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http://dx.doi.org/10.9713/kcer.2019.57.5.652

Analytical Solutions of Unsteady Reaction-Diffusion Equation with Time-Dependent Boundary Conditions for Porous Particles  

Cho, Young-Sang (Department of Chemical Engineering and Biotechnology, Korea Polytechnic University)
Publication Information
Korean Chemical Engineering Research / v.57, no.5, 2019 , pp. 652-665 More about this Journal
Abstract
Analytical solutions of the reactant concentration inside porous spherical catalytic particles were obtained from unsteady reaction-diffusion equation by applying eigenfunction expansion method. Various surface concentrations as exponentially decaying or oscillating function were considered as boundary conditions to solve the unsteady partial differential equation as a function of radial distance and time. Dirac delta function was also used for the instantaneous injection of the reactant as the surface boundary condition to calculate average reactant concentration inside the particles as a function of time by Laplace transform. Besides spherical morphology, other geometries of particles, such as cylinder or slab, were considered to obtain the solution of the reaction-diffusion equation, and the results were compared with the solution in spherical coordinate. The concentration inside the particles based on calculation was compared with the bulk concentration of the reactant molecules measured by photocatalytic decomposition as a function of time.
Keywords
Porous particles; Reaction diffusion equation; Eigenfunction expansion; Laplace transform; Time-dependent boundary conditions;
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Times Cited By KSCI : 1  (Citation Analysis)
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