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Numerical approximation of the Newtonian film blowing problem. (English) Zbl 1127.76008
Summary: We study the numerical approximation of a Newtonian model for film blowing. We prove that the approximations for the bubble radius, and the film thickness, converges to the true solution and establish the convergence rates. Numerical results are given which demonstrate the theoretical results obtained.

MSC:
76A20 Thin fluid films
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
76M10 Finite element methods applied to problems in fluid mechanics
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[1] Pearson, J.R.A.; Petrie, C.J.S., The flow of a tubular film. part 1: formal mathematical representation, J. fluid mech., 40, 1-19, (1970) · Zbl 0197.23801
[2] Pearson, J.R.A.; Petrie, C.J.S., The flow of a tubular film. part 2: interpretation of the model and discussion of solutions, J. fluid mech., 42, 609-625, (1970) · Zbl 0193.26201
[3] Han, C.D.; Park, J.Y., Studies on blown film extrusion I. experimental determination of elongational viscosity, J. appl. polym. sci., 19, 3257-3276, (1975)
[4] Han, C.D.; Park, J.Y., Studies on blown film extrusion II. analysis of deformation and heat transfer processes, J. appl. polym. sci., 19, 3277-3290, (1975)
[5] Han, C.D.; Park, J.Y., Studies on blown film extrusion III. bubble instability, J. appl. polym. sci., 19, 3291-3297, (1975)
[6] Tam, D.C.H., Mathematical analysis of the blown Newtonian film, ()
[7] Doufas, A.K.; McHugh, A.J., Simulation of film blowing including flow-induced crystallization, J. rheol., 45, 1085-1104, (2001)
[8] Sidiropoulos, V.; Tian, J.J.; Vlachopoulos, J., Computer simulation of film blowing, TAPPI journal, 79, 8, 113-118, (1996)
[9] Johnson, C., Numerical solution of partial differential equations by the finite element method, (1987), Cambridge University Press
[10] Brenner, S.C.; Scott, L.R., The mathematical theory of finite element methods, (1994), Springer-Verlag Publishing Cambridge · Zbl 0804.65101
[11] Luo, X.L.; Tanner, R.I., A computer study of film blowing, Polym. eng. sci., 25, 10, 620-629, (1985)
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