The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

G. I. Barenblatt, E. Beretta, M. Bertsch

Research output: Contribution to journalArticle


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 languageEnglish (US)
Pages (from-to)10024-10030
Number of pages7
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number19
StatePublished - Sep 16 1997


ASJC Scopus subject areas

  • General

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