### Abstract

We study the axisymmetric stretching of a thin sheet of viscous fluid driven by a centrifugal body force. Time-dependent simulations show that the sheet radius R(t) tends to infinity in finite time. As time t approaches the critical time t^{*}, the sheet becomes partitioned into a very thin central region and a relatively thick rim. A net momentum and mass balance in the rim leads to a prediction for the sheet radius near the singularity that agrees with the numerical simulations. By asymptotically matching the dynamics of the sheet with the rim, we find that the thickness h in the central region is described by a similarity solution of the second kind, with h (t ^{*} t)^{α} where the exponent α satisfies a nonlinear eigenvalue problem. Finally, for non-zero surface tension, we find that the exponent increases rapidly to infinity at a critical value of the rotational Bond number B = 1/4. For B > 1/4, surface tension defeats the centrifugal force, causing the sheet to retract rather than to stretch, with the limiting behaviour described by a similarity solution of the first kind.

Original language | English (US) |
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Pages (from-to) | 1-23 |

Number of pages | 23 |

Journal | Journal of Fluid Mechanics |

Volume | 659 |

DOIs | |

State | Published - Sep 2010 |

### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Keywords

- lubrication theory
- thin films

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## Cite this

*Journal of Fluid Mechanics*,

*659*, 1-23. https://doi.org/10.1017/S0022112010001564