Dynamics of Adsorption of Surfactant on A Bubble Surface in A Foam Fractionation Column

Abstract

The dynamics of adsorption of surfactant on a bubble surface in a foam fractionation column is simulated mathematically. The model for the adsorption dynamics is developed based on the Fick’s Law and verified using the Ward-Tordai equation as well as analytical solution of the diffusion equation using Laplace transformation. The adsorption isotherm is modelled using the Henry isotherm and the Langmuir isotherm. The analytical solution using the Laplace transformation confirms the numerical solution using the Henry isotherm. Manipulation of the Laplace transformation of the diffusion equation using the Henry isotherm, and solution of the rearranged equation using convolution results in theWard-Tordai equation. At high bulk concentration, it is obtained that the adsorption rate using the Langmuir isotherm is greater than the adsorption rate using the Henry isotherm. At early time, the surface concentration is proportional to square root of time, a fact which is evident from direct inspection of the Ward-Tordai equation.