Simplified approach to retention times of narrow binary pulses in the case of ideal chromatography model and Langmuir isotherm

Abstract

Analytical solution to ideal chromatography model has been established for binary Langmuir isotherm and rectangular injections. However, retention time of the less adsorbed species, which is of great theoretical and practical significance, cannot be given in a closed form and is conventionally solved by numerical integration with a floating boundary. A simplified approach is provided in this article. A 4th order algebraic equation was derived and used to solve the maximum concentration that can be further used to explicitly calculate retention time. Under most practical conditions, reliable initial guess can be easily acquired, allowing for the application of Newton-Raphson method for rapid determination of the root of the 4th order equation. In addition, derivatives of retention time with respective to isotherm parameters can be given in analytical forms.