Solution of Diffusion Dispersion Model Using Spline Collocation Method

The diffusion dispersion models are commonly used in chemical and process industries to mathematically describe the mass transport process of solid and semi-solid particles. In the present study, axial dispersion model is solved for Langmuir adsorption isotherm using spline functions. To find the solution, the model is converted into dimensionless form involving Peclet number (Pe). The axial domain (0 ≤ x ≤ 1) is partitioned into equal intervals and then spline collocation method is applied within each interval. The discretized form of model is solved using MATLAB software. The axial model is also solved for linear isotherm using spline collocation method. The results are compared with analytic solution obtained using Laplace transforms. The exit concentration profiles are drawn for various Peclet numbers ranging from 0 (perfect mixing) to ∞ (perfect displacement). The spline collocation method yields stable, accurate solution and reduces the size of computational work considerably.