The onset of convection in a finite container due to surface tension and buoyancy |
| |
| Institution: | 1. Theoretical Physics Division, Harwell Laboratory, Didcot, Oxon OX11 0RA, UK;2. Max-Planck-Institut für Ernährungsphysiologie, Rheinlanddamm 201, D-4600 Dortmund, Fed. Rep. Germany;1. Molecular Electronics and Photonics Research Unit, Department of Mechanical Engineering and Materials Science and Engineering, Cyprus University of Technology, 3041 Limassol, Cyprus;2. Department of Physics, Experimental Condensed Matter Physics Laboratory, University of Cyprus, 1678 Nicosia, Cyprus;1. Department of Geosciences, University of Tromsø – The Arctic University of Norway, Dramsveien 201, 9037 Tromsø, Norway;2. Czech Geological Survey, Klárov 3, 118 21 Praha 1, Czech Republic;3. Geological Survey of Namibia, 1 Aviation Road, Windhoek, Namibia;4. Institute of Geology AS CR, v.v.i., Rozvojová 269, 165 00 Praha 6, Czech Republic;5. Department of Earth Science, University of Bergen, Allégaten 41, 5007 Bergen, Norway;1. Universidade Federal de Santa Catarina, Departamento de Engenharia Química e de Alimentos, 88040-970 Florianópolis, Brazil;2. Universidade Federal do Paraná, Departamento de Engenharia Química, 89065-300 Curitiba, Brazil;3. Università del Sannio, Facoltà di Ingegneria, 82100 Benevento, Italy;1. Lab for Thin Films Nanosystems and Nanometrology, Physics Department, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece;2. Organic Electronic Technologies P.C. (OET), Antoni Tritsi 21B, GR-57001 Thessaloniki, Greece |
| |
| Abstract: | A method for predicting instabilities which combines recent techniques from bifurcation theory with the finite-element method is described. It is applied to the prediction of the onset of convection driven by both surface tension and buoyancy in rectangular containers. For zero buoyancy, the critical values of the Marangoni number for the first two bifurcations from the trivial solution are found for a two-dimensional cavity of aspect ratio 2. The variation of these critical values with aspect ratio is obtained by continuation methods and this reveals an interlacing of modes as the container size increases. It is established that the bifurcation to an even number of cells is transcritical rather than pitchfork and the turning point on the subcritical branch is located as a function of aspect ratio. The hysteresis associated with the transcritical bifurcation is small. As the surface tension forces decrease to zero, so that the convection is driven by buoyancy alone, the amount of hysteresis associated with the transcritical bifurcation becomes vanishingly small. The reason for this is not fully understood. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
