The effect of slip on the motion of a sphere close to a wall and of two adjacent spheres
The effect of slip on the motion of a sphere close to a wall and of two adjacent spheres
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DOI：
10.1007/bf01535282
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发表时间：
1973-07
影响因子：
1.3
通讯作者：
L. M. Hocking
中科院分区：
文献类型：
--
作者：
L. M. Hocking
球体朝向平面或另一个球体的运动受到它们之间的流体的抵抗，该力与间隙成反比。因此，除非修改斯托克斯方程，否则恒定力不可能在有限时间内产生接触。当间隙与空气分子的平均自由程具有相同量级时，必须修改空气运动的斯托克斯理论。本文采用麦克斯韦滑流近似表明，当间隙较小时，接近表面之间的阻力仅与间隙成对数关系，并且可以在有限时间内实现接触。从而消除了将斯托克斯理论应用于确定云滴碰撞效率问题的困难。计算出的接近阻力值用于确定球体落向平面的运动。如果将运动与不考虑滑流时的相应运动进行比较，当有滑移的球体接触时，没有滑移的球体与平面的距离仍为平均自由程的 1.3 倍。如果需要靠近收集器的粒子的轨迹，还必须考虑横向运动。在这种情况下，球体上的力和力偶在没有滑移的情况下与间隙呈对数关系，但当包括滑移的影响时，它们趋于恒定值。重力下落的液滴碰撞效率的一些计算（Hocking 和 Jonas [1]）已被修改，以包括碰撞液滴非常靠近时的滑移效应，并显示碰撞效率显着增加。
The motion of a sphere towards a plane or another sphere is opposed by the fluid between them with a force which is inversely proportional to the gap. In consequence, it is impossible for a constant force to produce contact in a finite time, unless the Stokes equations are modified. When the gap is of the same order as the mean free path of the air molecules, the Stokes theory for the motion of the air must be modified. The Maxwell slip flow approximation is used in this paper to show that, when the gap is small, the resisting force between the approaching surfaces becomes only logarithmically dependent on the gap, and contact can be achieved in a finite time. The difficulty in applying the Stokes theory to the problem of determining collision efficiencies for cloud droplets is thereby removed.The calculated values of the resistance to approach are used to determine the motion of a sphere falling towards a plane. If the motion is compared with the corresponding motion when no allowance is made for slip flow, the sphere without slip would still be at a distance of 1.3 times the mean free path from the plane, when the sphere with slip has made contact.Transverse motion must also be considered if the trajectory of a particle close to a collector is required. The forces and couples on the sphere in that situation have a logarithmic dependence on the gap without slip, but they tend to constant values when the effect of slip is included. Some calculations of collision efficiency of drops falling under gravity (Hocking and Jonas [1]) have been amended to include the effect of slip when the colliding drops are very close together, and show a significant increase in the collision efficiency.