= Vapour-tip peeling of a magma intrusion
{title2=$R\propto t^{3/10}$}
If a positive vapour-tip pressure magnitude $p_T$ sets $h_f\sim p_Tl_p^4/B$, 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 $\kappa_i\sim V/R^4$, hence
$$
R\sim\left(\frac{B^3Q^7t^9}{p_T\mu^2}\right)^{1/30}.
$$
Order-one coefficients require solving the local peeling profile. The scaling assumes a front region much shorter than the intrusion radius.
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