  We study non-isothermal diffusion transport of a weakly-soluble substance in
a liquid-saturated porous medium being in contact with the reservoir of this
substance. 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
non-dissolved phase coexist with the zones of undersaturated solution. The
effect is firstly considered for the case of annual oscillation of the surface
temperature of water-saturated ground being in contact with atmosphere. We
reveal the phenomenon of formation of a near-surface bubbly horizon due to the
temperature oscillation. An analytical theory of the phenomenon is developed.
Further, the treatment is extended to the case of higher frequency oscillations
and case of weakly-soluble solids and liquids.
