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Computation of dynamic adsorption with adaptive integral, finite difference, and finite element methods
Ying-Chih Liao1, Elias I Franses, Osman A Basaran
1School of Chemical Engineering, Purdue University, West Lafayette, IN 47907-1283, USA.
Journal of Colloid and Interface Science
|March 6, 2003
Summary
This study compares three numerical methods for analyzing diffusion and adsorption with nonlinear isotherms. The finite element (FE) method demonstrated superior efficiency and accuracy compared to integral (I) and finite difference (FD) methods.
Area of Science:
- Physical Chemistry
- Computational Science
Background:
- Diffusion-controlled adsorption and surface tension analysis with nonlinear isotherms necessitate complex numerical solutions.
- Existing numerical methods may lack efficiency or accuracy for these challenging problems.
Purpose of the Study:
- To develop and compare three numerical methods for solving diffusion-controlled adsorption problems with nonlinear isotherms.
- To evaluate the accuracy and efficiency of integral (I), finite difference (FD), and finite element (FE) methods.
Main Methods:
- Improved integral (I) method with adaptive time-stepping and error estimation.
- Developed finite difference (FD) and finite element (FE) methods incorporating grid stretching and predictor-corrector techniques.
- Validation using analytical solutions for the Henry isotherm.
Main Results:
- The finite element (FE) method proved to be the most efficient for achieving a given accuracy.
- All three methods provided comparable solutions for Langmuir and Frumkin isotherms.
- Adaptive time integration and grid generation enhanced the performance of FD and FE methods.
Conclusions:
- The finite element (FE) method is recommended for its superior efficiency in simulating diffusion-controlled adsorption with nonlinear isotherms.
- The developed numerical techniques offer robust solutions for complex surface phenomena.