Numerical investigation of optically induced microconvection in thin ferrofluid layers D. Zablotsky n , E. Blums Institute of Physics, Latvian University, Miera str. 32, Salaspils-1 LV-2169, Latvia article info Available online 18 November 2010 Keywords: Ferrofluid Microconvection Forced Rayleigh scattering abstract We consider a periodic concentration grating induced in a thin layer of ferrofluid by an optical grating of interfering laser beams under the action of an externally applied uniform magnetic field. The direction of the applied field is parallel to the concentration gradient. Under certain conditions microconvective instability may develop during relaxation of the grating, driven by the internal demagnetizing field due to the nonhomogenous distribution of concentration. A series of numerical simulations has been performed to determine the role of microconvection in the dissipation of the concentration grating. & 2010 Elsevier B.V. All rights reserved. 1. Introduction The microeffects concerning transfer of heat and colloidal particles attract scientific attention due to their cooperative nature. Ferrofluids are colloidal suspensions of magnetic nanoparticles and as such they possess superparamagnetic properties and an addi- tional control parameter—the magnetic field. Measurements of diffraction signal from the optically induced nanoparticle micro- structures (forced Rayleigh scattering) and direct visualization of these structures by holographic methods point to a strong influ- ence of the applied magnetic field [1]. Both chaotic and regular oscillations of the periodic structures have been observed in the experiments. It was hypothesized that these effects can be explained by the presence of microconvection driven by internal demagnetizing field due to nonuniform distribution of concentra- tion but no definite conclusion can be drawn. We will consider a periodic concentration grating induced in a thin layer of ferrofluid by interfering laser beams under the action of an externally applied uniform magnetic field. As soon as the optical grating is focused within the layer, the ferrofluid is locally heated and the corre- sponding concentration grating starts to develop due to the strong Soret effect characteristic for colloidal solutions. When diffusion and thermodiffusion reach equilibrium, the beams are switched off and the temperature nonhomogeneities immediately relax. Relaxation of concentration grating takes greater time due to the vastly different timescales. The stability analysis [2,3] suggests that the microconvective instability may develop at this stage causing enhanced mixing and significant increase in the measured effective diffusion coefficient. 2. Theory In the mathematical description of the process the layer is considered to be two-dimensional except for the temperature equation, where a conductive flux is applied in the transverse direction in order to remove the heat generated by the absorption of light. The direction of the applied magnetic field H 0 is parallel to the concentration gradient. The ferrofluid is viewed as a nonreacting binary mixture. In general, both components of the mixture need to be treated separately; however, at low concentrations of solid phase the mixture may be described as a whole, with a single velocity field u m . The equations of motion for the mixture may be derived from continuity and momentum equations for each phase and by introducing Kelvin’s force to describe the action of the magnetic field [4] rUu m ¼ r p r s r p r s rUj c ð1Þ r m @c @t þ u m Urc   ¼rUj c ð2Þ r m @u m @t þðu m UrÞu m   ¼rP m þ ZDu m þ m 0 ðMUrÞHrU j c  U sp   ð3Þ where r i is the density of the respective constituent and c is the particle concentration. The subscripts p , s , m refer to the particles, solvent and mixture, respectively, and the subscript 0 refers to the reference values. U sp refers to the velocity of the particles relative to the solvent. The phase densities are considered constant. The slip-flux of the ferroparticle concentration j c consists of regular diffusion, thermodiffusion (Soret effect) and a drift term Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jmmm Journal of Magnetism and Magnetic Materials 0304-8853/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2010.11.042 n Corresponding author. Tel.: + 371 67944664; fax: + 371 67901214. E-mail address: dmitrijs.zablockis@gmail.com (D. Zablotsky). Journal of Magnetism and Magnetic Materials 323 (2011) 1338–1342