Abstract
We show that the surface tension term \(- \varepsilon \, \mathrm {div}\left( \nabla c^\varepsilon \otimes \nabla c^\varepsilon \right) \) of the “model H” does generally not converge to the mean curvature functional of the interface as \(\varepsilon \searrow 0\), where \(c^\varepsilon \) is the solution to a convective Cahn-Hilliard equation with mobility constant converging to 0 too fast as \(\varepsilon \searrow 0\). In that case the motion of the interface is dominated by the convection term \(v \cdot \nabla c^\varepsilon \) of the convective Cahn-Hilliard equation.
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Acknowledgements
The authors acknowledge support by the SPP 1506 “Transport Processes at Fluidic Interfaces” of the German Science Foundation (DFG) through grant AB285/3-1, AB285/4-1 and AB285/4-2. The results are part of the second author’s PhD-thesis [13].
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Abels, H., Schaubeck, S. (2016). Nonconvergence of the Capillary Stress Functional for Solutions of the Convective Cahn-Hilliard Equation. In: Shibata, Y., Suzuki, Y. (eds) Mathematical Fluid Dynamics, Present and Future. Springer Proceedings in Mathematics & Statistics, vol 183. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56457-7_1
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DOI: https://doi.org/10.1007/978-4-431-56457-7_1
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