On the microconvective instability of an inhomogeneous magnetic fluid in a Hele--Shaw cell

M. Igonin^1,2

¹ Institute of Physics, University of Latvia, Salaspils-1, LV-2169 Latvia }
² UFR de Physique, Université Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France

Abstract
A convective instability of an inhomogeneous isothermal magnetic fluid in a Hele--Shaw cell is considered theoretically. A uniform external magnetic field is assumed parallel to the gradient of the gap-averaged concentration of magnetic nanoparticles. The non-potential driving force of the instability is due to the self-magnetic (demagnetizing) field of the ferrofluid. The linear stability of the quiescent state is explored for various concentration distributions along the cell. For the smoothed step-like and Gaussian distributions, we assume that the flow is governed by the Brinkman (Darcy--Stokes) law and determine the neutral curves by numerical stability analysis. For the periodic array of sharp parallel stripes the neutral curves and the threshold conditions for the onset of microconvection are obtained analytically. We discuss the relevance of the obtained results for the interpretation of the forced Rayleigh scattering experiments with transient concentration gratings in magnetic colloids. Figs 8, Refs 17.