Theoretical analysis of the influence of forced and inherent temperature fluctuations in an adiabatic chromatographic column

Abstract

A linearized non-isothermal equilibrium dispersive model (EDM) of liquid chromatography is investigated to quantify unavoidable thermal effects in adiabatic chromatographic columns. The considered model contains convection-diffusion partial differential equations (PDEs) for mass and energy balances in the mobile phase coupled with an algebraic equation for adsorption isotherm. The solution process successively employ Laplace transformation and linear transformation steps to uncouple the governing set of coupled differential equations. The resulting uncoupled systems of ordinary differential equations are solved using an elementary solution technique. The solutions are very useful to understand the speeds and shapes of concentration and thermal fronts in chromatographic columns. The moment generating property of the Laplace domain solutions is utilized to derive analytical temporal moments of the concentration and temperature profiles. These moments are seen as useful to estimate unknown model parameters from measured profiles. For illustration several case studies of practical interest are provided. To evaluate the range of applicability of analytical solutions, selected results are compared with numerical results applying a high resolution finite volume scheme considering nonlinear isotherms.