The Knudsen compressor, based on the temperature gradient driven rarefield flow phenomenon of thermal creep, is a solid-state, micro-mesoscale gas pump or compressor with no moving parts. Experimental studies have shown that micro-mesoscale Knudsen compressors can be operated efficiently by either resistive or radiant heating techniques, from inlet pressure up to about 10 atm down to 3×104 Pa. A study of the fundamental limitations encountered in reducing a micro-mesoscale Knudsen compressor’s operating inlet pressures to as low as 0.1 Pa is the primary focus of the present work. At low pressures, several issues that affect the efficient operation of micro-mesoscale Knudsen compressors have been identified. These include the large membrane channel sizes that are required because of relatively large molecular mean free paths, “reverse” thermal creep flows in the connector sections due to finite connector channel to membrane channel size ratios, and membrane channel exit vortices introduced by high conductance membrane channels. Mechanically machined aerogel membranes, with either capillaries or rectangular channels, have been investigated and demonstrated as attractive membrane candidates for the operation of low-pressure Knudsen compressors. Flow coefficients calculated from the linearized Boltzmann equation for long straight channels were adapted to estimate a Knudsen compressor’s performance. The Knudsen compressor pressure ratios observed in the experiments were lower than those estimated using the flow coefficients. Complex internal flow circulations, induced by a synergistic combination of membrane channel exit vortices and reverse thermal creep flows, are proposed as the cause of the lower pressure ratios. Such flow phenomena cannot be estimated by flow coefficients alone. Rigorous and co- - mputationally intensive simulation studies will be necessary to predict accurately the effects of these internal flow circulations.