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Controlling Sliding Droplets with Optimal Contact Angle Distributions and a Phase Field Model
Author(s) -
Bonart Henning,
Kahle Christian,
Repke Jens-Uwe
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900223
Subject(s) - contact angle , phase (matter) , tracking (education) , phase angle (astronomy) , mechanics , line (geometry) , field (mathematics) , optimal control , boundary (topology) , energy (signal processing) , phase field models , physics , mathematics , control theory (sociology) , classical mechanics , mathematical analysis , geometry , control (management) , computer science , mathematical optimization , optics , thermodynamics , pure mathematics , psychology , pedagogy , artificial intelligence , quantum mechanics
We consider the optimal control of a droplet on a solid by means of the static contact angle between the contact line and the solid. The droplet is described by a thermodynamically consistent phase field model from [Abels et al., Math. Mod. Meth. Appl. Sc., 22(3), 2012] together with boundary data for the moving contact line from [Qian et al., J. Fluid Mech., 564, 2006]. We state an energy stable time discrete scheme for the forward problem based on known results, and pose an optimal control problem with tracking type objective.