Diffusion-controlled reaction on an elliptic site.
The exact analytical solution for the concentration profile of a diffusion-controlled reaction at an elliptic site is presented. The resulting site reaction rate includes a factor of pi, the "diameter" of the major axis, the external reactant concentration, and the diffusion coefficient, divided by the complete elliptic integral of the first kind with an eccentricity squared argument. This rate reduces with zero eccentricity to the simple well-known form for diffusion control at a circular site. A comparison of these two rates for fixed site area permits a study of site shape on diffusion-controlled reaction rates. The reaction rate enhancement from the circular site case, which always occurs for noncircular site shapes, is discussed in the context of important site reactions in chemical physics and biophysics.
Strieder
William
W
D004058:Diffusion; D007700:Kinetics; D008956:Models, Chemical