Fingering instability of self-similar radial flow of miscible fluids in a Hele-Shaw cell
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916677781815296 |
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| author | Lister, John R. Dauck, Tim-Frederik |
| author_facet | Lister, John R. Dauck, Tim-Frederik |
| contents | The linear stability of miscible displacement for radial source flow at infinite Péclet number in a Hele-Shaw cell is calculated theoretically. The axisymmetric self-similar flow is shown to be unstable to viscous fingering if the viscosity ratio $m$ between ambient and injected fluids exceeds $3\over2$ and to be stable if $m<{3\over2}$. If $1<m<{3\over2}$ small disturbances decay at rates between $t^{-3/4}$ and $t^{-1}$ relative to the $t^{1/2}$ radius of the axisymmetric base-state similarity solution; if $m<1$ they decay faster than $t^{-1}$. Asymptotic analysis confirms these results and gives physical insight into various features of the numerically determined relationship between the growth rate and the azimuthal wavenumber and viscosity ratio. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01961 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fingering instability of self-similar radial flow of miscible fluids in a Hele-Shaw cell Lister, John R. Dauck, Tim-Frederik Fluid Dynamics The linear stability of miscible displacement for radial source flow at infinite Péclet number in a Hele-Shaw cell is calculated theoretically. The axisymmetric self-similar flow is shown to be unstable to viscous fingering if the viscosity ratio $m$ between ambient and injected fluids exceeds $3\over2$ and to be stable if $m<{3\over2}$. If $1<m<{3\over2}$ small disturbances decay at rates between $t^{-3/4}$ and $t^{-1}$ relative to the $t^{1/2}$ radius of the axisymmetric base-state similarity solution; if $m<1$ they decay faster than $t^{-1}$. Asymptotic analysis confirms these results and gives physical insight into various features of the numerically determined relationship between the growth rate and the azimuthal wavenumber and viscosity ratio. |
| title | Fingering instability of self-similar radial flow of miscible fluids in a Hele-Shaw cell |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2412.01961 |