The 15 th Riga and 6 th PAMIR Conference on Fundamentaland Applied MHD Magnetoelectrolysis THE EFFECT OF UNIFORM MAGNETIC FIELD ON THE STABILITY OF RAYLEIGH–BENARD CONVECTION IN THE ELECTROCHEMICAL SYSTEM D.A. Bograchev 1 , V.M. Volgin 2 , A.D. Davydov 1 1 Frumkin Istitute of Electrochemistry, Russian Academy of Sciences, 31 Leninskii pr., Moscow, 119071 Russia (bograchev@gmail.com) 2 Chair of Physicochemical Processes and Technology, Tula State University, 92 pr. Lenina, Tula, 300600 Russia Introduction. When a current is passed through a stagnant solution be- tween two horizontal electrodes, two states of the system can be observed: (1) The solution remains stagnant in spite of the variation in its density ρ near the electrodes. The buoyancy forces are balanced by the viscosity forces. (2) The buoyancy force initiates convective instability, the initially stagnant solution starts to flow: a solution with a higher density, which forms near the upper electrode, flows downward, and a solution with a lower density, which forms near the lower electrode, flows upward. For the limiting-current mode, to the approximation of solution electroneutrality, the problem of Rayleigh-Benard instability for a binary electrolyte is equivalent to the problem of heat convection that has been much studied [1, 2, 3, 4, 5]. In this case, only a monotonic convective instability can arise [6]. In a solution with a more complex composition, an oscillatory instabil- ity can arise along with the monotonic one. Several works were devoted to the study of monotonic and oscillatory instabilities in electrochemical systems with three types of ions [7, 8]. In these works, approximate solutions of the problem for the cathodic deposition (anodic dissolution) of metal were obtained. Systems with redox reactions were not considered in the literature. Moreover, the Rayleigh numbers, which were used in these studies, differ from the commonly accepted values. The problem of Rayleigh-Benard for heat convection in the magnetic field was studied by Chandrasekhar [1]. In this work, we will theoretically analyze the conditions of the onset of monotonic and oscillatory free-convective instabilities in the solution with three types of ions with concentrations c 1 , c 2 , and c 3 , diffusion coefficients D 1 , D 2 and D 3 , and charges z 1 , z 2 and z 3 , which is placed in the space between two plane horizontal electrodes, taking into account the migration transfer of a supporting electrolyte. The effect of applied magnetic field on the onset of free convective instability is discussed. 1. Mathematical model. Within the theory of dilute electrolytes, in the Boussinesq approximation, taking into account the electroneutrality of the solution, the equations of incompressible viscous liquid flow and the ionic transfer in the electrolyte layer between two horizontal electrodes can be written as follows ∂v ∂t +(v ·∇)= - 1 ρ b ∇p + ν ∆v + 1 ρ b i × b + g ρ b (ρ - ρ b ) , div(v)=0 , ∂c1 ∂t = D1∆c1 - v∇c1 , ∂c2 ∂t = D2∆c2 + ∇  Fz2D2c2 RT ∇ϕ  - v∇c2 , ∂c3 ∂t = D3∆c3 + ∇  Fz3D3c3 RT ∇ϕ  - v∇c3 , z1c1 + z2c2 + z3c3 =0, (1) where b is the magnetic flux density vector, g is the gravity acceleration vector. In the set of equations (1), the migration term in the transfer equation for electroactive component (c 1 ) is omitted; this is allowed at a high concentration of the supporting electrolyte, i.e., at c 2b ≫ c 1b . http://www.ipul.lv/pamir/ 123