On the Consistency of Dynamic Wetting Boundary Conditions for the Navier-Stokes-Cahn-Hilliard Equations
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| Format: | Preprint |
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2024
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| _version_ | 1866916315876294656 |
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| author | Demont, T. H. B. Stoter, S. K. F. Diddens, C. van Brummelen, E. H. |
| author_facet | Demont, T. H. B. Stoter, S. K. F. Diddens, C. van Brummelen, E. H. |
| contents | We investigate the limiting behavior of the Navier-Stokes-Cahn-Hilliard model for binary-fluid flows as the diffuse-interface thickness passes to zero, in the presence of fluid-fluid-solid contact lines. Allowing for motion of such contact lines relative to the solid substrate is required to adequately model multi-phase and multi-species fluid transport past and through solid media. Even though diffuse-interface models provide an inherent slip mechanism through the mobility-induced diffusion, this slip vanishes as the interface thickness and mobility parameter tend to zero in the so-called sharp-interface limit. The objective of this work is to present dynamic wetting and generalized Navier boundary conditions for diffuse-interface models that are consistent in the sharp-interface limit. We concentrate our analysis on the prototypical binary-fluid Couette-flow problems. To verify the consistency of the diffuse-interface model in the limit of vanishing interface thickness, we provide reference limit solutions of a corresponding sharp-interface model. For parameter values both at and away from the critical viscosity ratio, we present and compare the results of both the diffuse- and sharp-interface models. The close match between both model results indicates that the considered test case lends itself well as a benchmark for further research. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_06049 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Consistency of Dynamic Wetting Boundary Conditions for the Navier-Stokes-Cahn-Hilliard Equations Demont, T. H. B. Stoter, S. K. F. Diddens, C. van Brummelen, E. H. Numerical Analysis Fluid Dynamics We investigate the limiting behavior of the Navier-Stokes-Cahn-Hilliard model for binary-fluid flows as the diffuse-interface thickness passes to zero, in the presence of fluid-fluid-solid contact lines. Allowing for motion of such contact lines relative to the solid substrate is required to adequately model multi-phase and multi-species fluid transport past and through solid media. Even though diffuse-interface models provide an inherent slip mechanism through the mobility-induced diffusion, this slip vanishes as the interface thickness and mobility parameter tend to zero in the so-called sharp-interface limit. The objective of this work is to present dynamic wetting and generalized Navier boundary conditions for diffuse-interface models that are consistent in the sharp-interface limit. We concentrate our analysis on the prototypical binary-fluid Couette-flow problems. To verify the consistency of the diffuse-interface model in the limit of vanishing interface thickness, we provide reference limit solutions of a corresponding sharp-interface model. For parameter values both at and away from the critical viscosity ratio, we present and compare the results of both the diffuse- and sharp-interface models. The close match between both model results indicates that the considered test case lends itself well as a benchmark for further research. |
| title | On the Consistency of Dynamic Wetting Boundary Conditions for the Navier-Stokes-Cahn-Hilliard Equations |
| topic | Numerical Analysis Fluid Dynamics |
| url | https://arxiv.org/abs/2407.06049 |