Quando è possibile formare bolle in un fluido, e quando no

Virga, Epifanio G.

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 80 (1986) no. 7-12, pp. 545-550

Résumé

Bubbles are formed in a fluid by inflating a liquid film with a gas in which the pressure $\hat{\pi}(\nu)$ is a strictly decreasing function of the specific volume, unbounded as $\nu \rightarrow 0^{+}$. We show that, if $\hat{\pi}(\nu)$ grows as fast or faster than $\nu^{-2/3}$ as $\nu \rightarrow 0^{+}$, then there is at least one stable equilibrium configuration of any such bubble, no matter how much gas has been used to inflate it. On the other hand, if $\hat{\pi}(\nu)$ grows as slowly or slower than $\nu^{-1/3}$ as $\nu \rightarrow 0^{+}$, then any such bubble has no equilibrium configuration, when the amount of gas within it is too small.