The detachment of bubbles under a porous rigid surface during aluminum electrolysis

Mathematical Models and Methods in Applied Sciences

Volumn 12, Issue 11, 2002, Pages 1617-1652

  Kloucek, Petr ^a   Romerio, Michel V ^b  

^a Rice University   (United States)

^b EPFL   (Switzerland)

Author keywords

Bubble dynamics; Electrolytic processes; Nonlinear optimization

Indexed keywords

EID: 0036857790     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202502002264     Document Type: Article

References (19)

1. N.I. Akhiezer, The Calculus of Variations (Harwood Academic, 1988).
2. _, Elements of the Theory of Elliptic Functions, Translations of Mathematical Monographs, Vol. 79 (American Mathematical Society, 1990).
3. J.P. Antille, J. Descloux, M. Flueck and M.V. Romerio, Eigenmodes and interface description in a Hall-Heroult cell, TMS Light Metals (1999) 333-338.
4. K. Chandrasekkharan, Elliptic Functions, A Series of Comprehensive Studies in Mathematics, Vol. 281 (Springer-Verlag, 1985), 1st edition.
5. P.G. de Gennes, Wetting: Statistic and dynamics, Rev. Mod. Phys. 57 (1985) 527-848.
6. J. Descloux, Private communication (2001).
7. L.P. Einsenhart, An Introduction to Differential Geometry (Princeton Univ. Press, 1947).
8. J.W. Evans and R. Shekhar, Physical modeling of bubble phenomena, electrolyte flow and mass transfer in simulated advanced hall cells, Final Report DOE/ID-10281, University of California at Berkeley, Department of Materials Science and Mineral Engineering, March 1990.
9. R. Finn, Equilibrium Capillarity Surfaces, A Series of Comprehensive Studies in Mathematics, Vol. 284 (Springer-Verlag, 1986), 1st edition.
10. S. Fortin, M. Gerhardt and A.J. Gesing, Physical modelling of bubble behaviour and gas release from aluminum reduction cell anodes, TMS Light Metals (1984) 721-729.
11. A.G. Greenhill, Les Fonctions Elliptiques et Leuers Applications (Éditions Jacques, 1993), 1st edition.
12. C.T. Kelly, Iterative Methods for Optimization, Frontiers in Applied Mathematics, Vol. 284 (SIAM, 1999), 1st edition.
13. L.I. Kiss, Experimantal measurements, private communication.
14. P. Klouček and M.V. Romerio, The first order phase transition of bubbles at solid-liquid interface, Technical Report 1, École Polytechnbique Fédérale de Lausanne, January 2001.
15. L.D. Landau and E. Lifchitz, M̀canique des Fluides, Physique Théorique, Vol. 6 (Mir, 1990), 3rd edition.
16. L.I. Osipow, Surface Chemistry, Theory and Industrial Applications, A Series of Comprehensive Studies in Mathematics (Reinhold Publishing, 1962), 1st edition.
17. S. Ponscák, L.I. Kiss and R.T. But, Mathematical modelling of the growth of gas bubbles under the anode in the aluminum electrolysis cells, TMS Light Metals (1999) 57-72.
18. S. Ponscák et al., Mathematical modelling of the collective behaviour of gas bubbles under the anode, preprint (2000).
19. H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena, The Inter-national Series of Monographs on Physics (Oxford Univ. Press, 1973).