Yarranton HW, Masliyah JH
Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 2G6, Canada
J Colloid Interface Sci. 1997 Dec 15;196(2):157-169. doi: 10.1006/jcis.1997.5186.
Ostwald ripening at finite dispersed phase volumes was modeled successfully using linearized analytical solutions of the ripening equations and an explicit numerical routine. The numerical approach incorporated a number frequency distribution of drop radii rather than using a discrete number of drops. The effect of finite dispersed phase volume fraction was accounted for by using half the average separation distance between drops as the mass transfer boundary. The numerical predictions matched analytical predictions for infinitely dilute systems almost exactly and were in qualitative agreement with analytical predictions for infinitely concentrated systems. The numerical model was applied to the full range of dispersed phase concentrations and successfully predicted experimental cumulative frequency distributions. The growth rate, i.e. the change in the cube of the mean radius with time, was confirmed to be constant at any dispersed phase volume fraction. A simple expression was developed relating growth rate to dispersed phase volume fraction. Predicted growth rates at dispersed phase volume fractions less than 0.2 matched those found experimentally and by other numerical methods. Predicted growth rates at higher dispersed phase volume fractions agreed well with experimental data from the literature but were significantly higher than predictions from other numerical methods. Copyright 1997 Academic Press.
利用熟化方程的线性化解析解和显式数值程序，成功地对有限分散相体积下的奥斯特瓦尔德熟化进行了建模。数值方法采用了液滴半径的数频分布，而不是使用离散数量的液滴。通过将液滴之间平均间距的一半作为传质边界，考虑了有限分散相体积分数的影响。数值预测与无限稀释体系的解析预测几乎完全匹配，并且与无限浓缩体系的解析预测在定性上一致。该数值模型应用于整个分散相浓度范围，并成功预测了实验累积频率分布。生长速率，即平均半径的立方随时间的变化，在任何分散相体积分数下都被证实是恒定的。推导了一个将生长速率与分散相体积分数相关联的简单表达式。分散相体积分数小于0.2时的预测生长速率与实验值以及其他数值方法得到的结果相匹配。较高分散相体积分数下的预测生长速率与文献中的实验数据吻合良好，但显著高于其他数值方法的预测。版权所有1997年学术出版社。
