Coefficients of Slip in Gases and the Law of Reflection of Molecules from the Surfaces of Solids and Liquids

Abstract

First order correction term to Stokes Law of fall of droplets.—(1) Empirical. The experiments by which the value of the electronic charge was determined by the droplet method gave consistent results only when this law was modified by the factor ($1+\frac{\mathrm{Al}}{a}$), where $\frac{l}{a}$ is the ratio of mean free path to radius of droplet. (2) Hydrodynamic theory gives as a first approximation ($1+\frac{\xi }{a}$), where $\xi$ is the coefficient of slip. (3) Kinetic theory gives ($1+\frac{0.7004l}{a}$) in case all the molecules are diffusely reflected from the surface of the droplet, where $l$ is defined by the relation $\eta =.\mathrm{}3502\mathrm{}\rho \overline{c}l$. If, however, the fraction reflected diffusely is $f$, the fraction ($1-f$) being specularly reflected, then the factor is [$1+0.7004(\frac{2}{f}-1)\left(\frac{l}{a}\right)$]. The theory developed by Cunningham gave the numerical constant as 0.79, but this value is too high since experimental values of $A$ nearly as low as 0.70 have actually been obtained.