Theory of microscopic electrodeposition under a uniform parallel magnetic field - 1. Nonequilibrium fluctuations of magnetohydrodynamic (MHD) flow

Nonequilibrium fluctuations of concentration, velocity and so on are formulated for electrode reactions including electrodeposition under a uniform magnetic field parallel to electrode surface. In electrodeposition, nonequilibrium fluctuations occur on the both sides of the electrode surface and solution; on the electrode-surface side, three-dimensional (3D) and two-dimensional (2D) nucleation proceed under the control of symmetrical and asymmetrical nonequilibrium fluctuations, respectively. On the solution side, a characteristic laminar flow called magnetohydrodynamic (MHD) flow with microscopic convection flows called micro-MHD flows are induced, so that the fluctuations on the solution side are described as Fourier components of complex 2D plane waves traveling with the MHD flow. The fluctuations on the electrode-surface side are interfered with the micro-MHD flows, yielding characteristic 3D and 2D nuclei. In Part 1 of the present paper, the amplitudes of the micro-MHD flows and concentration fluctuation on the solution side are first established independent of the fluctuations on the electrode-surface side.