### Abstract

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds-i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Original language | English (US) |
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Pages (from-to) | 10024-10030 |

Number of pages | 7 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 94 |

Issue number | 19 |

DOIs | |

State | Published - Sep 16 1997 |

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### ASJC Scopus subject areas

- General

### Cite this

*Proceedings of the National Academy of Sciences of the United States of America*,

*94*(19), 10024-10030. https://doi.org/10.1073/pnas.94.19.10024

**The problem of the spreading of a liquid film along a solid surface : A new mathematical formulation.** / Barenblatt, G. I.; Beretta, Elena; Bertsch, M.

Research output: Contribution to journal › Article

*Proceedings of the National Academy of Sciences of the United States of America*, vol. 94, no. 19, pp. 10024-10030. https://doi.org/10.1073/pnas.94.19.10024

}

TY - JOUR

T1 - The problem of the spreading of a liquid film along a solid surface

T2 - A new mathematical formulation

AU - Barenblatt, G. I.

AU - Beretta, Elena

AU - Bertsch, M.

PY - 1997/9/16

Y1 - 1997/9/16

N2 - A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds-i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

AB - A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds-i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

UR - http://www.scopus.com/inward/record.url?scp=0030886940&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030886940&partnerID=8YFLogxK

U2 - 10.1073/pnas.94.19.10024

DO - 10.1073/pnas.94.19.10024

M3 - Article

VL - 94

SP - 10024

EP - 10030

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 19

ER -