Interfacial plug-current similarity profile
= Interfacial plug-current similarity profile
{title2=$h=H(1-r^2/R^2)^{1/4}$}
For fixed volume and equal ambient viscosities, radial volume conservation gives $u=r/(5t)$. Summing both ambient-face tractions gives $H^2=32\mu R/(5\pi\Delta\rho gt)$ and $R^5=125\Delta\rho gV^2t/(512\pi\mu)$. The edge slope is singular, so the profile is a leading bulk thin-current approximation.