Universality in the dynamics of vesicle translocation through a hole

We analyze the translocation process of a spherical vesicle, made of membrane and incompressible fluid, through a hole smaller than the vesicle size, driven by pressure difference $\mathrm{\Delta }P$. We show that such a vesicle shows certain universal characteristics which is independent of the details of the membrane elasticity; (i) there is a critical pressure $\mathrm{\Delta }{P}_{\mathrm{c}}$ below which no translocation occurs, (ii) $\mathrm{\Delta }{P}_{\mathrm{c}}$ decreases to zero as the vesicle radius $R_0$ approaches the hole radius $a$, satisfying the scaling relation $\mathrm{\Delta }{P}_{\mathrm{c}}\sim (R_0-a{)}^{3\mathrm{/}2}$, and (iii) the translocation time $\tau$ diverges as $\mathrm{\Delta }P$ decreases to $\mathrm{\Delta }{P}_{\mathrm{c}}$, satisfying the scaling relation $\tau \sim (\mathrm{\Delta }P-\mathrm{\Delta }{P}_{\mathrm{c}}{)}^{-1\mathrm{/}2}$.