Nonstationary Diffusion to a Spherical Electrode Under Potentiostatic Conditions

2 Nonstationary Diffusion to a Spherical Electrode Under Potentiostatic Conditions 

Diffusion to a spherical electrode is of particular importance, since electrochemical experiments are often performed with an electrode consisting of mercury drops falling down from a capillary (dropping mercury electrode). In case of symmetrical spherical diffusion, the active component is transferred to the electrode surface along the lines that are tangential to the surface and end up in the center of drop. 

Assume the origin is in the center of a spherical electrode with radius vq. To simplify the problem, also assume that the radius does not change over time (i.e. the electrode is a hanging mercury drop). This case can be more easily described using a spherical coordinate system rather than the Cartesian one. The second Pick s law has the following representation in spherical coordinates  

The initial and boundary conditions have the same physical meaning as the ones previously used for nonstationary diffusion to a planar electrode. Initially (when f = 0), the concentration of oxidized form at any distance from the electrode equals its bulk value (initial condition)  

The first boundary condition under potentiostatic conditimis the electrode remains under a potential that corresponds to the limiting diffusion current density, i.e. the concentration of oxidized form on the surface (r = tq) equals zero at any moment of electrolysis (t 0)  

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