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Conservation law and Lie symmetry analysis of Foam Drainage equation | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 5، دوره 2، شماره 1، اردیبهشت 2021، صفحه 37-44 اصل مقاله (412.95 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2020.18460.1036 | ||
| نویسندگان | ||
| Mehdi Nadjafikhah* ؛ Omid Chekini | ||
| Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran | ||
| چکیده | ||
| In this paper, using the Lie group analysis method, we study the group invariant of the Foam Drainage equation. It shows that this equation can be reduced to ODE. Also we apply the Lie-group classical, and the nonclassical method due to Bluman and Cole to deduce symmetries of the Foam Drainage equation. and we prove that the nonclassical method applied to the equation leads to new reductions, which cannot be obtained by Lie classical symmetries. Also this paper shows how to construct directly the local conservation laws for this equation. | ||
| کلیدواژه‌ها | ||
| Lie group analysis؛ Conservation law؛ Optimal system؛ Foam Drainage equation؛ Nonclassical symmetry | ||
| مراجع | ||
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[1] M. F. Ashby, A. G. Evans, N. A. Fleck, L. J. Gibson, J. W. Hutchinson, H. N. G. Wasley, Metal Foams: A Design Guide, Society of Automotive Engineers, Boston, Mass, USA, 2000.
[2] J. Banhart, Metallschaume, MIT, Bermen, Germany, 1997.
[3] A. Bhakta, E. Ruckenstein, Decay of standing foams: drainage, coalescence and collapse, Advances in Colloid and Interface Science, vol. 70, no. 1-3 (1997)1-123.
[4] M. Durand, D. Langevin, Physicochemical approach to the theory of foam drainage, European Physical Journal E, vol. 7, no. 1 (2002) 35-44.
[5] L. J. Gibson, M. F. Ashby, Cellular Solids: Structure & Properties, Cambridge University Press, Cambridge, UK, 1997.
[6] L. J. Gibson, M. F. Ashby, Cellular Solids: Structure and Properties, Cambridge University Press, Cambridge, UK, 1999.
[7] S. Hilgenfeldt, S. A. Koehler, H. A. Stone, Dynamics of coarsening foams: accelerated and self-limiting drainage, Physical Review Letters, vol. 86, no. 20 (2001) 4704-4707.
[8] S. A. Koehler, H. A. Stone, M. P. Brenner, J. Eggers, Dynamics of foam drainage, Physical Review E, vol. 58, no. 2 (1998) 2097-2106.
[9] R. A. Leonard, R. Lemlich, A study of interstitial liquid flow in foam, AIChE Journal, vol. 11 (1965) 18-29.
[10] S. Lie, F. Engel, Theorie der transformationsgruppen; Teubner: Leipzig, Germany, 1888.
[11] S. Lie, Vorlesungen ¨uber differentialgleichungen mit bekannten infinitesimalen transformationen; Teubner: Leipzig, Germany, 1891.
[12] A. H. Nayfeh, Introduction to Perturbation Techniques, John Wiley & Sons, New York, NY, USA, 1981.
[13] E. Noether, Invariante Variationsprobleme. Nachr. v. d. Ges. d. Wiss. zu G¨ottingen, Math. Phys. Kl. 1918, 235–257; English translation, Transp. Th. Stat. Phys. 1 (1971) 186-207.
[14] R. K. Prud’homme, S. A. Khan, Foams: Theory, Measurements and Applications, Marcel Dekker, New York, NY, USA, 1996.
[15] H. A. Stone, S. A. Koehler, S. Hilgenfeldt, M. Durand, Perspectives on foam drainage and the influence of interfacial rheology, Journal of Physics Condensed Matter, vol. 15, no. 1 (2003) S283-S290.
[16] S. D. Stoyanov, V. N. Paunov, E. S. Basheva, I. B. Ivanov, A. Mehreteab, G. Broze, Motion of the front between thick and thin film: hydrodynamic theory and experiment with vertical foam films, Langmuir, vol. 13, no. 6 (1997) 1400-1407.
[17] G. Verbist, D. Weaire, Soluble model for foam drainage, Europhysics Letters, vol. 26 (1994) 631-634.
[18] G. Verbist, D. Weaire, A soluble model for foam drainage, Europhysics Letters, vol. 26, no. 8 (1994) 631.
[19] G. Verbist, D. Weaire, A. M. Kraynik, The foam drainage equation, Journal of Physics Condensed Matter, vol. 8, no. 21 (1996) 3715-3731.
[20] D. Weaire, S. Hutzler, N. Pittet, D. Pardal, Steady-state drainage of an aqueous foam, Physical Review Letters, vol. 71, no. 16 (1993) 2670-2673.
[21] D. Weaire, S. Findlay, G. Verbist, Measurement of foam drainage using AC conductivity, Journal of Physics: Condensed Matter, vol. 7, no. 16 (1995) L217-L222.
[22] D. Weaire, S. Hutzler, G. Verbist, E. A. J. Peters, A review of foam drainage, Advances in Chemical Physics, vol. 102 (1997) 315-374.
[23] D. L. Weaire, S. Hutzler, The Physics of Foams, Oxford University Press, Oxford, UK, 2000.
[24] D. Weaire, S. Hutzler, S. Cox, N. Kern, M. D. Alonso, D. D. Drenckhan, The fluid dynamics of foams, Journal of Physics Condensed Matter, vol. 15, no. 1 (2003) S65-S73.
[25] J. I. B. Wilson, Essay review, scholarly froth and engineering skeletons, Contemporary Physics, vol. 44 (2003) 153-155. | ||
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