Non-linear diffusion of an axisymmetric thin liquid drop: Group-invariant solution and conservation law

E. Momoniat, D. P. Mason, F. M. Mahomed

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

The non-linear diffusion equation describing the axisymmetric spreading of a thin incompressible liquid drop under gravity on a horizontal plane is considered. A group-invariant solution is derived by finding a linear combination of the three Lie point symmetries admitted by the non-linear diffusion equation which conserves the total volume of the liquid drop and which satisfies the boundary condition of vanishing thickness at the rim. It is shown that conservation of the total volume of the liquid drop and the existence of a certain conservation law for the differential equation impose the same condition on the constants in the linear combination of the three Lie point symmetries.

Original languageEnglish
Pages (from-to)879-885
Number of pages7
JournalInternational Journal of Non-Linear Mechanics
Volume36
Issue number6
DOIs
Publication statusPublished - Sept 2001
Externally publishedYes

Keywords

  • Conservation law
  • Group-invariant solution
  • Lie point symmetry
  • Non-linear diffusion
  • Thin viscous fluid film

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Non-linear diffusion of an axisymmetric thin liquid drop: Group-invariant solution and conservation law'. Together they form a unique fingerprint.

Cite this