Journal of Magnetism and Magnetic Materials 65 (1987) 343-346 North-Holland, Amsterdam 343 zyxwvutsr FREE CONVECTION IN AN ISOTHERMIC MAGNETIC FLUID CAUSED BY MAGNETOPHORETIC TRANSPORT OF PARTICLES IN THE PRESENCE OF A NON-UNIFORM MAGNETIC FIELD zyxwvutsrqponmlkjihgfedcbaZYXWVU E. BLUMS Institute zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA of Physics, Latvian SSR Academy of Sciences, 229021 Riga, Salaspils, Latvian SSR, USSR If in a magnetic fluid, the temperature is not uniform there arises thermomagnetic convection due to the magnetization dependence on temperature. Non-uniform magnetization can also arise due to magnetodiffusion of colloidal particles. This non-uniformity is large enough to produce specific magnetic convection even under isothermic conditions. 1. Intmduction As known [l], the condition for the non- threshold convection without the account of barodiffusion in a magnetic field may be written as vpxg+p,,vMx vH+O. (1) Non-uniformity of the density p and magnetiza- tion zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA M is usually assumed to occur under non-iso- thermic conditions only, when vM = (iflM /aT)oT. But M is also a function of the magnetic particle concentration nk. In a non-uni- form magnetic field, there might arise a non-uni- form distribution of particle concentration, which can bring about magnetic convection. The latter is, in many ways, analogous to free convection arising at gravitational stratification of particles due to barodiffusion. In this case, the condition (1) in the absence of gravitation can be repre- sented as /~,,~vn~xvHtO. k (2) 2. Theoretical analysis Let us consider the specific features of mag- neto-diffusional convection with a plane boundary layer serving as an example. For the sake of simplicity, let us assume the gravitational sedi- mentation of particles and gravitational convec- tion to be negligibly small. In such a case, the equations for convection in a suspension of Brownian particles may be expressed as: $ = - vp + pvdu + /.@ZvH, (3) zyxwvuts dnk - =DAn,- zyxwvutsrqponmlkjihgfedcbaZYXWVUT Dmk dt -$%M, div(n,VH), (4) where D = kT/6rrpa is the Brownian diffusion coefficient, Mk the saturation magnetization of the particles material, mk the mass of magnetic particles, nk = (3cp/4a)a3 is their concentration determined by the volumetric fraction of the mag- netic phase ‘p and the particleradius a. Since the magnetic force in the Navier-Stokes equation (3) and the force of the magnetophoretic transport of the particles in the diffusion equation (4) depend on the same vectormultiplier MvH, the condition (2) is satisfied only in the case when solid boundaries, between which the magnetic fluid is contained, are not orthogonal to vector MvH. By introducing scale transformations x’ = x/L, y’. = (y/LyV ( vL/v)SCR,~/ ’ u’ = (uL/v)SCR,“~, u’ = eqs. (3) and (4) in the linear Bous- sinesq approximation for a plane stationary boundary layer at MvH = const take the follow- ing non-dimensional form (dashes are omitted 0304~8853/ 87/ $03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)