Chemical Reaction Engineering: Thiele modulus and its significance

Thiele modulus shows the effect of diffusion in the reaction kinetics. The Thiele modulus is given by mL = L(k/D)^0.5 The ratio of rate constant to diffusivity. The large vale of Thiele modulus represents small value of diffusivity i.e. diffusion resistance affects the overall rate of reaction. If mL<0.4, the diffusion resistance can be ignored. By calculating Thiele modulus, we can see the effect of diffusion resistance. If diffusion resistance is significant for a particular catalyst, we can decrease the resistance either by increasing the diffusivity i.e. increasing the temperature and decreasing the pressure, or by reducing the length of diffusion i.e. size the catalyst particles. Shorter the particles, lesser will be the length for diffusion and lesser will be the resistance.