WIAS Preprint No. 2451, (2017)

Thin film models for an active gel



Authors

  • Kitavtsev, Georgy
  • Münch, Andreas
  • Wagner, Barbara

2010 Mathematics Subject Classification

  • 76A15 80M35

2008 Physics and Astronomy Classification Scheme

  • 61.30.Jf 87.17.Aa 87.17.Jj

Keywords

  • Liquid crystals, asymptotic analysis, cell locomotion

DOI

10.20347/WIAS.PREPRINT.2451

Abstract

In this study we present a free-boundary problem for an active liquid crystal based on the Beris-Edwards theory that uses a tensorial order parameter and includes active contributions to the stress tensor to analyse the rich defect structure observed in applications such as the Adenosinetriphosphate (ATP) driven motion of a thin film of an actin filament network. The small aspect ratio of the film geometry allows for an asymptotic approximation of the free-boundary problem in the limit of weak elasticity of the network and strong active terms. The new thin film model captures the defect dynamics in the bulk as well as wall defects and thus presents a significant extension of previous models based on the Leslie-Erickson-Parodi theory. Analytic expressions are derived that reveal the interplay of anchoring conditions, film thickness and active terms and their control of transitions of flow structure.

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