### Abstract

Language | English |
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Title of host publication | Progress in Industrial Mathematics at ECMI 2010 |

Editors | Michael Günther , Andreas Bartel, Markus Brunk, Sebastian Schöps, Michael Striebel |

Place of Publication | Heidelberg |

Pages | 449-455 |

Number of pages | 7 |

Volume | 17 |

DOIs | |

Publication status | Published - 2012 |

### Publication series

Name | Mathematics in Industry: Progress in Industrial Mathematics at ECMI 2010 |
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Publisher | Springer Verlag |

Name | |
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Volume | 17 |

### Fingerprint

### Keywords

- optimisation
- partial differential equation
- quantitative finance

### Cite this

*Progress in Industrial Mathematics at ECMI 2010*(Vol. 17, pp. 449-455). (Mathematics in Industry: Progress in Industrial Mathematics at ECMI 2010). Heidelberg. https://doi.org/10.1007/978-3-642-25100-9_51

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*Progress in Industrial Mathematics at ECMI 2010.*vol. 17, Mathematics in Industry: Progress in Industrial Mathematics at ECMI 2010, Heidelberg, pp. 449-455. https://doi.org/10.1007/978-3-642-25100-9_51

**Asymptotics of a small liquid drop on a cone and plate rheometer.** / Cregan, V.; O'Brien, Stephen B.G.; McKee, Sean.

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

TY - CHAP

T1 - Asymptotics of a small liquid drop on a cone and plate rheometer

AU - Cregan, V.

AU - O'Brien, Stephen B.G.

AU - McKee, Sean

PY - 2012

Y1 - 2012

N2 - A cone and a plate rheometer is a laboratory apparatus used to measure the viscosity and other related parameters of a non-Newtonian liquid subject to an applied force. A small drop, of order millimetres, of the liquid is located between the horizontal plate and the shallow cone of the rheometer. Rotation of the cone ensues, the liquid begins to flow and the plate starts to rotate. Liquid parameters are inferred based on the difference in the applied rotational force and the resulting rotational force of the plate. To describe the flow of the drop, the initial drop configuration, before rotation commences, must be determined. The equilibrium drop profile is given by the solution to the well-known nonlinear Young-Laplace equation. We formulate asymptotic solutions for the drop profile based on the small Bond number. The modelling of the drop exhibits a rich asymptotic structure consisting of five distinct scalings which are resolved via the method matched asymptotics.

AB - A cone and a plate rheometer is a laboratory apparatus used to measure the viscosity and other related parameters of a non-Newtonian liquid subject to an applied force. A small drop, of order millimetres, of the liquid is located between the horizontal plate and the shallow cone of the rheometer. Rotation of the cone ensues, the liquid begins to flow and the plate starts to rotate. Liquid parameters are inferred based on the difference in the applied rotational force and the resulting rotational force of the plate. To describe the flow of the drop, the initial drop configuration, before rotation commences, must be determined. The equilibrium drop profile is given by the solution to the well-known nonlinear Young-Laplace equation. We formulate asymptotic solutions for the drop profile based on the small Bond number. The modelling of the drop exhibits a rich asymptotic structure consisting of five distinct scalings which are resolved via the method matched asymptotics.

KW - optimisation

KW - partial differential equation

KW - quantitative finance

U2 - 10.1007/978-3-642-25100-9_51

DO - 10.1007/978-3-642-25100-9_51

M3 - Chapter

SN - 9783642250996

VL - 17

T3 - Mathematics in Industry: Progress in Industrial Mathematics at ECMI 2010

SP - 449

EP - 455

BT - Progress in Industrial Mathematics at ECMI 2010

A2 - Günther , Michael

A2 - Bartel, Andreas

A2 - Brunk, Markus

A2 - Schöps, Sebastian

A2 - Striebel, Michael

CY - Heidelberg

ER -