• 作者： Chen, Shih H.
• 中文摘要： 本文以解析法探討單一粒徑分布球形液滴分散相系統之擴散。液滴與液滴間之距離近到必須考慮液滴粒子間之流力交互作用。基於愛因斯坦對布朗擴散運動之演繹,引入熱力學平衡力之原理,推導出兩種不同形式之布朗擴散係數。其一為均態液滴懸浮系統中之布朗擴散。利用兩球形液滴於低雷諾數下之流力交互作用可動度函數,求出兩液滴之相對擴散係數。另一者則考慮非均態(液滴之分布存在一濃度梯度)情況下之液滴布朗擴散。藉由對液滴懸浮系統平均沈降速度之了解,並引入統計熱力學的觀念,而獲得液滴分布不均勻下之擴散係數。結果發現,當液滴粒子數濃度提高時,其擴散係數亦相對地增大。在極限情況下,本文所獲得之結果也與過去相關文獻所探討之固體粒子布朗擴散一致。此外,氣泡微粒之布朗擴散,亦涵蓋予本文中。
• 英文摘要： A study of diffusion for a dispersion which the suspending droplets are spherical and have the same radius and fluid viscosity is considered. Droplets are assumed to be close enough to interact hydrodynamically. Based on the Einstein's prescription of Brownian motion that invokes an equilibrium and the droplets will be exerted by a thermodynamic force, the Brownian diffusivities in two different types of situation are deduced analytically. The first concerns a homogeneous dilute suspension which is being deformed locally, and the relative diffusivity of two spherical droplets with a given separation distance is derived from the properties of mobility functions due to the low-Reynolds-number flow caused by two hydrodynamically interacting droplets. The second concerns a suspension in which there is a gradient of concentration of droplets. The thermodynamic force on each droplet in this case is shown to be equal to the gradient of the chemical potential of droplets, which brings considerations of the multi-droplet excluded volume into the problem. Determination of the sedimentation velocity of droplets falling through fluid under gravity for which a theoretical result correct to the first order in volume fraction of the droplets is available. The diffusivity of the droplets is found to increase slowly as the concentration rises from zero. The results, presented in simple closed forms, agree very well with the existing solutions for the limiting cases of solid particles. Also, the limiting diffusion situation of spherical gas bubbles are considered in this article.
• 中文關鍵字： 擴散; 流體; 液滴; 稀薄; 膠體
• 英文關鍵字： Diffusion; Fluid; Drop; Dilute; Colloid