\[Slezov-2004\], \[Slezov-2005\]\]:

1.  The flux of the dissolved gas towards the bubble is assumed to be steady.

2.  The consideration is limited to bubbles with the radius that is large enough to neglect the Laplace pressure in comparison with the external pressure of the solution.

In the present paper, following our preceding works \[\[Kuchma-Gor-Kuni\], \[Gor-Kuchma-Sievert\]\], while exploiting the steady approximation, we take into account the Laplace pressure in the bubble considering the bubble from the very moment of its nucleation. Consideration of the time-dependent Laplace pressure in the bubble makes both gas density in the bubble and the equilibrium concentration of the dissolved gas at the surface of the bubble time-dependent as well.

Gas bubble growth in a solution taking into account the Laplace pressure was considered as early as in 1950 in the classical paper by Epstein and Plesset \[\[Epstein-Plesset\]\], where the authors obtained the equation for the bubble radius as a function of time. In order to relate the equilibrium concentration of the dissolved gas and the solution pressure, \[\[Epstein-Plesset\]\] presupposed the fulfillment of Henry’s law: i. e. the proportional dependence between these two values. Indeed, Henry’s law is fulfilled for the solution of $\rm CO_2$ in magmatic 