Effect of Biot number on unsteady reaction-diffusion phenomena and analytical solutions of coupled governing equations in porous particles with various shapes

Photocatalytic degradation of rhodamine-B by visible light assisted peroxymonosulfate activation using the Z-scheme MIL-100(Fe)/Bi2S3 composite: a combined experimental and theoretical approach

“…Also, the reactants are considered to have constant diffusivity inside the porous support. So, for the first order reaction with the mass transfer process, the material balance equation of the reactant in the porous shell support matrix is given by the following pore diffusion equation: 62,63 where C p ( r , t ) is the concentration of the reactant in the catalyst, r the radial distance from the core of the catalyst particle, t the treatment time, ε p the catalyst shell porosity, D e the effective pore diffusivity of the reactant inside the catalyst particle, R the radius of the catalyst particle, and k R the first order reaction rate constant, considered the same inside the particle and in the bulk reaction medium. Eqn (1) is coupled with the external bulk concentration ( C b ( t )), through the following initial and boundary conditions: C p ( r , t = 0) = 0where k f is the external mass transfer coefficient of reactants between the bulk phase and the catalyst particle surface.…”

“…Eqn (1) is coupled with the external bulk concentration ( C b ( t )), through the following initial and boundary conditions: C p ( r , t = 0) = 0where k f is the external mass transfer coefficient of reactants between the bulk phase and the catalyst particle surface. The bulk reactant concentration ( C b ( t )) varies with time as follows: 62,63 subject to C b ( t = 0) = C 0 . Here, V is the volume of the reaction medium, m p the weight of the catalyst particles, ρ p the density of the particles, C 0 the initial concentration of the reactant at the start of the reaction, and the total surface area of particle suspension in the medium.…”

“…Also, the reactants are considered to have constant diffusivity inside the porous support. So, for the first order reaction with the mass transfer process, the material balance equation of the reactant in the porous shell support matrix is given by the following pore diffusion equation: 62,63…”

“…where k f is the external mass transfer coefficient of reactants between the bulk phase and the catalyst particle surface. The bulk reactant concentration (C b (t)) varies with time as follows: 62,63…”

“…These parameters are essential for optimizing the reactor design and predicting the yield and performance of actual catalytic processes. [62][63][64][65] In this study, the variation of organic contaminant concentration inside the catalyst pores was simulated using a pore diffusion-surface reaction based model. Further, the temporal variation of bulk average concentration of the RhB dye was predicted and compared with the experimentally obtained data of RhB degradation.…”