The effect of anisotropic surface energy on the Rayleigh instability

Abstract

We determine the linear stability of a rod or wire subject to capillary forces arising from an anisotropic surface energy. The rod is assumed to be smooth with a uniform cross-section given by a two-dimensional equilibrium shape. The stability analysis is based on computing the sign of the second variation of the total energy, which is examined by solving an associated eigenvalue problem. The eigenproblem is a coupled pair of second-order ordinary di®erential equations with periodic coe±cients that depend on the second derivatives of the surface energy with respect to orientation variables. We apply the analysis to examples with uniaxial or cubic anisotropy, which illustrate that anisotropic surface energy plays a signi¯cant role in establishing the stability of the rod. Both the magnitude and sign of the anisotropy determine whether the contribution stabilizes or destabilizes the system relative to the case of isotropic surface energy, which reproduces the classical Rayleigh instability.

Annealing Effect on Electrospun Polymer Fibers and Their Transformation into Polymer Microspheres

“…This assumption is violated in many cases, concerning the effect of anisotropic surface energy. [ 14 ] The Rayleigh instability is commonly observed in metal nanowires. For example, Toimil-Molares et al reported the Rayleigh instability in copper nanowires annealed at temperatures between 400 and 600 ° C. [ 15 ] The copper nanowires fragment into chains of nanospheres, and the average diameter and spacing of the nanospheres second step is to thermally anneal the PMMA fi bers in ethylene glycol.…”

A tangent-plane marker-particle method for the computation of three-dimensional solid surfaces evolving by surface diffusion on a substrate

“…The unit normal vector n at each particle on the symmetry plane must lie in the plane, i.e., m z ¼ 0 in Eq. (12). Thus, n at particle P 1 is calculated by fitting a circular arc through P 1 and two closest adjacent particles P 2 and P 3 on the plane.…”

“…The linear stability of free circular wires with isotropic surface energy, with respect to axial or circumferential perturbations was examined by Nichols and Mullins [30]. Surface energy anisotropy was factored in the linear stability analysis of free wires by Cahn [4] and Gurski and McFadden [12] (In a related study, Kan and Wong [16] considered the three-dimensional linear stability of a two-dimensional profile of a retracting edge of a film on a substrate (assuming isotropic surface energy) [15,8,43] and found one unstable mode of perturbation; thus the edge becomes wavy when perturbed. They determined the growth rate of the perturbation as a function of the wavelength of the perturbation and the speed of the receding edge).…”

Characterization and properties of micro- and nanowires of controlled size, composition, and geometry fabricated by electrodeposition and ion-track technology

“…The thermal stability of nanomaterials is controlled by surface and diffusion processes and influenced by the material characteristics, temperature, and geometrical parameters [140–144]. In particular, it was predicted that nanowires may fragment into a chain of nanospheres above a temperature that is much lower than the corresponding bulk melting temperature T m .…”