### Abstract

Growth by permeation and drag-induced buckling instabilities have been observed in the dynamics of thin filaments in an isotropic-Smectic A (I - S_{A}) 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 language | English (US) |
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Title of host publication | Analysis of Multi-Fluid Flows and Interfacial Instabilities |

Publisher | Soc for Industrial & Applied Mathematics Publ |

Pages | 415-425 |

Number of pages | 11 |

State | Published - 1996 |

Event | Proceedings of the 1995 AMS-IMS-SIAM Joint Summer Research Conference - Seattle, WA, USA Duration: Jul 23 1995 → Jul 27 1995 |

### Other

Other | Proceedings of the 1995 AMS-IMS-SIAM Joint Summer Research Conference |
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City | Seattle, WA, USA |

Period | 7/23/95 → 7/27/95 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Analysis of Multi-Fluid Flows and Interfacial Instabilities*(pp. 415-425). Soc for Industrial & Applied Mathematics Publ.

**Nonlocal dynamics of stretching, buckling filaments.** / Shelley, Michael; Ueda, Tetsuji.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Analysis of Multi-Fluid Flows and Interfacial Instabilities.*Soc for Industrial & Applied Mathematics Publ, pp. 415-425, Proceedings of the 1995 AMS-IMS-SIAM Joint Summer Research Conference, Seattle, WA, USA, 7/23/95.

}

TY - GEN

T1 - Nonlocal dynamics of stretching, buckling filaments

AU - Shelley, Michael

AU - Ueda, Tetsuji

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0029715072&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029715072&partnerID=8YFLogxK

M3 - Conference contribution

SP - 415

EP - 425

BT - Analysis of Multi-Fluid Flows and Interfacial Instabilities

PB - Soc for Industrial & Applied Mathematics Publ

ER -