  We study non-isothermal diffusive transport of a weakly-soluble two-component
substance in a liquid-saturated porous medium being in contact with the
reservoir of this substance. Particular attention is given to the example case
of infiltration of nitrogen and oxygen from the atmosphere under the annual
temperature oscillation. The surface temperature of the porous medium
half-space oscillates in time, which results in a decaying solubility wave
propagating deep into the porous medium. In such a system, the zones of
saturated solution and nondissolved phase coexist with the zones of
undersaturated solution; these zones migrate with time. Moreover, the
solubility of a multicomponent substance depends on its composition, which
results in a much more intricate mathematical model of solubility as compared
to the single-component case. We describe the phenomenon of formation of a
near-surface bubbly horizon due to the temperature oscillation. An analytical
theory of the phenomenon is developed. For multicomponent solutions we report
the formation of diffusion boundary layer, which is not possible for
single-component solutions. We construct an analytical theory for this boundary
layer; in particular, we derive effective boundary conditions for the problem
of the diffusive transport beyond this layer.
