Vapour-tip peeling of a magma intrusion ($R\propto t^{3/10}$)

If a positive vapour-tip pressure magnitude $p_T$ sets $h_f\sim p_T{l}_p^4/B$, matching $h_f/l_p^2$ to the interior curvature ${\kappa }_i$ gives $l_p\sim (B{\kappa }_i/p_T{)}^{1/2}$. The viscous peeling of an elastic plate law then yields $\dot{R}\sim B^{3/2}{\kappa }_i^{7/2}/(\mu p_T^{1/2})$. For constant injected volume flux $Q$, $V=Qt$ and ${\kappa }_i\sim V/R^4$, henceOrder-one coefficients require solving the local peeling profile. The scaling assumes a front region much shorter than the intrusion radius.