Abstract
The magnitude of the current is derived for a mass transfer limited electrochemical reaction at a plane electrode in a rectangular channel under conditions of steady-state, fully developed laminar flow. An analytical solution is presented for the differential equation governing the convective diffusion, expressible in a series of exponential terms multiplied by parabolic cylinder functions. The solution contains no empirical parameters, and involves no a priori approximations, being generally valid over the entire range of diffusion layer thickness with respect to the thickness of the channel. The expression obtained for the current reconfirms a limiting flow rate exponent of 1/3 for a relatively thin diffusion layer. A comparison with earlier approaches to the problem is also presented.
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