Study of the simple wave effect in nonlinear preparative high performance liquid chromatography : the Hodograph method

The simple wave effect in preparative High Performance Liquid Chromatography with binary mixtures has been investigated both theoretically and experimentally. The Equilibrium Diffusive, Nonequilibrium Diffusive, and ideal model equations were solved using both finite difference and Orthogonal Collocation on Finite Element (OGEE) method. The numerical solution of different model equations with the OCFE method agrees with the analytical solution in the case of the calculation of the Shock layer thickness, while the solution of the finite difference methods agrees with the analytical solution only in certain case. The non-equilibrium diffusive model gives more realistic description of the dependence of the shock layer thickness on the flow rate than other models do. The shock layer and Hodograph Transform have been applied to the study of the elution profiles in the case of concentration and volume overload. It is found that the Hodograph Plot (Hodogram) is largely independent of the non-ideality of the chromatographic system when the column is overloaded with a volume several times larger than the dead volume of the column. It is proven that the ideal solution of the Hodogram agrees with all the numerical solutions of the non-ideal models with variable efficiency. The theoretical findings on hodograph plot have been applied to binary competitive isotherm measurement and the prediction of the total separation of binary displacement chromatography successively. The comparison of Hodograph Plot and Frontal Analysis has been conducted both theoretically and experimentally. Excellent agreement between theory and experiment results have been obtained with the hodograph plot method for the isotherm measurement, while reasonable agreement between theory and experiment results was obtained with the frontal analysis method. The Hodograph Plot method can be automated with ordinary chromatographs, and consumes less sample solution than the Frontal Analysis method.