Motion of a Particle in a Temperature Gradient; Thermal Repulsion as a Radiometer Phenomenon

Abstract

The dependence of the velocity of thermal repulsion of tricresyl phosphate droplets suspended in air on temperature gradient, pressure, and particle radius, $a$, was measured and compared with the velocities calculated from radiometer theory. Thermal repulsion is shown to be a radiometer effect. The velocity of thermal repulsion is directly proportional to the temperature gradient. The velocity of thermal repulsion at constant pressure increases with decreasing particle radius to a maximum when the mean free path, $L$, is about 1.5 times the radius, and then decreases. The velocity of thermal repulsion is approximately proportional to $\frac{1}{P}$ when $\frac{L}{a}l0.5$. The dependence of the force of thermal repulsion on temperature gradient, pressure, and particle radius are in agreement with the requirements of radiometer theory at high pressures. The resistance of air to the motion of tricresyl phosphate droplets is accurately given by Millikan's equation. The coefficient of slip on these droplets is 8.25\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ cm at 76-cm pressure and 30\ifmmode^\circ\else\textdegree\fi{}C. The measured velocities of thermal repulsion have been compared with the theoretical values calculated from the resistance of the medium and the radiometer forces as given by Albert Einstein and by Paul S. Epstein. The numerical agreement is satisfactory in view of the approximations in the theoretical derivations and the uncertainty in the heat conductivity of the tricresyl phosphate. Thermal repulsion can be used to determine the radius of particles too small to be measured by sedimentation velocity.