A continuum description of the buckling of a line of spheres in a transverse harmonic confining potential

S. Hutzler*, J. Ryan-Purcell, A. Mughal, D. Weaire

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (SciVal)
70 Downloads (Pure)

Abstract

A line of contacting hard spheres, placed in a transverse confining potential, buckles under compression or when tilted away from the horizontal, once a critical tilt angle is exceeded. This interesting nonlinear problem is enriched by the combined application of both compression and tilt. In a continuous formulation, the profile of transverse sphere displacement is well described by numerical solutions of a second-order differential equation (provided that buckling is not of large amplitude). Here we provide a detailed discussion of these solutions, which are approximated by analytic expressions in terms of Jacobi, Whittaker and Airy functions. The analysis in terms of Whittaker functions yields an exact result for the critical tilt for buckling without compression.

Original languageEnglish
Article number230293
Number of pages19
JournalRoyal Society Open Science
Volume10
Issue number7
DOIs
Publication statusPublished - 12 Jul 2023

Keywords

  • one-dimensional colloidal chains
  • Whittaker functions
  • buckling
  • Jacobi functions
  • Airy functions

Fingerprint

Dive into the research topics of 'A continuum description of the buckling of a line of spheres in a transverse harmonic confining potential'. Together they form a unique fingerprint.

Cite this