dorsal/arxiv
View SchemaBubbles and Filaments: Stirring a Cahn-Hilliard Fluid
| Authors | Lennon O Naraigh, Jean-Luc Thiffeault |
|---|---|
| Categories | |
| ArXiv ID | physics/0609258 |
| URL | https://arxiv.org/abs/physics/0609258 |
| DOI | 10.1103/PhysRevE.75.016216 |
| Journal | Phys. Rev. E 75, 016216 (2007) |
Abstract
The advective Cahn-Hilliard equation describes the competing processes of stirring and separation in a two-phase fluid. Intuition suggests that bubbles will form on a certain scale, and previous studies of Cahn-Hilliard dynamics seem to suggest the presence of one dominant length scale. However, the Cahn-Hilliard phase-separation mechanism contains a hyperdiffusion term and we show that, by stirring the mixture at a sufficiently large amplitude, we excite the diffusion and overwhelm the segregation to create a homogeneous liquid. At intermediate amplitudes we see regions of bubbles coexisting with regions of hyperdiffusive filaments. Thus, the problem possesses two dominant length scales, associated with the bubbles and filaments. For simplicity, we use use a chaotic flow that mimics turbulent stirring at large Prandtl number. We compare our results with the case of variable mobility, in which growth of bubble size is dominated by interfacial rather than bulk effects, and find qualitatively similar results.
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"abstract": "The advective Cahn-Hilliard equation describes the competing processes of\nstirring and separation in a two-phase fluid. Intuition suggests that bubbles\nwill form on a certain scale, and previous studies of Cahn-Hilliard dynamics\nseem to suggest the presence of one dominant length scale. However, the\nCahn-Hilliard phase-separation mechanism contains a hyperdiffusion term and we\nshow that, by stirring the mixture at a sufficiently large amplitude, we excite\nthe diffusion and overwhelm the segregation to create a homogeneous liquid. At\nintermediate amplitudes we see regions of bubbles coexisting with regions of\nhyperdiffusive filaments. Thus, the problem possesses two dominant length\nscales, associated with the bubbles and filaments. For simplicity, we use use a\nchaotic flow that mimics turbulent stirring at large Prandtl number. We compare\nour results with the case of variable mobility, in which growth of bubble size\nis dominated by interfacial rather than bulk effects, and find qualitatively\nsimilar results.",
"arxiv_id": "physics/0609258",
"authors": [
"Lennon O Naraigh",
"Jean-Luc Thiffeault"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1103/PhysRevE.75.016216",
"journal_ref": "Phys. Rev. E 75, 016216 (2007)",
"title": "Bubbles and Filaments: Stirring a Cahn-Hilliard Fluid",
"url": "https://arxiv.org/abs/physics/0609258"
},
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