Nonlocal dynamics of stretching, buckling filaments

Michael J. Shelley, Tetsuji Ueda

Research output: Contribution to conferencePaperpeer-review


Growth by permeation and drag-induced buckling instabilities have been observed in the dynamics of thin filaments in an isotropic-Smectic A (I - SA) phase transition of liquid crystal fluid, and in lipid bilayer tubes evolving in a fluid medium. With motivation from the experiments with liquid crystal, we have been studying the dynamics of a growing elastic filament immersed in a Stokes fluid. By combining results from slender body theory, Green's function methods, and elasticity theory, we express the self-induced velocity of the filament as the nonlocal consequence of forces the filament exerts upon the incompressible fluid by its elastic response and growth. An elastic buckling instability results from the combination of local length growth (permeation) and fluid drag, which creates compressive tension within the filament. For numerical simulation we use methods, developed for interfacial flows with surface tension, for which curvature effects are handled naturally. Our numerical simulations show successive bucklings of the growing filament. Nonlocal interactions of the filament with itself are shown to prevent self-intersections, suggesting that 'local-drag' models are not sufficient in capturing the global aspects of the flow.

Original languageEnglish (US)
Number of pages11
StatePublished - 1996
EventProceedings of the 1995 AMS-IMS-SIAM Joint Summer Research Conference - Seattle, WA, USA
Duration: Jul 23 1995Jul 27 1995


OtherProceedings of the 1995 AMS-IMS-SIAM Joint Summer Research Conference
CitySeattle, WA, USA

ASJC Scopus subject areas

  • General Mathematics


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