Abstract
Lie groups are used to solve the equation governing the flow of a thin liquid film subject to centrifugal spreading and viscous resistance. A new implicit solution is found. It is shown how this relates to the previous known solutions for the spreading of an initially flat film, the steady state and a separable solution. New permissible forms for the film evolution are also studied, including solutions exhibiting finite time blow-up. Near the contact line, where the film height tends to zero, an approximate explicit solution is obtained which may be used to describe a film with any size contact angle.
Original language | English |
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Pages (from-to) | 192-199 |
Number of pages | 8 |
Journal | International Journal of Non-Linear Mechanics |
Volume | 41 |
Issue number | 2 |
DOIs | |
Publication status | Published - Mar 2006 |
Externally published | Yes |
Keywords
- Lie groups
- Rotation-driven spreading
- Thin film
ASJC Scopus subject areas
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics