So this equation can be rewritten as: $$\label{Extremum-Eq-1}
\sqrt{\frac{8}{3}} \sqrt{R_\sigma} (\zeta + 1) R^{3/2} - 3RR_\sigma - R_\sigma^2 = 0\; .$$ Using Eq. (\[Strong-For-Extr\]) we can also omit the second addend in Eq. (\[Extremum-Eq-1\]) in comparison with the third one. After such a simplification Eq. (\[Extremum-Eq-1\]) becomes solvable; and for $R_m$ we have: $$\label{R_m}
R_m \simeq \frac{\sqrt[3]{3}}{2} \frac{R_\sigma}{(\zeta + 1)^{2/3}}\; .$$ Substituting Eq. (\[R\_m\]) in the second addend in Eq. (\[Extremum-Eq-1\]) we can find a first-order correction to $R_m$ in Eq. (\[R\_m\]). We have $$\label{R_m_1}
R_m \simeq \frac{\sqrt[3]{3}}{2} \frac{R_\sigma}{(\zeta + 1)^{2/3}} \left( 1 + \frac{3 \sqrt[3]{3}}{2} \frac{1}{(\zeta + 1)^{2/3}}\right)^{2/3}\; .$$ Numerical solution of Eq. (\[Extremum-Eq\]) for $\zeta = 30$ gives for inaccuracy of approximate solution Eq. (\[R\_m\_1\]) the value less than $2\%$, and this value evidently decreases with the increase of $\zeta$.

As soon as we explained the behavior of the value $\dot{R}$ and found the value of $R_m$ we can use the ideas proposed for Henry’s law to determine the stages of bubble growth. On each stage the character of bubble growth is different from any other. The three consecutive stages of growth are still defined by Eqs. (\[1-st\]), (\[2-nd\]) and (\[3-rd\]).

In the next two sections we will 