Comparison Between Solutions of Solid Diffusion Equation in a Spherical Adsorbent Particle
Hongxia Xi · Journal of South China University of Technology · 2000
This paper discusses different boundary conditions(B.C.) in which the different solutions of solid diffusion equation are deduced, makes the comparison between the analytical solution and the numerical solution deduced respectively under these B.C., and then evaluates some other approximations for adsorption rate. Result shows that the some B.C. used previously to deduce the analytical solution is unreasonable or physically ambiguous. The reasonable boundary condition(B.C.) for the diffusion in the spherical particle should be that the concentration gradient at the particle central is equal to zero. The numerical method of the solid diffusion equation corresponding to this B.C. is suggested. The concentration profiles and the volume_average adsorbed amounts q-(t) are calculated respectively by using the numerical and analytical solutions, and then LDF model and a quadratic driving force model are evaluated on the basis of the q-(t) calculated by the numerical solution. The results indicate that there exits slight difference between the q-(t) calculated separately from the numerical and analytical solutions in the initial period of the adsorption, and that, in the initial period of the adsorption, the relative error of the LDF model is up to 95%, and that of the quadratic driving force model is about 29%. By taking ±10% error as the limit of the validity of the approximations, the LDF model is valid at τ＞0 05, and the quadratic driving force model is valid at τ＞0.0007.