Dead‑core formation in catalytic reaction and diffusion processes with generalized diffusion flux
Piotr Skrzypacz
(Department of Mathematics, School of Sciences and Humanities, Nazarbayev University)
Bek Kabduali, Alua Kadyrbek, Sławomir Szafert, Vsevolod Andreev, Boris Golman
Dead-core and non-dead-core solutions to the nonlinear diffusion-reaction equation based on the generalized diffusion flux with gradient-dependent diffusivity and the power-law reaction kinetics in catalyst slabs are established. The formation of dead zones, i.e., zones with vanishing reactant concentration, is characterized by the critical Thiele modulus that is derived as a function of reaction order and diffusion exponent in the generalized diffusion flux. The effects of reaction order and diffusion exponent on the reactant concentration distribution in the slab and dead-zone length are analyzed. It is particularly demonstrated that by contrast to the model based on the standard Fickian diffusion, dead-zone can exist in the case of first-order reactions. Also, the relationship between critical Thiele moduli for models based on the generalized and standard Fickian diffusion fluxes is established.