Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach
| Autor: | Piotr Szymczak, liang yu, Anthony J. C. Ladd |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
010504 meteorology & atmospheric sciences Mechanical Engineering Laurent series Mathematical analysis Conformal map Function (mathematics) Péclet number Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Physics::Fluid Dynamics symbols.namesake Unit circle Hele-Shaw flow Mechanics of Materials 0103 physical sciences symbols Cylinder Potential flow 0105 earth and related environmental sciences |
| Zdroj: | Journal of Fluid Mechanics. 903 |
| ISSN: | 1469-7645 0022-1120 |
| Popis: | We apply conformal mapping to find the evolving shapes of a dissolving cylinder in a potential flow. Similar equations can be used to describe melting in a flowing liquid phase. Results are compared with microfluidic experiments and numerical simulations. Shapes predicted by conformal mapping agree almost perfectly with experimental observations, after a modest (20 %) rescaling of the time. Finite-volume simulations show that the differences with experiment are connected to the underlying assumptions of the analytical model: potential flow and diffusion-limited dissolution. Approximate solutions of the equations describing the evolution of the shape of the undissolved solid can be derived from a Laurent expansion of the mapping function from the unit circle. Asymptotic expressions for the evolution of the area of the disk and the shift in its centre of mass have been derived at low and high Peclet number. Analytic approximations to the leading-order Laurent coefficients provide additional insight into the mechanisms underlying pore-scale dissolution. |
| Databáze: | OpenAIRE |
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