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Simulation of Droplet Impact with Dynamic Contact Angle Boundary Conditions

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Singular Phenomena and Scaling in Mathematical Models

Abstract

The numerical simulation of dynamic wetting processes is of interest for a vast variety of industrial processes, where practical experiments are costly and time-consuming. In these simulations, the dynamic contact angle is a key parameter, but the modeling of its behavior is poorly understood so far. In this article, we simulate droplet impact on a dry flat surface by using two different contact angle models. Both models show good qualitative and quantitative agreement with experimental results. For our numerical method, we solve the three-dimensional Navier-Stokes equations with finite differences on a staggered grid. The free surface is captured by a level-set method, and the contact angle determines the shape of the level-set function at the boundary. Additionally, we investigate the mass-conservation properties of two volume-correction methods, which are invaluable for the analysis of the droplet behavior.

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Notes

  1. 1.

    Then, contact angles at corner cells of the geometry have to fulfill further restrictions as described in [6].

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Acknowledgements

The authors acknowledge the support from the Sonderforschungsbereich 611 “Singular Phenomena and Scaling in Mathematical Models” of the Deutsche Forschungsgemeinschaft DFG. We are grateful to Kensuke Yokoi (Cardiff University) for providing the experimental and numerical results of the droplet impact and the permission to use the corresponding pictures in this article.

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Authors and Affiliations

  1. Institut für Numerische Simulation, Rheinische Friedrich-Wilhelms-Universität Bonn, Wegelerstr. 6, D-53115, Bonn, Germany

    Michael Griebel & Margrit Klitz

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  1. Michael Griebel
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  2. Margrit Klitz
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Correspondence to Michael Griebel .

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  1. Universität Bonn Institut für Numerische Simulation, Bonn, Germany

    Michael Griebel

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Griebel, M., Klitz, M. (2014). Simulation of Droplet Impact with Dynamic Contact Angle Boundary Conditions. In: Griebel, M. (eds) Singular Phenomena and Scaling in Mathematical Models. Springer, Cham. https://doi.org/10.1007/978-3-319-00786-1_13

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