Persistence of multicomponent-vesicle instabilities beyond the linear regime

Determine whether the pearling (axisymmetric n = 0), buckling (n = 1), and wrinkling (n ≥ 2) instabilities predicted by the linear stability analysis of cylindrical multicomponent vesicles governed by Stokes flow coupled to Cahn–Hilliard surface diffusion persist over longer time durations in the full nonlinear evolution of the vesicle shape and composition fields.

Background

The paper develops a linear stability framework for cylindrical multicomponent vesicles by coupling Stokes flow with the Cahn–Hilliard equation on the membrane. It identifies parameter regimes where axisymmetric pearling and non-axisymmetric buckling/wrinkling modes become unstable and quantifies their growth rates and dominant wavenumbers.

However, the analysis is restricted to the linear regime. The authors explicitly flag uncertainty about the long-time behavior of these instabilities once nonlinear effects become significant, indicating the need for future work to examine whether the predicted modes actually persist during extended evolution. This motivates a nonlinear investigation of the coupled hydrodynamics and phase-separation dynamics to confirm or refute persistence of the modes.

References

We cannot ensure that these instabilities will persist during longer time durations. This analysis is left for a later study.

— Linear stability of cylindrical, multicomponent vesicles  (2402.19297 - Venkatesh et al., 2024) in Section 5.3, Wavenumber dependence of growth rates

In particular, it remains unclear whether the interfacial instabilities identified by our linear analysis persist beyond the nearly radially symmetric configuration and how such instabilities develop nonlinearly into more complex morphologies.

— Speed and stability of segregated waves in a pressure-based model of heterogeneous cell populations  (2609.09043 - Falcó et al., 8 Sep 2026) in Section 'Discussion and perspectives' (Section 5)