下按指数缩放，这些指数与动力学数据一致。提出了一种基于粒子速度和碰撞横截面的质量或大小依赖性来预测动力学指数和核均匀性的标度论证，并且发现它不仅对于本研究，而且对于其他研究人员在对聚集核进行各种选择时所做的工作，对于粒子体积分数的稀溶液和中间值都能给出准确的结果。
