Computation of dynamic adsorption with adaptive integral, finite difference, and finite element methods

• Published in: Journal of colloid and interface science 2003-02, Vol.258 (2), p.310-321
• Main Authors: Liao, Ying-Chih, Franses, Elias I., Basaran, Osman A.
• Format: Article
• Language: English
• Subjects: Adsorption; Chemistry; Computer Simulation; Diffusion; Diffusion-controlled adsorption; Dynamic adsorption; Exact sciences and technology; Finite difference method; Finite element method; Gas-liquid interface and liquid-liquid interface; General and physical chemistry; Integral method; Models, Theoretical; Numerical solutions; Surface physical chemistry; Surface Tension; Surface-Active Agents - chemistry
• ISSN: 0021-9797; 1095-7103
• DOI: 10.1016/S0021-9797(02)00096-6

Analysis of diffusion-controlled adsorption and surface tension in one-dimensional planar coordinates with a finite diffusion length and a nonlinear isotherm, such as the Langmuir or Frumkin isotherm, requires numerical solution of the governing equations. This paper presents three numerical methods for solving this problem. First, the often-used integral (I) method with the trapezoidal rule approximation is improved by implementing a technique for error estimation and choosing time-step sizes adaptively. Next, an improved finite difference (FD) method and a new finite element (FE) method are developed. Both methods incorporate (a) an algorithm for generating spatially stretched grids and (b) a predictor–corrector method with adaptive time integration. The analytical solution of the problem for a linear dynamic isotherm (Henry isotherm) is used to validate the numerical solutions. Solutions for the Langmuir and Frumkin isotherms obtained using the I, FD, and FE methods are compared with regard to accuracy and efficiency. The results show that to attain the same accuracy, the FE method is the most efficient of the three methods used.