Chen SH
Department of Chemical Engineering, Hwa Hsia College of Technology and Commerce, Taipei, 235, Taiwan, Republic of China
J Colloid Interface Sci. 1999 Jan 1;209(1):31-43. doi: 10.1006/jcis.1998.5828.
An analytical study of Brownian motion in a dispersion of fluid drops is considered. The droplets, which are spherical and may differ in radius, are assumed to be close enough to interact hydrodynamically. Based on Einstein's description of Brownian motion that invokes an equilibrium and in which droplets are affected by a thermodynamic force, the Brownian diffusivities in two different situations are deduced. The first interaction concerns a homogeneous dilute suspension that is deformed locally. The relative diffusivity of two droplets with a given separation distance is derived from the mobility functions due to the low-Reynolds-number flow that arises because of two hydrodynamically interacting droplets. The second interaction concerns a suspension in which there is a concentration gradient 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 the multidroplet excluded volume into the problem. For a determination of the average settling velocity of droplets falling through fluid under gravity, 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. These results are generalized for an inhomogeneous suspension of several different species of droplet, and expressions for the diagonal and off-diagonal elements of the diffusivity matrix are obtained. The results, presented in simple closed forms, agree very well with the existing solutions for the limited cases of solid spheres. Moreover, the limiting diffusion situation of spherical gas bubbles is also considered. Copyright 1999 Academic Press.
本文考虑了对流体滴分散体系中布朗运动的分析研究。假设液滴为球形，半径可能不同，且彼此靠得足够近，从而产生流体动力学相互作用。基于爱因斯坦对布朗运动的描述，该描述引入了平衡概念，且液滴受热力作用影响，推导了两种不同情况下的布朗扩散系数。第一种相互作用涉及局部变形的均匀稀悬浮液。对于给定间距的两个液滴，其相对扩散系数由低雷诺数流动产生的迁移率函数得出，这种低雷诺数流动是由两个流体动力学相互作用的液滴引起的。第二种相互作用涉及存在液滴浓度梯度的悬浮液。在这种情况下，每个液滴上的热力被证明等于液滴化学势的梯度，这就将多液滴排除体积纳入了问题。对于确定液滴在重力作用下穿过流体下落的平均沉降速度，可得到一个在液滴体积分数上精确到一阶的理论结果。发现随着浓度从零开始增加，液滴的扩散系数缓慢增大。这些结果被推广到几种不同种类液滴的非均匀悬浮液中，并得到了扩散系数矩阵对角元和非对角元的表达式。以简单封闭形式给出的结果与固体球体有限情况下的现有解非常吻合。此外，还考虑了球形气泡的极限扩散情况。版权所有1999年学术出版社。
