Damkoehler number diffusion

Figure 8 Analysis of the appropriate characteristic dimensions for specific heat transfer surface requirements in a chemical reactor exhibiting typical reaction rates. Da = Damkoehler number, NTU = number of thermal transfer units, Nu = Nusselt number, a = thermal diffusivity. (From Ref. 9.)... 

Figure 4.36. Graphical representation of the concept of effectiveness factors (a) The effectiveness factor of reaction, rj, as a function of the Damkoehler number of the second kind, Dan, or of the Thiele modulus, (j) (cf. Equ. 4.74). (b) The effective reaction rate, r ff, as a function of the diameter of the particle, d. Part (b) can be used to obtain the value of for a given average diameter, of a population of floes with a distribution d. The range of validity of kinetic control (r js) and of diffusion control (Wfds) is indicated in part a.

At any depth z of a soil layer, there is competition between reaction processes and dispersion/diffusion and advection processes. The ratio of these competing processes is expressed by the Damkoehler number which is the ratio of the rate of loss by chemical transformation to the rate of loss by diffusion/dispersion and advection (Cowan et al., 1995) and is defined as... 

When the Damkoehler number is 1, rates of transformation losses and diffusion/ advection transport are equal. This happens when z is the characteristic depth or the average depth of penetration for chemical molecules moving into a soil layer from its surface (Cowan et al., 1995). When Ada is 1, Equation 8.5 can be rearranged to find the z corresponding to the characteristic penetration depth, a parameter we label z. ... 

---