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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

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Heuristic computational approach for nonlinear reaction-diffusion kinetics in catalytic systems.

Saad Jamshed¹, Muhammad Shoaib¹, Hijaz Ahmad^2,3,4

¹Department of Physics, AIR University, PAF Complex, E-9, Islamabad, 44000, Pakistan.

Scientific Reports

|October 29, 2025

Summary

This study introduces a hybrid genetic algorithm (GA) and collocation method to solve Lane-Emden equations in chemical engineering diffusion-reaction systems. The approach effectively models concentration profiles across various geometries and parameters.

Keywords:

Biocatalysts Catalyst Collocation method Genetic algorithm Lane-Emden equations Numerical methods

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Area of Science:

Chemical Engineering
Mathematical Modeling
Reaction Kinetics

Background:

The Lane-Emden equations are fundamental for modeling phenomena like heat and mass transfer and chemical reactions.
Understanding concentration profiles in catalyst and biocatalyst systems is crucial in chemical engineering.

Purpose of the Study:

To solve Lane-Emden equations within diffusion-reaction systems using a novel hybrid approach.
To investigate the influence of key parameters on concentration profiles in cylindrical and spherical geometries.

Main Methods:

A hybrid method combining a collocation technique with genetic algorithms (GA) was developed.
The methodology was applied to analyze diffusion-reaction systems with catalyst and biocatalyst models.
The impact of Thiele modulus (ρ), dimensionless activation energy (µ), and dimensionless heat of reaction (α) was systematically evaluated.

Main Results:

The hybrid GA-based approach successfully solved the Lane-Emden equations for diffusion-reaction systems.
Concentration profiles were effectively modeled for both catalyst and biocatalyst systems.
The method demonstrated efficacy across a wide range of parameter values (low and high ρ, µ, α).

Conclusions:

The proposed hybrid genetic algorithm approach offers a robust solution for Lane-Emden equations in chemical engineering.
This method addresses limitations of previous techniques and highlights the power of GA in complex diffusion-reaction modeling.