Immiscible thermo-viscous fingering in Hele-Shaw cells
We investigate immiscible radial displacement in a Hele-Shaw cell with a temperature dependent viscosity using two coupled high resolution numerical methods. Thermal gradients created in the domain through the injection of a low viscosity fluid at a different temperature to the resident high viscosi...
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| Format: | Article |
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Elsevier
2017
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| Online Access: | https://eprints.nottingham.ac.uk/41853/ |
| _version_ | 1848796368396615680 |
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| author | Jackson, S.J. Power, H. Giddings, Donald |
| author_facet | Jackson, S.J. Power, H. Giddings, Donald |
| author_sort | Jackson, S.J. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We investigate immiscible radial displacement in a Hele-Shaw cell with a temperature dependent viscosity using two coupled high resolution numerical methods. Thermal gradients created in the domain through the injection of a low viscosity fluid at a different temperature to the resident high viscosity fluid can lead to the formation of unstable thermo-viscous fingers, which we explore in the context of immiscible flows. The transient, multi-zone heat transfer is evaluated using a newly developed auxiliary radial basis function-finite collocation (RBF-FC) method, which locally captures variation in flux and field variable over the moving interface, without the need for ghost node extrapolation. The viscosity couples the transient heat transfer to the Darcy pressure/velocity field, which is solved using a boundary element - RBF-FC method, providing an accurate and robust interface tracking scheme for the full thermo-viscous problem.
We explore the thermo-viscous problem space using systematic numerical experiments, revealing that the early stage finger growth is controlled by the pressure gradient induced by the varying temperature and mobility field. In hot injection regimes, negative temperature gradients normal to the interface act to accelerate the interface, promoting finger bifurcation and enhancing the viscous fingering instability. Correspondingly, cold injection regimes stabilise the flow compared to isothermal cases, hindering finger formation. The interfacial mobility distribution controls the late stage bifurcation mode, with non-uniformities induced by the thermal diffusivity creating alternate bifurcation modes. Further numerical experiments reveal the neutral stability of the thermal effects on the fingering evolution, with classical viscous fingering dynamics eventually dominating the evolution. We conclude the paper with a mechanistic summary of the immiscible thermo-viscous fingering regime, providing the first detailed analysis of the thermal problem in immiscible flows. |
| first_indexed | 2025-11-14T19:46:52Z |
| format | Article |
| id | nottingham-41853 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:46:52Z |
| publishDate | 2017 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-418532020-05-04T19:12:25Z https://eprints.nottingham.ac.uk/41853/ Immiscible thermo-viscous fingering in Hele-Shaw cells Jackson, S.J. Power, H. Giddings, Donald We investigate immiscible radial displacement in a Hele-Shaw cell with a temperature dependent viscosity using two coupled high resolution numerical methods. Thermal gradients created in the domain through the injection of a low viscosity fluid at a different temperature to the resident high viscosity fluid can lead to the formation of unstable thermo-viscous fingers, which we explore in the context of immiscible flows. The transient, multi-zone heat transfer is evaluated using a newly developed auxiliary radial basis function-finite collocation (RBF-FC) method, which locally captures variation in flux and field variable over the moving interface, without the need for ghost node extrapolation. The viscosity couples the transient heat transfer to the Darcy pressure/velocity field, which is solved using a boundary element - RBF-FC method, providing an accurate and robust interface tracking scheme for the full thermo-viscous problem. We explore the thermo-viscous problem space using systematic numerical experiments, revealing that the early stage finger growth is controlled by the pressure gradient induced by the varying temperature and mobility field. In hot injection regimes, negative temperature gradients normal to the interface act to accelerate the interface, promoting finger bifurcation and enhancing the viscous fingering instability. Correspondingly, cold injection regimes stabilise the flow compared to isothermal cases, hindering finger formation. The interfacial mobility distribution controls the late stage bifurcation mode, with non-uniformities induced by the thermal diffusivity creating alternate bifurcation modes. Further numerical experiments reveal the neutral stability of the thermal effects on the fingering evolution, with classical viscous fingering dynamics eventually dominating the evolution. We conclude the paper with a mechanistic summary of the immiscible thermo-viscous fingering regime, providing the first detailed analysis of the thermal problem in immiscible flows. Elsevier 2017-10-12 Article PeerReviewed Jackson, S.J., Power, H. and Giddings, Donald (2017) Immiscible thermo-viscous fingering in Hele-Shaw cells. Computers and Fluids, 156 . pp. 621-641. ISSN 1879-0747 Thermo-Viscous Fingering; Immiscible; RBF; BEM http://www.sciencedirect.com/science/article/pii/S004579301730124X doi:10.1016/j.compfluid.2017.04.004 doi:10.1016/j.compfluid.2017.04.004 |
| spellingShingle | Thermo-Viscous Fingering; Immiscible; RBF; BEM Jackson, S.J. Power, H. Giddings, Donald Immiscible thermo-viscous fingering in Hele-Shaw cells |
| title | Immiscible thermo-viscous fingering in Hele-Shaw cells |
| title_full | Immiscible thermo-viscous fingering in Hele-Shaw cells |
| title_fullStr | Immiscible thermo-viscous fingering in Hele-Shaw cells |
| title_full_unstemmed | Immiscible thermo-viscous fingering in Hele-Shaw cells |
| title_short | Immiscible thermo-viscous fingering in Hele-Shaw cells |
| title_sort | immiscible thermo-viscous fingering in hele-shaw cells |
| topic | Thermo-Viscous Fingering; Immiscible; RBF; BEM |
| url | https://eprints.nottingham.ac.uk/41853/ https://eprints.nottingham.ac.uk/41853/ https://eprints.nottingham.ac.uk/41853/ |