Rayleigh-Plateau instability of anisotropic interfaces. Part 2. Limited instability of elastic interfaces

Cylindrical vesicle and cell membranes under tension can undergo a Rayleigh-Plateau instability leading to break-up. In Part 1 (Graessel et al., J. Fluid Mech., vol. xxx, 2021, Ax) we showed that anisotropic tension, created by active biological processes underneath the cell membrane, can significantly influence this process for a liquid-liquid interface. Here, we study the combined influence of anisotropic tension and membrane elasticity on the Rayleigh-Plateau instability. We analytically derive the dispersion relation for an interface endowed with bending and/or shear elasticity considering explicitly the dynamics of the suspending fluid. We find that the combination of bending elasticity and tension anisotropy leads to three qualitatively different regimes for the Rayleigh-Plateau scenario: (i) the classical regime in which short wavelengths are stable and long wavelengths are unstable, (ii) the suppressed regime in which the system is stable against all perturbation wavelengths and (iii) the restricted regime, in which a stable region at short and another one at long wavelengths are separated by a range of unstable modes centred around the dimensionless wavenumber . The width of this unstable range as well as the dominant wavelength of the instability depend on the bending modulus and tension anisotropy. For shear elasticity and area dilatation, on the other hand, only the classical and the suppressed regimes are observed, with the transition between them being independent of the tension anisotropy.

Automated summary

This study examines the Rayleigh-Plateau instability of cylindrical vesicles and cell membranes under tension, considering the combined influence of anisotropic tension and membrane elasticity. The research shows that the combination of bending elasticity and tension anisotropy leads to three qualitatively different regimes for the Rayleigh-Plateau scenario, while shear elasticity and area dilatation only exhibit the classical and suppressed regimes.