A proper mobility formula for large, heavy particles in gases in any regime Original Research Article

The age-old problem of the derivation of a proper formula for the mechanical (or electrical) mobility of large, heavy (l.h.) particles in a simple neutral gas in any regime is carefully examined and solved under the usual hypotheses that the l.h. particles are subject to the action of a constant external force and undergo only elastic collisions with the gas particles. By a convenient procedure, a general mobility formula is obtained which not only properly corrects the well-known result derived by Cunningham for an l.h. hard sphere in a hard-sphere gas, but also applies to the general case in which both the l.h.-particle–gas-particle and gas-particle–gas-particle interactions are arbitrary. In addition, on the basis of the new formula, the fair success of the Cunningham formula (regarded as a semiempirical formula) in fitting the experimental results is explained. Other interesting aspects of the new formula are also examined, and its limits of validity are briefly discussed.