### Abstract

Capillary forces determine the shape of a liquid interface. Although often not considered, elastic solids with a free surface are also subjected to surface forces and these become important for materials of low Young's modulus. Here we consider two equivalent problems where a capillary free surface deforms due to vortices: (i) in a steady viscous flow [solved by Jeong and Moffatt, J. Fluid Mech. 241, 1 (1992)], and (ii) in an elastic medium. The equations of linear incompressible elasticity and viscous flow are strictly identical, and the two-dimensional problems that we consider are solved using complex variable methods. Despite the similarity, the kinematics of the free surface is very different for the viscous and elastic cases. We show for the present problem that these kinematics result in displacement and velocity fields of different topology. Unexpectedly, the resulting surface deflections are even of opposite sign

Original language | English |
---|---|

Article number | 033001 |

Number of pages | 8 |

Journal | Physical review E: Statistical, nonlinear, and soft matter physics |

Volume | 91 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2015 |

## Fingerprint Dive into the research topics of 'Interface deformations due to counter-rotating vortices: Viscous versus elastic media'. Together they form a unique fingerprint.

## Cite this

Snoeijer, J. H., & van Wijngaarden, L. (2015). Interface deformations due to counter-rotating vortices: Viscous versus elastic media.

*Physical review E: Statistical, nonlinear, and soft matter physics*,*91*(3), [033001]. https://doi.org/10.1103/PhysRevE.91.033001