Buckling Instability In Bilayer Membranes

We have analyzed the patterns generated when a stress field is introduced to the inner layer of a cylindrically symmetric bilayer membrane through a combination of analytic calculations, numerical simulations, and experiments. A wrinkled structure forms that we explain in terms of a competition between bending and stretching energies under a suitable geometrical constraint. The wavelength, $\lambda$, at the onset of the instability is found theoretically and experimentally to be $\lambda=\pi\sqrt{8B/T_{c}}$, where $T_{c}$ is the critical tension of the inner layer marking the onset of the instability, and $B$ is the bending modulus of the membrane. We have also investigated the formation of pseudo-fractal structures that emerge beyond the onset of the instability. We further explain the existence of defects in the regular pattern as a consequence of multiple metastable states in the effective potential that describes this system.