Cooling by Flow Through Narrow Pores

We consider the possibility of cooling He-3 atoms in dilute solutions with liquid He-4 by "filtering out" the hot atoms through a screen of small holes or channels. The proposed method is somewhat analogous to that employed to evaporatively cool trapped gases, and the specific heat of the He-3-He-4 mixture makes it feasible to use in a device to refrigerate other samples. Three methods are considered: 1) Effusion through holes having diameters larger than a mean free path allowing atoms to pass through easily; 2) Particle waveguide-like motion (also effusive) using very narrow channels that greatly restrict the quantum states of the atoms in them; and 3) Wall-limited diffusion through channels of various widths, in which the wall scattering is disordered so that local density equilibrium is established within a channel. The methods studied all require sufficiently low temperatures and holes or channels with sufficiently small dimensions that temperature equilibrium between the escaping gas and the original gas is avoided; that is, we assume that channel dimensions are smaller than the mean free path for atom-atom interactions. We find that the particle waveguide and the wall-limited diffusion methods using channels on the order of the de Broglie wavelength give cooling. Recent advances in nano-filters give these methods some hope of being practical.