Geometry-induced formation and merging of multiple dead zones in diffusion-reaction problems
Abstract
This study focuses on dead-core solutions for a two-dimensional isothermal reaction-diffusion problem involving a single chemical reaction described by power-law kinetics within a bounded reactor domain. The steady-state nonlinear diffusion-reaction boundary value problem is solved numerically by applying a suitable time-stepping technique. The lumped finite element technique with piecewise linear shape functions is utilized to discretize the spatial domain. Dead zones, defined as regions inside a reactor where no reaction occurs because the reactant has been completely consumed, present a major difficulty in the design and operation of chemical reactors. The impact of the reaction exponent and the Thiele modulus on the concentration fields and on the size of such inactive regions is numerically investigated. The findings indicate that particular reactor shapes can lead to the formation of several separate dead zones.
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BibTeX
@misc{skrzypacz2026geometryinduced,
title = {{Geometry-induced formation and merging of multiple dead zones in diffusion-reaction problems}},
author = {Piotr Skrzypacz and Boris Golman and Jan Valdman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.02587},
eprint = {2606.02587},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.02587},
}
RIS
TY - UNPB
TI - Geometry-induced formation and merging of multiple dead zones in diffusion-reaction problems
AU - Piotr Skrzypacz
AU - Boris Golman
AU - Jan Valdman
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2606.02587
UR - https://arxiv.org/abs/2606.02587
AB - This study focuses on dead-core solutions for a two-dimensional isothermal reaction-diffusion problem involving a single chemical reaction described by power-law kinetics within a bounded reactor domain. The steady-state nonlinear diffusion-reaction boundary value problem is solved numerically by applying a suitable time-stepping technique. The lumped finite element technique with piecewise linear shape functions is utilized to discretize the spatial domain. Dead zones, defined as regions inside a reactor where no reaction occurs because the reactant has been completely consumed, present a major difficulty in the design and operation of chemical reactors. The impact of the reaction exponent and the Thiele modulus on the concentration fields and on the size of such inactive regions is numerically investigated. The findings indicate that particular reactor shapes can lead to the formation of several separate dead zones.
ER -