On advancing contact lines with a 180-degree contact angle
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Thu, 02/02/2012 16:00 |
Eugene Benilov (Limerick) |
Industrial and Applied Mathematics Seminar  |
DH 1st floor SR |
| This work builds on the foundation laid by Benney & Timson (1980), who examined the flow near a contact line and showed that, if the contact angle is 180 degrees, the usual contact-line singularity does not arise. Their local analysis, however, does not allow one to determine the velocity of the contact line and their expression for the shape of the free boundary involves undetermined constants - for which they have been severely criticised by Ngan & Dussan V. (1984). As a result, the ideas of Benny & Timson (1980) have been largely forgotten. The present work shows that the criticism of Ngan & Dussan V. (1984) was, in fact, unjust. We consider a two-dimensional steady Couette flow with a free boundary, for which the local analysis of Benney & Timson (1980) can be complemented by an analysis of the global flow (provided the slope of the free boundary is small, so the lubrication approximation can be used). We show that the undetermined constants in the solution of Benney & Timson (1980) can all be fixed by matching their local solution to the global one. The latter also determines the contact line's velocity, which we compute among other characteristics of the global flow. | |||