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

Abstract

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 number 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.

Keywords

• Photocatalysis
• Effectiveness factor
• Robin boundary condition
• Mathematical modelling
• Sherwood number
• Thiele modulus