The general law of fall of a small spherical body through a gas, and its bearing upon the nature of molecular reflection from surfaces
The general law of fall of a small spherical body through a gas, and its bearing upon the nature of molecular reflection from surfaces
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DOI：
10.1103/physrev.22.1
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发表时间：
1923-07-01
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影响因子：
--
通讯作者：
Millikan, RA
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作者：
Millikan, RA
一个小的球形物体在任何压力下通过气体下落的定律。-(1)理论推导。当液滴的自由径与半径之比la较小时，液滴的运动阻力完全是由粘度引起的，与a成正比；当la较大时，液滴的运动阻力完全是由分子撞击的惯性引起的，与a成正比。方程：F= 6 π η av [1+ A ' l A]−1满足这两个理论条件。然而，从动力学理论来看，A '不是恒定的，而是从一个较低的理论极限变化。7004（漫反射）为1小，到1.164为1大。因此，我们令A ' = A+ B ε−c A l，并写出完整的方程：F= 6 π η av[1+(A+ B ε−c A l) l A]−1。(2)实验验证。通过油滴法，已经确定了空气中油滴的A′值在0.5到134之间的广泛范围内。这些结果与理论方程在±2%或更小的实验误差范围内一致，并给出A=。864， B= 0.290, c= 1.25。对其他液滴所得结果的讨论表明，虽然A随气体的性质而变化，甚至随液滴的物质而变化，但对于大多数可能在大气中沉降的粒子来说，（A+ B）在2%到3%的范围内是相同的。(3)区分漫反射、镜面反射、径向反射和分子的凝结再蒸发。径向反射在热力学和动力学上都是不可能的；冷凝和再蒸发与（A+ B）观测值不一致。这个观测值只有通过大约1/10的镜面反射和9/10的漫反射的组合才能得到满足，漫反射被定义为表面上每个元素的再发射，并且在满足麦克斯韦分布定律的方向上，所有分子撞击在该元素上。该协议为分子的镜面反射的存在增加了新的证据，因为1/10也被先前在空气中得到的油滴的A值所指示。(4)表面机械粗糙度的影响。作者的结果与Knudsen和Gaede的结果之间的明显差异，似乎表明完全漫反射，可以用微小的机械突起的影响来解释，这些突起被认为存在于作者的毛细管内部。
Law of fall of a small spherical body through a gas at any pressure.—(1) Theoretical derivation. When the ratio of free path to radius of droplet, l a, is small, the resistance to motion is due entirely to viscosity and is proportional to a, while when l a is large the resistance is due entirely to the inertia of the molecules hit and is proportional to a 2. The equation: F= 6 π η av [1+ A′ l a]− 1 satisfies both these theoretical conditions. From Kinetic theory, however, it has been shown that A′ is not constant but varies from a lower theoretical limit of. 7004 (diffuse reflection) for l a small, to 1.164 for l a large. We therefore put A′= A+ B ε− c a l and write the complete equation: F= 6 π η av[1+(A+ B ε− c a l) l a]− 1.(2) Experimental verification. By the oil drop method, values of A′ have been determined for a wide range of values of l a, from 0.5 to 134, for oil drops in air. These results are found to agree within the experimental error of±2 per cent or less with the theoretical equation, and give A=. 864, B= 0.290, c= 1.25. A discussion of results obtained with other drops indicates that while A varies with the nature of the gas and even more with the material of the droplet,(A+ B) is within two or three per cent the same for most sorts of particles which might settle through the atmosphere.(3) Differentiation between diffuse reflection, specular reflection, radial reflection, and condensation and re-evaporation of molecules. Radial reflection is shown to be thermodynamically and dynamically impossible; condensation and re-evaporation to be inconsistent with the observed value of (A+ B). This observed value is satisfied only by a combination of about 1/10 of specular reflection with 9/10 of diffuse reflection, this last being defined as a reemission from each element of surface and in such directions as to satisfy the Maxwell distribution law, of all molecules which impinge upon that element. The agreement adds new evidence for the existence of specular reflection of molecules since 1/10 had also been indicated by the values of A previously obtained for oil-drops in air.(4) Effects of mechanical roughness of the surface. The apparent discrepancies between the author's results and those of Knudsen and Gaede, which seemed to indicate complete diffuse reflection, are explained by the effects of minute mechanical proturberances which are thought to have existed on the insides of these authors' capillary tubes.