Packed-bed reactors are widely used in the gas, oil, and petrochemical industries, particularly for solid-catalyzed heterogeneous reactions in which the packing serves as the catalyst. Fixed-bed absorbers/desorbers are also ubiquitous within various process industries where because of physicochemical limitations traditional separation operations such as distillation, solvent extraction, crystallization, evaporation, etc. are not applicable. For detailed mathematical treatment of these systems, it is a matter of common practice to consider a bed of monodisperse spherical particles and write unsteady-state mole balances on both the flowing and the stationary phases and in compliance of the physics of the system impose various simplifying assumptions. This leads to a system of coupledevolution partial differential equations (PDEs) that must be solved by analytical/approximation/numerical methods depending on the degree of tractability of the coupled PDE's at hand. In the last decade, fabrication of inert core/core-shell/hollow spherical particles in various sizes from different materials has proved to be of intense interest. The motivations for fabrication of the aforementioned particles are their potential utilization in a wide variety of applications such as drug delivery, cosmetics, dyes and inks, acoustic insulation, in the development of piezoelectric transducers, drug encapsulation, ultrasound imaging, chromatography, catalysts, fillers, coatings, adsorptive filters, and photonic band gap materials. Hollow/inert core spherical particles may demonstrate properties that are remarkably different from those of the core particles. It is established that the structure, composition, and size of these particles can be tuned to tailor their optical, electrical, thermal, mechanical, electro-optical, magnetic, and catalytic properties. Hollow/shell particles demonstrate lower density, higher specific surface area, and particular optical properties. To the best of our knowledge, there is no experimental data regarding reactive sorption in packed beds of inert core/shell core/hollow spherical particles that can allow simultaneous consideration/integration of these processes, and mathematical modeling of such systems are scarce and is limited to the use of numerical methods and simulations. In this research, the transient behavior of reactive-diffusive fixed-bed packed with inert core/shell core/hollow/thin film coated monodisperse spherical rigid particles is investigated. We modeled the reactive desorption system with linear mass exchange law between the flowing and the stationary phases. The coupled governing partial differential equations were integrated analytically using Laplace transformations. The analytical closed form solution involves two infinite integrals. The closed form solution was integrated using an adaptive integration method and the breakthrough curves of the system were studied under the influence of the system parameters. The limiting cases are discussed, a simple error function type closed form asymptotic solution for fixed-bed desorbers with monodisperse spherical particles is obtained, and results are generalized for similar kinetics of reactive fixed-bed systems for diffusion/absorption into the inert core monodisperse sphericalpacking. Effect of mass transfer resistance is also investigated. Keywords : Packed-bed; Inert core spherical packing; Reactive-desorption; Reactive-absorption; Reactive-diffusion; effectivesurface film resistance; Reactive-diffusion, Hollow sphere
