Abstract
Analytical solutions of transient concentration profile inside particles were calculated by solving rection-diffusion equation in spherical, cylindrical, and slab-type porous particles, assuming first order irreversible reaction. Time-dependent concentration in bulk fluid phase was assumed as exponential decay for each particle, and convective boundary conditions were taken using arbitrary Biot number to obtain a general solution by eigenfunction expansion or Laplace transform method. Factors affecting average transient concentration inside particles were studied by adjusting Biot number, reaction time, and Thiele modulus as well as the position inside particles. To predict transient bulk concentration in batch photocatalytic reactor containing porous particles, coupled differential equations were solved by Laplace transform to obtain analytical solutions of bulk concentration as well as average concentration inside porous particles as a function of reaction time. The factors affecting transient concentrations were investigated by adjusting the concentration and porosity of the catalytic particles, morphology of the particles, and Thiele modulus in batch-mode reactor to study reduction speed of reactant concentration during photocatalytic reaction. The solutions from coupled differential equations were useful for the prediction of transient behavior in batch-type photocatalytic reactor and were compared with the results from CSTR containing slab-type photocatalytic particles with various space time.
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Acknowledgements
This research was supported by the Industrial Core Technology Development Program (10077545, Development of icephobic coating materials for extreme environment) funded by the Ministry of Trade, industry & Energy (MI, Korea), Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1A6A1 A03015562), and Information & communications Technology Promotion (IITP) grant funded by the Korea Government (MSIT) and Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea Government (MOITIE).
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Effect of Biot number on unsteady reaction-diffusion phenomena and analytical solutions of coupled governing equations in porous particles with various shapes
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Cho, YS., Sung, S. Effect of Biot number on unsteady reaction-diffusion phenomena and analytical solutions of coupled governing equations in porous particles with various shapes. Korean J. Chem. Eng. 37, 1836–1858 (2020). https://doi.org/10.1007/s11814-020-0625-z
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DOI: https://doi.org/10.1007/s11814-020-0625-z