Non-advective rate of curved step advance on smooth crystal face under steady-state conditions

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For low to moderate supersaturations, crystals grow by lateral build-up of new layers. The edges of the layers are known as "steps". We consider the rate of step advance on a flat crystal face under the influence of bulk diffusion in the complete absence of advection, assuming a steady-state. In such circumstances, the step velocity tends asymptotically to zero as the radius of curvature increases. This counters the Gibbs-Thomson effect according to which the rate of step advance should asymptotically increase ceteris paribus with increasing radius of curvature. Because of these competing effects, the rate of step advance is expected to be non-monotonous in the radius of curvature.