Geodesic
Periodic Steady-state Solutions of a Liquid Film Model via a Classical Method
Canadian mathematical bulletin, Tome 61 (2018) no. 1, pp. 3-15

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, periodic steady-state of a liquid film flowing over a periodic uneven wall is investigated via a classical method. Specifically, we analyze a long-wave model that is valid at the near-critical Reynolds number. For the periodic wall surface, we construct an iteration scheme in terms of an integral form of the original steady-state problem. The uniform convergence of the scheme is proved so that we can derive the existence and the uniqueness as well as the asymptotic formula of the periodic solutions.
DOI : 10.4153/CMB-2017-035-5
Mots-clés : 34E05, 34E10, 34E15, film flow, classical methods, asymptotic analysis 
Alhasanat, Ahmad; Ou, Chunhua. Periodic Steady-state Solutions of a Liquid Film Model via a Classical Method. Canadian mathematical bulletin, Tome 61 (2018) no. 1, pp. 3-15. doi: 10.4153/CMB-2017-035-5
@article{10_4153_CMB_2017_035_5,
     author = {Alhasanat, Ahmad and Ou, Chunhua},
     title = {Periodic {Steady-state} {Solutions} of a {Liquid} {Film} {Model} via a {Classical} {Method}},
     journal = {Canadian mathematical bulletin},
     pages = {3--15},
     year = {2018},
     volume = {61},
     number = {1},
     doi = {10.4153/CMB-2017-035-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-035-5/}
}
TY  - JOUR
AU  - Alhasanat, Ahmad
AU  - Ou, Chunhua
TI  - Periodic Steady-state Solutions of a Liquid Film Model via a Classical Method
JO  - Canadian mathematical bulletin
PY  - 2018
SP  - 3
EP  - 15
VL  - 61
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-035-5/
DO  - 10.4153/CMB-2017-035-5
ID  - 10_4153_CMB_2017_035_5
ER  - 
%0 Journal Article
%A Alhasanat, Ahmad
%A Ou, Chunhua
%T Periodic Steady-state Solutions of a Liquid Film Model via a Classical Method
%J Canadian mathematical bulletin
%D 2018
%P 3-15
%V 61
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-035-5/
%R 10.4153/CMB-2017-035-5
%F 10_4153_CMB_2017_035_5

[1] [1] Alekseenko, S. V., Markovich, D. M., Evseev, A. R., Bobylev, A. V., Tarasov, B. V., and Karsten, V. M., Experimental investigation of liquid distribution over structured packing. AIChE J. 54 (2008), 1424–1430. Google Scholar

[2] [2] Benjamin, T. B., Wave formation in laminar flow down an inclined plane. J. Fluid Mech. 2 (1957), 554–574. http://dx.doi.Org/10.1017/S0022112057000373. Google Scholar

[3] [3] Blyth, M. G., Effect ofan electric field on the stability of contaminated film flow down an inclined plane. J. Fluid Mech. 595 (2008), 221–237. http://dx.doi.Org/10.1017/S0022112007009147. Google Scholar

[4] [4] Gonzalez, A. and Castellanos, A., Nonlinear electrohydrodynamic waves on films falling down an inclined plane. Physical Review e 43 (1996), no. 4, 3573–3578. Google Scholar

[5] [5] Hastings, S. P. and McLeod, J. B., Classical methods in ordinary differential equations. With applications to boundary value problems. Graduate Studies in Mathematics, 129, American Mathematical Society, Providence, RI, 2012. Google Scholar

[6] [6] Jacobson, N., Basic algebra. I. W. H. Freeman and Co., San Francisco, CA, 1974. Google Scholar

[7] [7] Kistler, S. F. and Schweizer, P. M., Liquid film coating. Chapman and Hall, New York, 1997. Google Scholar

[8] [8] Stone, H. A. and Kim, S., Microfluidics: Basic issues, applications, and challenges. AIChE Journal 47 (2001), no. 6, 1250–1254. Google Scholar

[9] [9] Tseluiko, D. and Blyth, M. G., Effect ofinertia on electrified film flow over a wavy wall. J. Engrg Math. 65 (2009), 229–242. http://dx.doi.org/10.1007/s10665-009-9283-1. Google Scholar

[10] [10] Tseluiko, D., Blyth, M. G., and Papageoriou, D. T., Stability offilm flow over inclined topography based on a long-wave nonlinear model. J. Fluid Mech. 729 (2013), 638–671. http://dx.doi.org/10.1017/jfm.2013.331. Google Scholar

[11] [11] Weinstein, S. J. and Ruschak, K. J., Coating flows. Annu. Rev. Fluid. Mech. 36 (2004), 29–53. Google Scholar

[12] [12] Whitesides, G. M. and Stroock, A. D., Flexible methods for microfluidics. Physics Today 54 (2001), 42–48. Google Scholar

Cité par Sources :