Scholarly Research Excellence

Digital Open Science Index

Commenced in January 2007 Frequency: Monthly Edition: International Publications Count: 29064


Select areas to restrict search in scientific publication database:
16957
An Analytical Method to Analysis of Foam Drainage Problem
Abstract:
In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.
Digital Object Identifier (DOI):

References:

[1] J. J. Bikerman, Foams. New York: Springer-Verlag, 1973.
[2] R. K. Prud’homme and S. A. Khan, Foams: Theory, Measurements and Applications, New York: Marcel Dekker, 1996.
[3] 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, vol. 13, 1997, pp. 1400- 1407.
[4] H.A. Stone, S.A. Koehler, S. Hilgenfeldt, M. Durand, Perspectives on foam drainage and the influence of interfacial rheology, J. Phys. Condens, 15 (2003) 283-290.
[5] J.I.B. Wilson, Essay review, scholarly froth and engineering skeletons, Contemp. Phys, 44 (2003) 153-155.
[6] S. Hilgenfeldt, S.A. Koehler, H.A. Stone, Dynamics of coarsening foams: accelerated and self-limiting drainage, Phys. Rev. Lett , 20 (2001) 4704-4707.
[7] L.J. Gibson, M.F. Ashby, Cellular Solids: Structure & Properties, Cambridge University Press, Cambridge, 1997.
[8] J. Banhart, Metallschaume, MIT-Verlag, Bermen, 1997.
[9] S.A.Koehler, H.A.Stone, M.P. Brenner, Eggers J., Dynamics of foam drainage, Phys. Rev, 58 (199 8) 2097-2106.
[10] M. Duranda, D. Langevin, Physicochemical approach to the theory of foam drainage, Eur. Phys. J. E, 7 (2002) 35-44.
[11] R. A. Leonard and R. Lemlich, AIChE J. 11, 18 (1965).
[12] I. I. Gol’dfarb, K. B. Kann, and I. R. Shreiber, Fluid Dyn. 23, 244 (1988).
[13] D. Weaire and S. Hutzler, The Physics of Foams, Oxford University Press, Oxford, 2000.
[14] G. Verbist, D. Weaire, A soluble model for foam drainage, Europhys. Lett, 26 (1994), 631-634.
[15] G. Verbist, D.Weaire, A. M. Kraynik, The foam drainage equation, J. Phys. Condens. Matter, 8 (1996) 3715-3731.
[16] G Verbisty, D Weairez and A M Kraynik, The foam drainage equation, J. Phys.: Condens. Matter 8 (1996) 3715-3731
[17] X.B. Hu, Y.T. Wu, Application of the Hirota bilinear formalism to a new integrable differential-difference equation, Phys. Lett. A, 246 (1998) 523-529.
[18] M. Wang, Y. Zhou, Z. Li, Applications of a homogeneous balance method to exact solution of nonlinear equations in mathematical physics, Phys. Lett. A, 216 (1996) 67-75.
[19] V.O. Vakhnenko, E.J. Parkes, A.J. Morrison, A Bäcklund transformation and the inverse scattering transform method for the generalized Vakhnenko equation, Chaos Solitons Fractals 17 (2003) 683-692.
[20] G. Adomian, Nonlinear dissipative wave equations, Appl. Math. Lett. 11 (1998) 125-126.
[21] M.T. Darvishi, F. Khani, A.A. Soliman, The numerical simulation for stiff systems of ordinary differential equations, Comput. Math. Appl. 54 (2007) 1055-1063.
[22] A.V. Karmishin, A.I. Zhukov, V.G. Kolosov, Methods of Dynamics Calculation and Testing for Thin-walled Structures, Moscow: Mashinostroyenie, 1990.
[23] J. H. He ,Variational iteration method: a kind of nonlinear analytical technique :some example. International Journal of Nonlinear Mechanics 34(4) (1999) 699.
[24] Sara Barati and Karim Ivaz, Variational Iteration Method for Solving Systems of Linear Delay Differential Equations, International Journal of Computational and Mathematical Sciences, 6 (2012) 132-135.
[25] A. Nikkar, S. Esmaeilzade Toloui, K. Rashedi and H. R. Khalaj Hedayati, Application of energy balance method for a conservative X1/3 force nonlinear oscillator and the Doffing equations. Int. J. Numer. Method Appl., 5(1) ( 2011) 57-66.
[26] Y. Khan, R. Taghipour, M. Fallahian, A. Nikkar, A new approach to modified regularized long wave equation , Neural Computing and Applications. ( 26 July 2012), pp. 1-7, doi:10.1007/s00521-012-1077-0
[27] M. Sajid, I. Ahmad, T. Hayat, M. Ayub, Unsteady flow and heat transfer of a second grade fluid over a stretching sheet, Commun. Nonlinear Sci. Numer. Simul. 14 (1) (2009) 96-108.
[28] F. Khani, M. Ahmadzadeh Raji, S. Hamedi-Nezhad, A series solution of the fin problem with a temperature-dependent thermal conductivity, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 3007-3017.
[29] M.A.Helal, M.S.Mehanna, The tanh method and adomian decomposition method for solving the foam drainage equation, Applied Mathematics and Computation, 190 (2007) 599-609.
[30] E.Hesameddini, H.Latifizadeh, Reconstruction of Variational Iteration Algorithms using the Laplace Transform, Int. J. Nonlinear Sci. Numer. Simul. 10 (2009) 1377-1382
[31] A. Nikkar, J. Vahidi, M.J. Ghomi and M. Mighani, Reconstruction of variation Iteration Method for Solving Fifth Order Caudrey-Dodd- Gibbon (CDG) Equation", International journal of Science and Engineering Investigations, 1(6) (2012) 38-41.
Vol:12 No:11 2018Vol:12 No:10 2018Vol:12 No:09 2018Vol:12 No:08 2018Vol:12 No:07 2018Vol:12 No:06 2018Vol:12 No:05 2018Vol:12 No:04 2018Vol:12 No:03 2018Vol:12 No:02 2018Vol:12 No:01 2018
Vol:11 No:12 2017Vol:11 No:11 2017Vol:11 No:10 2017Vol:11 No:09 2017Vol:11 No:08 2017Vol:11 No:07 2017Vol:11 No:06 2017Vol:11 No:05 2017Vol:11 No:04 2017Vol:11 No:03 2017Vol:11 No:02 2017Vol:11 No:01 2017
Vol:10 No:12 2016Vol:10 No:11 2016Vol:10 No:10 2016Vol:10 No:09 2016Vol:10 No:08 2016Vol:10 No:07 2016Vol:10 No:06 2016Vol:10 No:05 2016Vol:10 No:04 2016Vol:10 No:03 2016Vol:10 No:02 2016Vol:10 No:01 2016
Vol:9 No:12 2015Vol:9 No:11 2015Vol:9 No:10 2015Vol:9 No:09 2015Vol:9 No:08 2015Vol:9 No:07 2015Vol:9 No:06 2015Vol:9 No:05 2015Vol:9 No:04 2015Vol:9 No:03 2015Vol:9 No:02 2015Vol:9 No:01 2015
Vol:8 No:12 2014Vol:8 No:11 2014Vol:8 No:10 2014Vol:8 No:09 2014Vol:8 No:08 2014Vol:8 No:07 2014Vol:8 No:06 2014Vol:8 No:05 2014Vol:8 No:04 2014Vol:8 No:03 2014Vol:8 No:02 2014Vol:8 No:01 2014
Vol:7 No:12 2013Vol:7 No:11 2013Vol:7 No:10 2013Vol:7 No:09 2013Vol:7 No:08 2013Vol:7 No:07 2013Vol:7 No:06 2013Vol:7 No:05 2013Vol:7 No:04 2013Vol:7 No:03 2013Vol:7 No:02 2013Vol:7 No:01 2013
Vol:6 No:12 2012Vol:6 No:11 2012Vol:6 No:10 2012Vol:6 No:09 2012Vol:6 No:08 2012Vol:6 No:07 2012Vol:6 No:06 2012Vol:6 No:05 2012Vol:6 No:04 2012Vol:6 No:03 2012Vol:6 No:02 2012Vol:6 No:01 2012
Vol:5 No:12 2011Vol:5 No:11 2011Vol:5 No:10 2011Vol:5 No:09 2011Vol:5 No:08 2011Vol:5 No:07 2011Vol:5 No:06 2011Vol:5 No:05 2011Vol:5 No:04 2011Vol:5 No:03 2011Vol:5 No:02 2011Vol:5 No:01 2011
Vol:4 No:12 2010Vol:4 No:11 2010Vol:4 No:10 2010Vol:4 No:09 2010Vol:4 No:08 2010Vol:4 No:07 2010Vol:4 No:06 2010Vol:4 No:05 2010Vol:4 No:04 2010Vol:4 No:03 2010Vol:4 No:02 2010Vol:4 No:01 2010
Vol:3 No:12 2009Vol:3 No:11 2009Vol:3 No:10 2009Vol:3 No:09 2009Vol:3 No:08 2009Vol:3 No:07 2009Vol:3 No:06 2009Vol:3 No:05 2009Vol:3 No:04 2009Vol:3 No:03 2009Vol:3 No:02 2009Vol:3 No:01 2009
Vol:2 No:12 2008Vol:2 No:11 2008Vol:2 No:10 2008Vol:2 No:09 2008Vol:2 No:08 2008Vol:2 No:07 2008Vol:2 No:06 2008Vol:2 No:05 2008Vol:2 No:04 2008Vol:2 No:03 2008Vol:2 No:02 2008Vol:2 No:01 2008
Vol:1 No:12 2007Vol:1 No:11 2007Vol:1 No:10 2007Vol:1 No:09 2007Vol:1 No:08 2007Vol:1 No:07 2007Vol:1 No:06 2007Vol:1 No:05 2007Vol:1 No:04 2007Vol:1 No:03 2007Vol:1 No:02 2007Vol:1 No:01 2007