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Journal of Applied Mechanics and Technical Physics

2014 year, number 5

A Method of Rectifying Current at Microscales

E. A. Demekhin1,2, M. G. Baryshev1, G. S. Ganchenko1, E. V. Gorbacheva1
1Kuban' State University, Krasnodar, 350040 Russia
2Lomonosov Moscow State University, Moscow, 117192 Russia
Keywords: nano– and microflows, Nernst—Planck—Poisson equations, concentration polarization, electrolyte, ionic double layer, nano– and microdiodes, quasispectral Galerkin method, τ-variant of the Galerkin method, stiff systems, Gear method

Abstract

A method for rectifying electric current in micro and nanoscale devices is proposed based on the asymmetric concentration of polarization in an electrolyte solution in the case where the current in a microdiode successively passes through two mutually undissolvable fluids with different dielectric constants and diffusion coefficients in tubes with different dimensions. It is assumed that both fluids contain the ions of a completely dissociated substance which provide electric charge transfer upon application of a potential difference to the walls of the device, and the interface between the two fluids has a charge. The process is described by a one–dimensional nonstationary Nernst—PlanckPoisson system. The boundary conditions on the electrodes are the impermeability condition for anions and the Arrhenius equation which defines the flow of cations. The system of equations was solved numerically: the unknowns were decomposed into a complete system of orthogonal functions of the spatial variable, and the resulting dynamical system for the Galerkin coefficients was integrated over time by the Gear method because of its stiffness. The parameters of the system that have the most significant effect on the degree of rectification are determined, and their optimum values are evaluated.