The rate of collisions due to Brownian or gravitational motion of small drops
The rate of collisions due to Brownian or gravitational motion of small drops
复制标题
DOI：
10.1017/s0022112091000861
复制
发表时间：
1991-09
影响因子：
3.7
通讯作者：
Xiaoguang Zhang;Robert H. Davis
中科院分区：
文献类型：
--
作者：
Xiaoguang Zhang;Robert H. Davis
考虑含有分散在第二不混溶流体中的一种流体的液滴的稀分散体。液滴足够小，惯性可以忽略不计，并且保持球形。两个不同大小的液滴由于布朗扩散或重力沉降而处于相对运动中。当液滴变得接近时，它们由于流体动力学扰动和货车德瓦尔斯吸引力而彼此相互作用，并且在有利的条件下，它们将彼此碰撞并合并。两滴碰撞的速率是通过求解布朗聚结的扩散方程来预测的，并且通过使用轨迹分析来跟踪重力诱导聚结的滴对的相对运动。我们分析的重点是液滴相互作用对其碰撞率的影响，这些都是描述的碰撞效率。由于液滴相对运动的流体动力学阻力随着液滴流体和周围流体的粘度比的减小而减小，因此碰撞效率随着粘度比的减小而增大。从刚性球体的粘性滴的碰撞行为的定性差异被证明;有限的碰撞率的预测，即使在没有吸引力的情况下，只要滴变形是可以忽略不计的，而刚性颗粒与光滑的表面将不会接触在流体连续体中，除非存在一个吸引力，这是能够克服抵抗相对运动的润滑力。两个球形液滴之间的流体动力学相互作用占准确地确定两个球的相对迁移率函数从以前的解决方案，两个液滴移动沿着和正常的他们的中心线。这些解决方案是基于广泛分离的液滴的反射方法，润滑理论的液滴在近接触，和一般分离的双球坐标。流体动力学相互作用对降低引力碰撞率的作用比布朗碰撞率的作用大。
A dilute dispersion containing drops of one fluid dispersed in a second, immiscible fluid is considered. The drops are sufficiently small that inertia is negligible and that they remain spherical. Two drops of different size are in relative motion due to either Brownian diffusion or gravitational sedimentation. When the drops become close, they interact with each other owing to hydrodynamic disturbances and van der Waals attractions, and, under favourable conditions, they will collide with each other and coalesce. The rate at which two drops collide is predicted by solving the diffusion equation for Brownian coalescence, and by using a trajectory analysis to follow the relative motion of pairs of drops for gravity-induced coalescence. The emphasis of our analysis is on the effects of drop interactions on their collision rate, and these are described by the collision efficiency. Since the hydrodynamic resistance to the drop relative motion reduces with a decreasing ratio of the viscosities of the drop fluid and the surrounding fluid, the collision efficiency increases with decreasing viscosity ratio. A qualitative difference in the collision behaviour of viscous drops from that of rigid spheres is demonstrated; finite collision rates for drops are predicted even in the absence of attractive forces, provided that drop deformation is negligible, whereas rigid particles with smooth surfaces will not come into contact in a fluid continuum unless an attractive force is present which is able to overcome the lubrication forces resisting the relative motion. Hydrodynamic interactions between two spherical drops are accounted for exactly by determining the two-sphere relative mobility functions from previous solutions for two drops moving along and normal to their line of centres. These solutions are based on the method of reflections for widely separated drops, lubrication theory for drops in near-contact, and bispherical coordinates for general separations. The hydrodynamic interactions have a greater effect on reducing the rate of gravity collisions than the rate of Brownian collisions.