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August 16, 2026SIAM Journal on Applied Mathematics

Analysis of Traveling-Wave Equations in Sorption Processes

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Authors

MAMaría AguarelesJAJoan Anglada-LloverasEBEsther Barrabés

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Overview

Mathematical analysis demonstrates robust traveling-wave front formation in adsorption filter columns, indicating reliable contaminant saturation profiling even under moderate dispersion.

Key Points

  • To model the spatiotemporal evolution of contaminant concentration and adsorption along a filter column using a reduced traveling-wave formulation.
  • Formulated a system of partial differential equations and applied a traveling-wave reduction to obtain a second-order ordinary differential equation governed by the inverse Péclet number.
  • Treated the leading-order approximation as a slow-fast system and proved the persistence of the heteroclinic connection via analytical continuation.
  • Validated the analytical results through numerical simulations and evaluated model robustness across varying inverse Péclet values using sensitivity analysis.
  • Proved the rigorous persistence of a heteroclinic connection representing a sharp traveling transition from a clean downstream adsorbent to upstream complete saturation.
  • Demonstrated that the reduced leading-order traveling-wave approximation remains remarkably robust and accurate for moderate values of the inverse Péclet number.

Cite This Study

Aguareles et al. (2026) studied this question.

synapsesocial.com/papers/6a8179bcf2fb91fc834ad083https://doi.org/10.1137/25m1768163
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