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Simulations and experimental investigation of paint film leveling

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Abstract

The surface structure of a paint film is the result of the interplay of a variety of physical influences, e.g., the superposition of droplets during spray application, the surface tension-driven leveling, and the viscosity increase in the leveling phase. A numerical simulation program is presented that incorporates all the relevant mechanisms of paint film structure formation during and after spray application. The simulation program was validated by comparing simulations and leveling experiments. The influence of the initial film geometry and viscosity on the leveling behavior is demonstrated. For the investigations, model liquids and commercial paints with an increasing complexity of the physical properties were chosen: Newtonian flow behavior without solvent evaporation, Newtonian flow behavior with solvent evaporation, viscoelastic paints with non-Newtonian flow behavior. Four variants are proposed regarding how thixotropy can be measured and how a mathematical model can be created. The advantages and disadvantages of the variants with regard to the implementation of thixotropy in the simulations are listed. A method to predict the leveling behavior of thixotropic paints with simultaneous recovery of the viscous and elastic properties from rheological measurements using discrete relaxation time spectra is presented.

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Abbreviations

A :

Amplitude (m)

E :

Shrinkage due to evaporation (m/s)

g :

Gravitational constant (m/s2)

G′:

Storage modulus (Pa)

G″:

Loss modulus (Pa)

h :

Medium film thickness (m)

h l :

Film thickness at a given point (m)

h surf :

Height of the surface above the average substrate height as reference plane at a given point (m)

k :

A constant

k relax i :

Weighting factor in relaxation time spectrum (Pa·s)

R q :

Root-mean-square roughness (m)

t :

Time (s)

t relax i :

Relaxation time (s)

v :

Leveling velocity (1/s)

x :

x-coordinate (m)

y :

y-coordinate (m)

\(\dot{\gamma }\) :

Shear rate (1/s)

ε :

Local relative error (%)

η :

Dynamic viscosity (Pa·s)

η relax i :

Weighting factor for viscosity calculation from relaxation time spectrum (Pa)

θ :

Inclination angle (°)

λ :

Structure wavelength of the paint film surface (m)

σ :

Surface tension coefficient (N/m)

τ :

Shear stress (Pa)

ω :

Angular frequency (1/s)

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Acknowledgments

We would like to thank the Forschungsgesellschaft für Pigmente und Lacke e.V. for the financial support of the work.

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Authors and Affiliations

  1. Department of Coating Systems and Painting Technology, Fraunhofer Institute for Manufacturing Engineering and Automation IPA, Nobelstrasse 12, 70569, Stuttgart, Germany

    Fabian Seeler, Oliver Tiedje & Matthias Schneider

  2. John Deere GmbH & Co. KG, John-Deere-Strasse 8, 76646, Bruchsal, Germany

    Christian Hager

Authors
  1. Fabian Seeler
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  2. Christian Hager
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  3. Oliver Tiedje
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  4. Matthias Schneider
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Correspondence to Fabian Seeler.

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Seeler, F., Hager, C., Tiedje, O. et al. Simulations and experimental investigation of paint film leveling. J Coat Technol Res 14, 767–781 (2017). https://doi.org/10.1007/s11998-017-9934-5

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