Hexatic Undulations in Curved Geometries

TL;DR

This paper investigates how hexatic order affects surface undulations in curved geometries, revealing frequency shifts and stability changes in various physical systems like vesicles, droplets, and jets.

Contribution

It introduces the impact of hexatic order on capillary wave spectra and instability thresholds in curved geometries, extending understanding beyond planar cases.

Findings

Hexatic order causes a measurable frequency shift in surface undulations.

It alters the threshold for fission and Plateau-Rayleigh instabilities.

Applications include vesicles, droplets, jets, and multielectron bubbles.

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.