A MIXED BOOLEAN AND DEPOSIT MODEL FOR THE MODELING OF METAL PIGMENTS IN PAINT LAYERS
DOI:
https://doi.org/10.5566/ias.1220Keywords:
heterogeneous media, optical properties, paints, random microstructure modelsAbstract
Pigments made of metal particles of around 10 µm or 20 µm produce sparkling effects in paints, due to the specular reflection that occurs at this scale. Overall, the optical aspect of paints depend on the density and distribution in space of the particles. In this work, we model the dispersion of metal particles of size up to 50 µm, visible to the eyes, in a paint layer. Making use of optical and scanning electron microscopy (SEM) images, we estimate the dispersion of particles in terms of correlation functions. Particles tend to aggregate into clusters, as shown by the presence of oscillations in the correlation functions. Furthermore, the volume fraction of particles is non-uniform in space. It is highest in the middle of the layer and lowest near the surfaces of the layer. To model this microstructure, we explore two models. The first one is a deposit model where particles fall onto a surface. It is unable to reproduce the observed measurements. We then introduce a "stack" model where clusters are first modeled by a 2D Poisson point process, and a bi-directional deposit model is used to implant particles in each cluster. Good agreement is found with respect to SEM images in terms of correlation functions and density of particles along the layer height.References
Altendorf H, Jeulin D (2011).
Random walk based stochastic modeling of 3D fiber systems.
Phys Rev E 83(4):041804.
Azzimonti DF, Willot F, Jeulin D (2013).
Optical properties of deposit models for paints: full-fields FFT computations and representative volume element.
J Modern Opt 60(7):1-10.
Chawla N, Sidhu R, Ganesh V (2006).
Three-dimensional visualization and microstructure-based modeling of deformation in particle-reinforced composites.
Acta Mater 54:1541-48.
Cummings KD, Garland JC, Tanner DB (1984).
Optical properties of a small-particle composite.
Phys Rev B 30(8):4170-82.
Couka E, Willot F, Jeulin D, Ben Achour M, Chesnaud A, Thorel A (2015).
Modeling of the multiscale dispersion of nanoparticles in a hematite coating.
J Nanosci Nanotech 15(5):3515-21.
Dumazet S (2010).
Modélisation de l'apparence visuelle des matériaux - rendu physiquement réaliste.
PhD thesis, Châtenay-Malabry, Ecole centrale de Paris.
Escoda J, Jeulin D, Willot W, Toulemonde C (2015).
D morphological modeling of concrete using multiscale Poisson polyhedra.
J Microscopy, doi: 10.1111/jmi.12213.
Feder J (1980).
Random sequential adsorption.
J Theo Bio 87(2):237-54.
Jean A, Jeulin D, Forest S, Cantournet S, N'Guyen F (2011).
A multiscale microstructure model of carbon black distribution in rubber.
J Microsc 241(3):243-60.
Moreaud M, Jeulin D, Morard V, Revel R (2012).
TEM image analysis and modelling: application to boehmite nanoparticles.
J Microsc 245(2):186-99.
Otsu N (1979).
A threshold selection method from gray-level histograms.
IEEE Trans Syst Man Cybern 9:62-6.
Paciornik S, Da Fonseca Martins Gomes O, Delarue A, Schamm S, Jeulin D, Thorel A (2002).
Multi-scale analysis of the dielectric properties and structure of resin/carbon-black nanocomposites.
Eu Physical J Applied Phys 21(1):17-26.
Schmitt M, Preteux F (1986).
Un nouvel algorithme en morphologie mathématique: les r,h maxima et r,h minima.
ième Semaine Internationale de l'Image Electronique 469-475.
Streitberger H (2008).
Top coat performance. In: Automotive paints and coatings, Second edition, Ch. 6, H.-J. Streitberger and K.-F. Dössel, eds,
Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany.
Yang S, Gao D, Muster T, Tulloh A, Furman S, Mayo S, Trinchi A (2010 a).
Microstructure of a paint primer - a data-constrained modeling analysis.
Mater Sci Forum 656:1686-89.
Yang YS, Tulloh AM, Muster T, Trinchi A, Mayo SC, Wilkins SW (2010 b).
Data-constrained microstructure modeling with multi-spectrum X-ray CT.
Proc SPIE 7804:1-9.
