A MIXED BOOLEAN AND DEPOSIT MODEL FOR THE MODELING OF METAL PIGMENTS IN PAINT LAYERS
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 me...
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2015-06-01
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doaj-d93d3247d5a64894879d08218b73d51a2020-11-24T21:25:05ZengSlovenian Society for Stereology and Quantitative Image AnalysisImage Analysis and Stereology1580-31391854-51652015-06-0134212513410.5566/ias.1220931A MIXED BOOLEAN AND DEPOSIT MODEL FOR THE MODELING OF METAL PIGMENTS IN PAINT LAYERSEnguerrand Couka0François Willot1Dominique Jeulin2Centre de Morphologie Mathématique MINES ParisTech, PSL Research UniversityCentre de Morphologie Mathématique MINES ParisTech, PSL Research UniversityCentre de Morphologie Mathématique MINES ParisTech, PSL Research UniversityPigments 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.http://www.ias-iss.org/ojs/IAS/article/view/1220heterogeneous mediaoptical propertiespaintsrandom microstructure models |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Enguerrand Couka François Willot Dominique Jeulin |
spellingShingle |
Enguerrand Couka François Willot Dominique Jeulin A MIXED BOOLEAN AND DEPOSIT MODEL FOR THE MODELING OF METAL PIGMENTS IN PAINT LAYERS Image Analysis and Stereology heterogeneous media optical properties paints random microstructure models |
author_facet |
Enguerrand Couka François Willot Dominique Jeulin |
author_sort |
Enguerrand Couka |
title |
A MIXED BOOLEAN AND DEPOSIT MODEL FOR THE MODELING OF METAL PIGMENTS IN PAINT LAYERS |
title_short |
A MIXED BOOLEAN AND DEPOSIT MODEL FOR THE MODELING OF METAL PIGMENTS IN PAINT LAYERS |
title_full |
A MIXED BOOLEAN AND DEPOSIT MODEL FOR THE MODELING OF METAL PIGMENTS IN PAINT LAYERS |
title_fullStr |
A MIXED BOOLEAN AND DEPOSIT MODEL FOR THE MODELING OF METAL PIGMENTS IN PAINT LAYERS |
title_full_unstemmed |
A MIXED BOOLEAN AND DEPOSIT MODEL FOR THE MODELING OF METAL PIGMENTS IN PAINT LAYERS |
title_sort |
mixed boolean and deposit model for the modeling of metal pigments in paint layers |
publisher |
Slovenian Society for Stereology and Quantitative Image Analysis |
series |
Image Analysis and Stereology |
issn |
1580-3139 1854-5165 |
publishDate |
2015-06-01 |
description |
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. |
topic |
heterogeneous media optical properties paints random microstructure models |
url |
http://www.ias-iss.org/ojs/IAS/article/view/1220 |
work_keys_str_mv |
AT enguerrandcouka amixedbooleananddepositmodelforthemodelingofmetalpigmentsinpaintlayers AT francoiswillot amixedbooleananddepositmodelforthemodelingofmetalpigmentsinpaintlayers AT dominiquejeulin amixedbooleananddepositmodelforthemodelingofmetalpigmentsinpaintlayers AT enguerrandcouka mixedbooleananddepositmodelforthemodelingofmetalpigmentsinpaintlayers AT francoiswillot mixedbooleananddepositmodelforthemodelingofmetalpigmentsinpaintlayers AT dominiquejeulin mixedbooleananddepositmodelforthemodelingofmetalpigmentsinpaintlayers |
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