A mathematical model for Resin transfer molding. (English) Zbl 1091.76011

Summary: The known pseudo-concentration model is a generalization of the classical model of two immiscible fluids when the interface between the two fluids is not a sufficiently regular curve. In addition, it provides efficient and robust numerical methods. The aim of this article is to prove existence of solutions to a mathematical model, based on the pseudo-concentration function model, for the filling of shallow molds with polymers. Numerical methods and numerical simulations as well as a comparison with experimental results have been presented in [O. Diallo, ”Modélisation et simulation numérique de résines réactives dans un milieu poreux”, thèse de doctorat, Univ. Claude Bernard (Lyon I), Villeurbanne, 2000; O. Diallo, J. Pousin and T. Sassi, ”A posteriori error estimates for the transport equation applied to resin transfer molding problems”, in 16th IMACS World Congress Proceedings (Lausanne, 2000), Longman, Harlow, 2000, see also Adv. Comput. Math. 23, No. 3, 241–263 (2005; Zbl 1071.65144)]. The proposed model is 2-D, the chemical reactivity of the fluid is accounted for by means of the conversion rate satisfying a Kamal-Sourour model, and the temperature is not considered. We prove the existence of a renormalized solution to the mathematical model, and an analysis of time stability is carried out illustrating that the proposed model is suitable for describing the polymer state.


76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35Q35 PDEs in connection with fluid mechanics
76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
76M25 Other numerical methods (fluid mechanics) (MSC2010)


Zbl 1071.65144
Full Text: DOI Numdam EuDML


[1] Agassant, J.F., Demay, Y., and Fortin, A.. Prediction of stationary interfaces in coextrusion flows. Polymer engineering and science, 34:121-134, 1994. N 14.
[2] Brézis, H.. Analyse fonctionnelle. Masson, Paris, 1983. · Zbl 0511.46001
[3] Bardos, C.Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; théorèmes d’approximation. application à l’équation de transport. Ann. Sci. École Normale Supérieure, 4eme série, t. 3:185-233, 1970. · Zbl 0202.36903
[4] Coddington, E.A. and Norman, L.. Ordinary differential equations. Mcgran-hill book compagny, New-York; Toronto ; London, 1955. · Zbl 0064.33002
[5] Crouzeix, M. and Mignot, A.. Approximation des équations différentielles ordinaires. Masson, Paris, 1992.
[6] Diallo, O.. Modélisation et simulation numérique de résines réactives dans un milieu poreux. PhD Thesis, Claude Bernard UniversityLyon 1, 2000.
[7] Diallo, O., Pousin, J., and Sassi, T.. A posteriori error estimates for the transport equation applied to resin transfert molding problems. In R. OwensM. Deville, 16th IMACS world congres Proceeding. Longman, 2000.
[8] Kamal, M.R. and Sourour, S.. Kinetics and thermal characterization of thermoset cure. Polymer Engineering and science, 13:59-64, 1973.
[9] Maitre, E. and Witomski, P.. Transport equation with boundary conditions for free surface localization. Numer. Math., 84:275-303, 1999. No. 2. · Zbl 0957.76090
[10] Nouri, A. and Poupaud, F.. An existence theorem for the multifluid stokes problem. Quart. Appl. Math., 55:421-435, 1997. N 3. · Zbl 0882.35091
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