Abstract
We revisit the spreading of a thin drop of incompressible Newtonian fluid on a uniformly heated or cooled smooth planar surface. The dynamics of the moving contact line are modelled by a Tanner Law relating the contact angle to the speed of the contact line. The present work builds
on an earlier theoretical investigation by Ehrhard and Davis (JFM, 229,365{388 (1991)) who derived the non-linear partial differential equation governing the evolution of the drop. The (implicit) exact solution to the
two-dimensional version of this equation in the limit of quasi-steady motion is obtained. Numerically calculated and asymptotic solutions are presented and compared. In particular, multiple solutions are found for a drop hanging
beneath a suffciently cooled substrate. If time permits, some basic models for evaporative spreading will be considered.
| Original language | English |
|---|---|
| Publication status | Accepted/In press - 11 May 2005 |
| Event | Edinburgh Mathematical Society Postgraduate Students' Meeting - Edzell, Scotland Duration: 10 May 2005 → 12 May 2005 |
Conference
| Conference | Edinburgh Mathematical Society Postgraduate Students' Meeting |
|---|---|
| City | Edzell, Scotland |
| Period | 10/05/05 → 12/05/05 |
Keywords
- heated or cooled horizontal substrate
- non-linear partial differential equation
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Dunn, G. (Accepted/In press). The non-isothermal spreading of a thin drop on a heated or cooled horizontal substrate. Paper presented at Edinburgh Mathematical Society Postgraduate Students' Meeting, Edzell, Scotland, .