Passivation of irregular surfaces accessed by diffusion

We investigate the process of progressive passivation of irregular surfaces accessed by diffusion. More precisely, we quantify through numerical simulations how the activity of the von Koch surface is gradually transferred from its initially active (or absorbing) regions to its less accessible regions. We show that in three dimensions, in sharp contrast with the two-dimensional case, the size of the successive active zones steadily decreases during the passivation process, even though a large quantity of alive surface remains available. As a consequence, in three dimensions, the evolution of the efficiency of a surface accessed by diffusion (i.e., by a Laplacian field) can exhibit long-tail behaviors that, unlike in two dimensions, strongly depend on its specific geometry. This fact has important implications for the design of heterogeneous catalysts under deactivation conditions, for the performance of heat exchangers subjected to passivation by “fouling,” and for changes in the behavior of the digestive system, where the activity of the absorbing intestinal membrane can be substantially affected by inflammatory disorders.