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 language | English |
---|---|
Pages (from-to) | 879-885 |
Number of pages | 7 |
Journal | International Journal of Non-Linear Mechanics |
Volume | 36 |
Issue number | 6 |
DOIs | |
Publication status | Published - Sept 2001 |
Externally published | Yes |
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