Hexatic Undulations in Curved Geometries

Abstract

We discuss the influence of two-dimensional hexatic order on capillary waves and undulation modes in spherical and cylindrical geometries. In planar geometries, extended bond-orientational order has only a minor effect on the fluctuations of liquid surfaces or lipid bilayers. However, in curved geometries, the long-wavelength spectrum of these ripples is altered. We calculate this frequency shift and discuss applications to spherical vesicles, liquid metal droplets, bubbles and cylindrical jets coated with surface-active molecules, and to multielectron bubbles in liquid helium at low temperatures. Hexatic order also leads to a shift in the threshold for the fission instability of charged droplets and bubbles, and for the Plateau-Rayleigh instability of liquid jets.

42 pages, 7 figures; References added and minor revisions; to appear in Phys. Rev. E

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• Defect generation and deconfinement on corrugated topographies
• Tuneable defect-curvature coupling and topological transitions in active shells
• Effects of orientational order on modulated cylindrical interfaces
• Self-Dual Bending Theory for Vesicles
• Hyperuniformity in active fluids reshapes nucleation and capillary-wave dynamics