In this paper we present results of a two-dimensional (z,r) treatment of the mass and energy transfer processes that occur during the operation of a thermal diffusion cloud chamber. The location of the wall is considered in solving the mass and energy transport equations, in addition to the vertical distance, z, between the upper and lower plate surfaces. We examine the effect of aspect (diameter to height) ratio on chamber operation; the effects of operation with either a dry or a wet interior chamber wall on temperature, supersaturation, nucleation rate, and total density profiles in the chamber; the effect of overheating the interior of the chamber wall on these conditions within the cloud chamber; and the effects associated with using different density background gases on the operation of the chamber. In a second paper, immediately following, we apply the formalism and the solutions developed in this paper to address the important problem of buoyancy-driven convection that can accompany (seemingly normal) operation of thermal diffusion cloud chambers in nearly all ranges of total pressure and temperature.