An analytical solution of the effectiveness factor of photocatalytic reactors based on Robin boundary conditions

An analytical expression of the effectiveness factor of photocatalytic reactors that accounts for external mass transfer limitations is presented. The solution is based on Robin boundary conditions introducing the Sherwood number as the parameter that accounts for the external mass transfer limitations. Regions highlighting free diffusion, diffusion limitations, and external mass transfer limitations are identified based on the Thiele Modulus and the Sherwood number. At low values of the Sherwood number, the internal diffusion and reaction rate-limiting regions are surpassed by the external mass transfer limitations. A cut-off value of the Sherwood num-ber below which external mass transfer limitations cannot be ignored is 0.55. The evaluation of the model showed that under Dirichlet boundary condition the model converges to literature models from similar studies. This 1-D model looked at the Sherwood number across a broad scope and accounted for a broader range of limitations associated with immobilized photocatalytic films.

Automated summary

This paper presents an analytical expression for the effectiveness factor of photocatalytic reactors accounting for external mass transfer limitations, using Robin boundary conditions and the Sherwood number as a parameter for these limitations. The study identifies regions of free diffusion, diffusion limitations, and external mass transfer limitations based on the Thiele modulus and Sherwood number. At low Sherwood number values, external mass transfer limitations surpass internal diffusion and reaction rate limitations. The cutoff value for the Sherwood number below which external mass transfer limitations cannot be ignored is 0.55. The model evaluation shows convergence with literature models under Dirichlet boundary conditions and considers a broader range of limitations associated with immobilized photocatalytic films.