• 作者： Lu, Shih-Yuan; Chen, Tsi-Chung
• 中文摘要： 本文探討粒子大小分布對含球形粒子分散液之擴散控制速率常數之影響。我們討論兩種工業上重要且本質不同的粒子大小分佈－常態分佈與對數常態分布。本文中發展出一套可產生給定粒子體積分率與分布參數之粒子群。此兩種粒子分布之分散液有極為不同的行為表現。常態分布分散液之正規化速率常數幾乎與分布參數無關，而對數常態分布分散液之正規化速率常數隨著粒子分布之變寬而減小。進一步看，常態分布分散液之正規化速率常數滿足Torquato和Yeong所提出的普遍正規關係式與一以比表面積為基礎的正規關係式，而此兩種正規關係式都無法規範對數常態分布分散液之正規化速率常數。兩種分散液之正規化速率常數如預期地均隨粒子體積分率之增加而增加。
• 英文摘要： The effects of particle polydispersity on the normalized overall rate constant of spherical dispersions under the diffusion-controlled situation are investigated. Two industrially important but inherently different particle size distributions, normal and log-normal distributions, are studied. A numerical scheme for generating normally or log-normally distributed particles given a fixed particle volume fraction and normalized standard deviation or geometric standard deviation is developed to facilitate the study. Results for the two particle size distributions show dramatically different behavior. For dispersions with normally distributed particles, the normalized overall rate constant is almost invariant with respect to variation in the normalized standard deviation, while that for dispersions containing log-normally distributed particles decreases with increasing particle size spread. It is further found that, for the normal distribution case, the overall rate constant fits well with a universal scaling relation, proposed by Torquato and Yeong based on curve-fitting of rate constants of 8 classes of dispersion microstructure, and a specific surface area based scaling relation. The overall rate constant of the log-normal case however cannot be described by either scaling relation. The normalized overall rate constants of both distributions increase, as they should, with increasing particle volume fraction.
• 中文關鍵字： 擴散控制; 反應速率常數; 球形分散; 第一到達時間模擬; 多分散度; 分布
• 英文關鍵字： Diffusion Control; Reaction Rate Constant; Spherical Dispersion; First Passage Time Simulation; Polydispersity; Distribution