The self-similar solution for draining in the thin film equation

Jan Bouwe Van Den Berg, Mark Bowen, John R. King, M. M A El-Sheikh

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We investigate self-similar solutions of the thin film equation in the case of zero contact angle boundary conditions on a finite domain. We prove existence and uniqueness of such a solution and determine the asymptotic behaviour as the exponent in the equation approaches the critical value at which zero contact angle boundary conditions become untenable. Numerical and power-series solutions are also presented.

Original languageEnglish
Pages (from-to)329-346
Number of pages18
JournalEuropean Journal of Applied Mathematics
Volume15
Issue number3
DOIs
Publication statusPublished - 2004 Jun
Externally publishedYes

Fingerprint

Zero angle
Thin Film Equation
Contact Angle
Self-similar Solutions
Contact angle
Boundary conditions
Power Series Solution
Thin films
Critical value
Existence and Uniqueness
Asymptotic Behavior
Exponent

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

The self-similar solution for draining in the thin film equation. / Van Den Berg, Jan Bouwe; Bowen, Mark; King, John R.; El-Sheikh, M. M A.

In: European Journal of Applied Mathematics, Vol. 15, No. 3, 06.2004, p. 329-346.

Research output: Contribution to journalArticle

Van Den Berg, Jan Bouwe ; Bowen, Mark ; King, John R. ; El-Sheikh, M. M A. / The self-similar solution for draining in the thin film equation. In: European Journal of Applied Mathematics. 2004 ; Vol. 15, No. 3. pp. 329-346.
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