A Determination by the Constant Deflection Method of the Value of the Coefficient of Slip for Rough and for Smooth Surfaces in Air

Abstract

Coefficient of slip for rough and smooth surfaces in air, determined by the constant deflection method.---The apparent coefficient of viscosity measured by this exceptionally precise method does not come out constant for the lower pressures unless correction is made for the slip at the surfaces. The relation ${{\ensuremath{\eta}}_{p}}^{\ensuremath{'}}(1+k{\ensuremath{\zeta}}_{p})=\ensuremath{\eta}$ = constant, between ${{\ensuremath{\eta}}_{p}}^{\ensuremath{'}}$, the apparent viscosity coefficient, and ${\ensuremath{\zeta}}_{p}$, the coefficient of slip, enables ${\ensuremath{\zeta}}_{p}$ to be determined from measurements of ${{\ensuremath{\eta}}_{p}}^{\ensuremath{'}}$ at pressures of 0.2 mm or lower. The apparatus included a vacuum-tight chamber inside which a cylinder of radius 5.341 cm was suspended by a steel wire concentric with a cylinder of radius 6.063 cm which could be rotated at a constant slow rate so as to cause a steady deflection of the inner cylinder. The accuracy of this method of measuring ${{\ensuremath{\eta}}_{p}}^{\ensuremath{'}}$ is so great that the values of ${\ensuremath{\zeta}}_{76}=\frac{{\ensuremath{\zeta}}_{p}p}{76}$ all lie within \ifmmode\pm\else\textpm\fi{} 4 per cent of the mean. The chief difficulty was in keeping the air pure because of the gradual evolution of gas, probably hydrogen, inside the apparatus; but by taking observations only shortly after evacuation this effect was avoided. For brass surfaces, $\ensuremath{\zeta}$, reduced to 23\ifmmode^\circ\else\textdegree\fi{} and 76 cm, came out 66.15 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}7}$ which is practically the theoretical minimum deduced by Millikan for a completely diffusing surface, 65.9 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}7}$. For surfaces coated with shellac, the coefficient was found to be 97 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}7}$ for a fresh surface, in agreement with the value obtained by Lee from droplet measurements, but it decreased steadily with time, presumably because of a roughening due to oxidation, falling in two months to within 3 per cent of the theoretical minimum. The early part of this work was done in collaboration with E. L. Harrington.Coefficient of viscosity of air at 0.1 mm is the same as at atmospheric pressure when correction is made for the slip effect. The constancy of the values obtained for $\ensuremath{\zeta}$ provides new evidence that the coefficient is independent of the pressure.