Determination of the saturated region shape for liquid impregnation into laminated porous material
Matematičeskoe modelirovanie, Tome 22 (2010) no. 6, pp. 69-83.

Voir la notice de l'article provenant de la source Math-Net.Ru

Numerical solution of the problem of liquid impregnation into laminated porous material is presented. For case steady-state process with high contrast of layer's thickness and permeability this problem is formulated as specific free boundary problem, which is characterized by small angle between free boundary and interlaminar boundary. Proposed iterative method of solution is efficient for angle greater by 0.003. The comparison of numerical results and known asymptotic analysis results is presented.
Keywords: layer, saturated region shape.
Mots-clés : interface
@article{MM_2010_22_6_a6,
     author = {M. M. Alimov},
     title = {Determination of the saturated region shape for liquid impregnation into laminated porous material},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {69--83},
     publisher = {mathdoc},
     volume = {22},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_6_a6/}
}
TY  - JOUR
AU  - M. M. Alimov
TI  - Determination of the saturated region shape for liquid impregnation into laminated porous material
JO  - Matematičeskoe modelirovanie
PY  - 2010
SP  - 69
EP  - 83
VL  - 22
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2010_22_6_a6/
LA  - ru
ID  - MM_2010_22_6_a6
ER  - 
%0 Journal Article
%A M. M. Alimov
%T Determination of the saturated region shape for liquid impregnation into laminated porous material
%J Matematičeskoe modelirovanie
%D 2010
%P 69-83
%V 22
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2010_22_6_a6/
%G ru
%F MM_2010_22_6_a6
M. M. Alimov. Determination of the saturated region shape for liquid impregnation into laminated porous material. Matematičeskoe modelirovanie, Tome 22 (2010) no. 6, pp. 69-83. http://geodesic.mathdoc.fr/item/MM_2010_22_6_a6/

[1] Mathur R., Heider D., Hoffmann C., Gillespie J. W. (jr.), Advani S. G., Fink B. K., “Flow front measurements and model validation in the vacuum assisted resin transfer molding process”, Polymer Composites, 22:4 (2001), 477–490 | DOI

[2] Alimov M. M., Kornev K. G., “Impregnation of liquids into a laminated porous material with a high permeability contrast”, Physics of Fluids, 19 (2007), 102108-1–102108-11 | DOI | Zbl

[3] Alimov M. M., “Asimptoticheskii analiz ustanovivshegosya protsessa nasyscheniya sloistogo poristogo materiala”, PMM, 79:5 (2009), 799–808 | MR

[4] Muskat M., The Flow of Homogeneous Fluids through Porous Media, I. W. Edwards, Inc., Ann Arbor, Michigan, 1946; Masket M., Techenie odnorodnykh zhidkostei v poristoi srede, Gostoptekhizdat, M.–L., 1949, 628 pp.

[5] Polubarinova-Kochina P. Ya., Teoriya dvizheniya gruntovykh vod, Nauka, M., 1977, 664 pp. | MR

[6] Gurevich M. I., Teoriya strui idealnoi zhidkosti, Nauka, M., 1979, 536 pp. | Zbl

[7] Lamb H., Hydrodynamics, Cambridge Univ. Press, 1924 ; Lamb G., Gidrodinamika, Gostekhizdat, M.–L., 1947, 928 pp. | MR

[8] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1973, 736 pp. | MR

[9] Koppenfels W., Stalman F., Praxis der Konformen Abbildung, Springer, Berlin, 1959 ; Koppenfels V., Shtalman Ts., Praktika konformnogo otobrazheniya, IL, M., 1963, 406 pp. | MR | Zbl

[10] Alimov M. M., “Reshenie metodom iteratsii zadachi nasyscheniya dvusloinogo poristogo materiala”, Uchenye zapiski Kazanskogo gosudarstvennogo universiteta. Ser. fiz.-mat. nauki, 150, no. 3, 2008, 88–103