TY - JOUR
TI - Analysis of equilibrium dispersive model of liquid chromatography considering a quadratic-type adsorption isotherm
AU - Rehman Jamil Ur
AU - Muneer Adeel
AU - Qamar Shamsul
JN - Thermal Science
PY - 2022
VL - 26
IS - 3
SP - 2069
EP - 2080
PT - Article
AB - A single-component equilibrium dispersive model of liquid chromatography is solved analytically for a quadratic-type adsorption isotherm. The consideration of quadratic isotherm leads to a non-linear advection-diffusion PDE that hinders the derivation of analytical solution. To over come this difficulty, the Hopf-Cole and exponential transformation techniques are applied one after another to convert the given advection-diffusion PDE to a second order linear diffusion equation. These transformations are applied under the assumption of small non-linearity, or small volumes of injected concentrations, or both. Afterwards, the Fourier transform technique is applied to obtain the analytical solution of the resulting linear diffusion equation. For detailed analysis of the process, numerical temporal moments are obtained from the actual time domain solution. These moments are useful to observe the effects of transport parameters on the shape, height and spreading of the elution peak. A second-order accurate, high resolution semi-discrete finite volume scheme is also utilized to approximate the same model for non-linear Langmuir isotherms. Analytical and numerical results are compared for different case studies to gain knowledge about the ranges of kinetic parameters for which our analytical results are applicable. The effects of various parameters on the mechanism are analyzed under typical operating conditions available in the liquid chromatography literature.