Temperature Effects on Liquid Chromatography Dynamics

Analysis of a Chromatographic Model with Irreversible and Reversible Reactions

This post briefly introduces the underlying physical process. It motivates current research work and highlights previous contributions in this field. Furthermore, it summarizes the post’s contents in different sections.

## Laplace Transformation

Pierre-Simon Laplace who was an astronomer and mathematician, while working on probability theory, introduced Laplace transformation for the first time. Since then, it has been used to derive analytical solutions to problems frequently. When the Laplace transform technique is applied to the function in the time variable.

## Introduction

The main novelty of this thesis project is the linearization of the non-isothermal equilibrium dispersive model to derive analytical expressions for mass, energy, and temporal moments considering two different sets of BCs. The model comprises of single component, axial dispersion and linearized adsorption isotherm. The Laplace transformation technique is applied as a tool to determine analytical solutions for the considered two sets of BCs. Furthermore, the first four statistical temporal moments are calculated from Laplace-transformed analytical solutions. Moment analysis has been thoroughly considered in the literature. published articles have considered isothermal models and simple boundary conditions.

In this post, we extend this analysis to non-isothermal models by deriving analytical solutions and the first four temporal moments for two types of BCs, such as Danckwerts and Dirichlet BCs. Moreover, the expression of HETP curve is derived from the first two moments of Dirichlet BCs. To verify that our analytical expressions are error-free, the analytical results are compared with the numerical results of HR-FVS. Various test problems are considered to investigate the influence of adsorption enthalpies, axial dispersion, and differences in the injected and reference temperatures on the elution curves.

## Temperature Effects on Liquid Chromatography Dynamics

In this chapter, some basic prerequisites for the non-isothermal EDM are provided. It gives some basic terminologies and concepts of the model under investigation indicating the dynamic behavior of the solute in the chromatographic column. Different case studies of practical interest are presented. Moments up to the fourth order by considering the Laplace-transformed solutions obtained.

This chapter incorporates terminology and basic concepts related to the theoretical description of the chromatographic technique. Mathematical modeling is a requisite part of the description of the chromatographic process for elaborating the dynamical behavior of the solute in the chromatographic column filled with adsorbent. Moreover, the 1D and non-isothermal equilibrium dispersive model of chromatography is presented.

## Chromatography

Chromatography is the capability to isolate solute components using separating characteristics of components to endure in a stationary phase versus a mobile phase. Once a component is isolated from the mixture of components, it can be detached and quantified.

**Solvent**: The substance that dissolves a solute to be separated.**Mobile phase:** The substance moving through the column comprises solute and solvent,

which can be liquid in LC or GC.**Eluent**: Fluid entering the column.**Eluate**: Fluid exiting the column.Chromatogram: Visual output representing detector response as a function of time.**Retention time:** time taken by a mixture component to leave the column.Mobile phase velocity: rate change of distance for the mobile phase in a chromatographic column.

## Temporal moments

Parameters can be estimated using information obtained from higher temporal moments which are derived by applying Laplace transformation.

In this work, the well-known method of statistical moments considering a single solute component for analyzing chromatographic peaks is presented, i.e. Nc = 1. These results can be used to estimate model parameters and validate numerical techniques. The following well-known expressions are applied to generate temporal moments from Laplace domain solutions.

## Temperature Effects on Liquid Chromatography Dynamics

The effects of both inlet temperature and the ratio of specific heats. It can be observed that the adsorption and desorption coupling remain the same. However, an increase in inlet temperature enhances the desorption without affecting adsorption. While the overall temperature of the column enhances adsorption with no change in desorption.