## Abstract

The axisymmetric spreading under gravity of a thin liquid drop on a horizontal plane with suction or blowing of fluid at the base is considered. The thickness of the liquid drop satisfies a non-linear diffusion equation with a source term. For a group invariant solution to exist the normal component of the fluid velocity at the base, v_{n}, must satisfy a first-order quasi-linear partial differential equation. The general form of the group invariant solution for the thickness of the liquid drop and for v_{n} is derived. Two particular solutions are considered. Each solution depends essentially on only one parameter which can be varied to yield a range of models. In the first solution, v_{n} is proportional to the thickness of the liquid drop. The base radius always increases even for suction. In the second solution, v_{n} is proportional to the gradient of the thickness of the liquid drop. The thickness of the liquid drop always decreases even for blowing. A special case is the solution with no spreading or contraction at the base which may have application in ink-jet printing.

Original language | English |
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Pages (from-to) | 1013-1026 |

Number of pages | 14 |

Journal | International Journal of Non-Linear Mechanics |

Volume | 39 |

Issue number | 6 |

DOIs | |

Publication status | Published - Aug 2004 |

Externally published | Yes |

## Keywords

- Asymmetric thin liquid drop
- Group invariant solution
- Lie point symmetries
- Non-linear diffusion equation

## ASJC Scopus subject areas

- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics