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Hydrodynamics of fingering instability in the presence of a magnetic field
Mostaghimi, P ; Sharif University of Technology
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- Type of Document: Article
- DOI: 10.1088/0169-5983/48/5/055504
- Publisher: Institute of Physics Publishing
- Abstract:
- The hydrodynamics of two immiscible fluids in a rectangular Hele-Shaw cell under the influence of a magnetic field is studied, both theoretically and numerically. A linear stability analysis is conducted to determine the effect of magnetic fields on the formation of viscous fingers. As a result, an analytical solution is found to calculate the growth rate of perturbations. For numerical simulation of the two-phase flow, the interfacial tension is treated as a body force using the continuum surface force model and the interface tracking is performed by the volume of fluid method. The variations of the width and growth rate of fingers in an unstable displacement versus Hartmann number, a dimensionless number characterizing the strength of the applied magnetic field, are investigated. By varying the value of Hartmann number systematically, a suppressing effect on the formation of viscous fingers is observed. Consequently, it is detected that there exists a minimum Hartmann number preventing the formation of viscous fingers and ensuring a stable displacement. Our numerical simulations are in agreement with the results of the linear stability analysis and quantify the effect of magnetic fields in mitigating viscous fingering effects and improving the efficiency of the fluid displacement
- Keywords:
- Hartmann number ; Hele-Shaw cell ; Linear stability analysis ; viscous fingering ; volume of fluid (VOF) ; Computational fluid dynamics ; Fluid dynamics ; Hydrodynamics ; Magnetic fields ; Magnetism ; Numbering systems ; Numerical methods ; Numerical models ; Stability ; Two phase flow ; Applied magnetic fields ; Continuum surface force models ; Effect of magnetic field ; Fingering instabilities ; Hartmann numbers ; Hele-Shaw cells ; Viscous fingering ; Volume of fluids ; Linear stability analysis
- Source: Fluid Dynamics Research ; Volume 48, Issue 5 , 2016 ; 01695983 (ISSN)
- URL: http://iopscience.iop.org/article/10.1088/0169-5983/48/5/055504