The Thiele modulus is a dimensionless number that quantifies the relative importance of reaction rate to diffusion rate in a porous catalyst. It is defined as:
\[ \phi = \frac{L}{\sqrt{D/k}} \]
where \( L \) is the characteristic length (e.g., particle radius), \( D \) is the effective diffusivity, and \( k \) is the reaction rate constant. A high Thiele modulus indicates that the process is diffusion-limited, while a low value suggests that the reaction rate controls the process.
