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Hydrodynamic instabilities of miscible and immiscible magnetic fluids in a Hele-Shaw cell

Abstract : The dissertation treats analytically and numerically the instabilities exhibited by magnetic fluids in a Hele-Shaw cell under a uniform magnetic field. Considered are both two immiscible magnetic fluids whose interface is a well-defined planar curve and a single fluid with an inhomogeneous gap-averaged concentration of magnetic particles (or a diffused interface between miscible ferrofluids). The inhomogeneous demagnetizing field of a ferrofluid sample excites a two-dimensional convection or modifies the existing flow. In the first part, we undertake a detailed linear stability analysis in the miscible case for selected concentration distributions along the cell. The results apply also to the periodical grating induced in the forced Rayleigh scattering experiments. We demonstrate that the Brinkman equation better describes the viscous dissipation in a Hele-Shaw flow than the conventional Darcy law. We find that viscosity, and not diffusion, renders the length scale of the flow comparable to the cell thickness at strong forcing. In the second half of our study, we model the non-linear dynamics of an immiscible interface between ferrofluids by a boundary-integral method. We describe the modification of the Saffman–Taylor finger by the magnetostatic force. We also obtain "dendritic" structures close to those observed experimentally and analyze some aspects of pattern formation.
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Contributor : Maksim Igonin <>
Submitted on : Monday, December 27, 2004 - 5:06:56 PM
Last modification on : Wednesday, December 9, 2020 - 3:06:03 PM
Long-term archiving on: : Monday, September 20, 2010 - 12:08:23 PM


  • HAL Id : tel-00007716, version 2


Maksim Igonin. Hydrodynamic instabilities of miscible and immiscible magnetic fluids in a Hele-Shaw cell. Condensed Matter [cond-mat]. Université Paris-Diderot - Paris VII, 2004. English. ⟨tel-00007716v2⟩



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