negligible, the bubble dynamics is evident for the case of steady-state diffusion and can be even described analytically for the non-steady case \[\[Grinin-Kuni-Gor\], \[Scriven-1959\]\].

From the moment of bubble nucleation and till Eq. (\[R&gt;&gt;Laplace\]) becomes valid, Laplace pressure influences bubble growth. Thus both quantities $P_R$ and $n_R$ become radius-dependent (and, therefore, time-dependent). For $P_R$ now we have $$\label{Mech-Eq}
P_R = \Pi + \frac{2 \sigma}{R}\; .$$

In order to write the equation for $n_R$ we need to know the solubility law. For the simplest case of Henry’s law the equilibrium concentration of dissolved gas is proportional to the corresponding pressure $$\label{Chem-Eq-Henry}
\frac{n_R}{n_\infty} = \frac{P_R}{\Pi}\; .$$ However, Henry’s law is fulfilled only in such systems where there is no molecules dissociation during gas dissolution. In another important case when the gas molecules completely dissociate in the solvent into two parts the Henry’s law is replaced with so-called Sievert’s law (see e. g. \[\[Darken-Gurry\]\]), and, therefore, Eq. (\[Chem-Eq-Henry\]) is replaced with the following one: $$\label{Chem-Eq}
\frac{n_R}{n_\infty} = \sqrt{\frac{P_R}{\Pi}}\; .$$ Sievert’s law is fulfilled for water vapor dissolved in a silicate melt \[\[Stolper\]\]. Such solutions are important both for glass production \[\[Cable-Frade\]\] and for volcanic systems \[\[Navon\], \[Chernov-2004\]\].

The replacement of Eq. (\[Chem-Eq-Henry\]) with 