Abstract
Universality in the behavior of multilayer radial Hele-Shaw flows is discovered by semi-analytical methods. In particular, it is found numerically that the maximum injection rate for a stable flow decreases proportional to ${t}^{\ensuremath{-}1/3}$ regardless of the number of interfaces and increases at a rate proportional to the number of interfaces to the two-thirds power at large time $t\ensuremath{\gg}1$. However, at earlier times the number of interfaces can increase the maximum stable injection rate by a much greater amount.
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