Numerical simulation of thin paint film flow
Being able to predict the visual appearance of a painted steel sheet, given its topography before paint application, is of crucial importance for car makers. Accurate modeling of the industrial painting process is required.
The equations describing the leveling of the paint film are complex and their numerical simulation requires advanced mathematical tools, which are described in detail in this paper. Simulations are validated using a large experimental data base obtained with a wavefront sensor developed by Phasics™.
The conducted simulations are complex and require the development of advanced numerical tools, like those presented in this paper.
- Orchard, SE (1961) On surface levelling in viscous liquids and gels. Appl Sci Res 11: pp. 451-464
- Overdiep, WS (1986) The levelling of paints. Prog Org Coat 14: pp. 159-175 CrossRef
- Wilson, SK (1993) The levelling of paint films. IMA J Appl Math 50: pp. 149-166 CrossRef
- Howison, SD, Moriarty, JA, Ockendon, JR, Terrill, EL (1997) A mathematical model for drying paint layers. J Eng Math 32: pp. 377-394 CrossRef
- Weidner, DE, Schwartz, LW, Eley, RR (1996) Role of surface tension gradients in correcting coating defects in corners. J Colloid Interface Sci 179: pp. 66-75 CrossRef
- Eres, MH, Weidner, DE, Schwartz, LW (1999) Three-dimensional direct numerical simulation of surface-tension-gradient effects on the leveling of an evaporating multicomponent fluid. Langmuir 15: pp. 1859-1871 CrossRef
- Schwartz, LW, Roy, RV, Eley, R, Petrash, S (2001) Dewetting patterns in a drying liquid film. J Colloid Interface Sci 234: pp. 363-374 CrossRef
- Gaskell, PH, Jimack, PK, Sellier, M, Thompson, HM, Wilson, MCT (2004) Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography. J Fluid Mech 509: pp. 253-280 CrossRef
- Gaskell, PH, Jimack, PK, Sellier, M, Thompson, HM (2006) Flow of evaporating gravity-driven thin liquid films over topography. Phys Fluids.
- Phasics: [http://www.phasicscorp.com/]Phasics: [http://www.phasicscorp.com/]
- Figliuzzi B, Jeulin D, Lemaitre A, Manneville P, Fricout G, Piezanowski JJ: Rheology of thin films from flow observations. Exp. Fluids, submitted.Figliuzzi B, Jeulin D, Lemaitre A, Manneville P, Fricout G, Piezanowski JJ: Rheology of thin films from flow observations. Exp. Fluids, submitted.
- Benney, DJ (1966) Long waves on liquid films. J Math Phys 45: pp. 150-155
- Shkadov, VY (1967) Wave flow regimes of a thin layer of viscous fluid subject to gravity. Izv AN SSSR Mekhanika Zhidkosti i Gaza 2: pp. 43-51
- Shkadov, VY (1977) Solitary waves in a layer of viscous liquid. Izv AN SSSR Mekhanika Zhidkosti i Gaza 1: pp. 63-66
- Ruyer-Quil, C, Manneville, P (2000) Improved modeling of flows down inclined planes. Eur Phys J B 15: pp. 357-369 CrossRef
- Ruyer-Quil, C, Manneville, P (1998) Modeling film flows down inclined planes. Eur Phys J B 6: pp. 277-292 CrossRef
- Oron, A, Davis, SH, Bankoff, SG (1997) Long scale evolution of thin liquid films. Rev Mod Phys 69: pp. 931-980 CrossRef
- Fletcher, CAJ (1991) Computational Techniques for Fluid Dynamics. Springer, Berlin CrossRef
- Manneville, P (2010) Instabilities, Chaos and Turbulence. Imperial College Press, London
- Bogacki, P, Shampine, L (1989) A 3(2) pair of Runge-Kutta formulas. Appl Math Lett 2: pp. 321-325 CrossRef
- Cash, JR, Karp, AH (1990) A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Trans Math Softw 16: pp. 201-222 CrossRef
- Press, WH, Teukolsky, SA, Vetterling, WT, Flannery, BP (2007) Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, Cambridge
- Mallat, S (2008) A Wavelet Tour of Signal Processing. Academic Press, San Diego
- Lee, SH, Zahouani, H, Caterini, R, Mathia, TG (1998) Morphological characterization of engineered surfaces by wavelet transform. Int J Mach Tools Manuf 38: pp. 581-589 CrossRef
- Chen, Q, Yang, S, Li, Z (1999) Surface roughness evaluation by using wavelets analysis. Precis Eng 23: pp. 209-212 CrossRef
- Liu, JJ, Kim, D, Han, C (2007) Use of wavelet packet transform in characterization of surface quality. Ind Eng Chem Res 46: pp. 5152-5158 CrossRef
- Numerical simulation of thin paint film flow
- Open Access
- Available under Open Access This content is freely available online to anyone, anywhere at any time.
Journal of Mathematics in Industry
- Online Date
- January 2012
- Online ISSN
- Additional Links
- thin films
- numerical simulation
- industrial painting process
- lubrication approximation
- Author Affiliations
- 1. Centre de Morphologie Mathématique, École des Mines ParisTech, 77300, Fontainebleau, France
- 2. UMR Navier, 2 allée Kepler, 77420, Champs-sur-Marne, France
- 3. ArcelorMittal Global R&D, 57283, Maizières-lès-Metz Cedex, France
- 4. LadHyX, École Polytechnique, 91128, Palaiseau, France