Analysis of a one-component sorption in a single adsorbent particle by the orthogonal collocation method IV. One-point collocation method and linear-driving-force approximation*
Pavol Rajniak · 1985
A generally acceptable mathematical model for a sorption process (Second Fick's law) is studied in this paper. Various solutions of this diffusion equation are compared. A close connection of the one-point collocation method with a linear-driving -force approximation is shown. An attempt has been made to extend the applicability of the one-point collocation method for solving the mathematical model in the first steps of the sorption process. В работе изучается общепринятая математическая модель для описания процесса сорбции (второй закон Фика). Сравниваются различные реше ния этого диффузионного уравнения. Показана близкая взаимосвязь ме тода одноточечной коллокации с приближением линейной движущей силы. Сделана попытка расширить приложимость метода одноточечной коллокации для решения математической модели на первых стадиях процесса сорбции. In the previous papers we presented an analysis of the mathematical models of a one-component sorption in a single adsorbent particle under the isothermal behaviour assumption [1] and under the nonisothermal behaviour assumption [2]. The transients of average values of dimensionless adsorbate concentration and temperature rise in the particle were solved by the orthogonal collocation method in connection with the integration technique for solving the resulting system of ordinary differential equations. It was mentioned that for the first rapid steps of the adsorption process a greater number of collocation points is needed, but further a smaller number is sufficient for the same accuracy. A one-point collocation method is reported in this paper. A close connection of the one-point collocation with a linear-driving-force (LDF) approximation is shown. It is also explained why