Universality in the dynamics of vesicle translocation through a hole

Abstract

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 $\Delta P$. 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 $\Delta P_{\mathrm{c}}$ below which no translocation occurs, (ii) $\Delta P_{\mathrm{c}}$ decreases to zero as the vesicle radius $R_0$ approaches the hole radius $a$, satisfying the scaling relation $\Delta P_{\mathrm{c}}\sim (R_0-a{)}^{3/2}$, and (iii) the translocation time $\tau$ diverges as $\Delta P$ decreases to $\Delta P_{\mathrm{c}}$, satisfying the scaling relation $\tau \sim (\Delta P-\Delta P_{\mathrm{c}}{)}^{-1/2}$.