Millikan, R. A. (1923) Coefficients of Slip in Gases and the Law of Reflection of Molecules from the Surfaces of Solids and Liquids. Physical Review, 21 (3). pp. 217238. ISSN 0031899X. https://resolver.caltech.edu/CaltechAUTHORS:MILpr23a

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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+Al / a), where l / a is the ratio of mean free path to radius of droplet. (2) Hydrodynamic theory gives as a first approximation (1+ xi / a), where xi is the coefficient of slip. (3) Kinetic theory gives (1+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 =.3502 rho cbarl. If, however, the fraction reflected diffusely is f, the fraction (1f) being specularly reflected, then the factor is [1+0.7004(2 / f1)(l / a)]. 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. Coefficient of slip between gases and solids.—(1) Stokes' law method. Since xi =Al, xi may be computed directly from A. (2) Rotating cylinder method of determining viscosity is also capable of giving values of xi accurate to one per cent. If theta 0 is the limiting deflection for high pressures, and theta the deflection for a low pressure, then xi for that low pressure is ( theta 0 theta ) / K, where K is a geometrical constant of the apparatus. Values obtained by this method agree closely with those obtained by the first method. (3) Capillary effusion method. If the rate of flow of gas for unit pressure difference is T0 for high pressures and T for a low pressure, then xi for that low pressure is R(TT0) / 4T0, where R is the radius. (4) Values of xi / l vary with the surface, for instance from 0.70 for airmercury, and 0.87 for airoil and airglass, to 1.07 for airfresh shellac. They also vary with the gas, for instance from 0.81 for hydrogenoil and 0.82 for CO2oil to 0.86 for airoil, and 0.90 for heliumoil. Coefficient of diffuse reflection of gas molecules, determined from the relation A=(2 eta / rho cbar)(2 / f1) gives values of f which vary with the surface from 0.79 for airfresh shellac and 0.89 for airglass to 1.00 for airmercury. The values also vary with the gas from 0.87 for heliumoil and 0.895 for airoil to 0.92 for CO2oil and hydrogenoil. The values are for 23° C.
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Issue or Number:  3  
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Deposited On:  15 Dec 2005  
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