Dispersion-convolution model for simulating peaks in a flow injection system

Abstract

A dispersion-convolution model is proposed for simulating peak shapes in a single-line flow injection system. It is based on the assumption that an injected sample plug is expanded due to a “bulk” dispersion mechanism along the length coordinate, and that after traveling over a distance or a period of time, the sample zone will develop into a Gaussian-like distribution. This spatial pattern is further transformed to a temporal coordinate by a convolution process, and finally a temporal peak image is generated. The feasibility of the proposed model has been examined by experiments with various coil lengths, sample sizes and pumping rates. An empirical dispersion coefficient ( D*) can be estimated by using the observed peak position, height and area ( t p * , h* and A t * ) from a recorder. An empirical temporal shift ( Φ*) can be further approximated by Φ* = D* /u 2, which becomes an important parameter in the restoration of experimental peaks. Also, the dispersion coefficient can be expressed as a second-order polynomial function of the pumping rate Q, for which D*( Q) = δ 0 + δ 1 Q + δ 2 Q 2. The optimal dispersion occurs at a pumping rate of Q opt = δ 0 / δ 2 . This explains the interesting “Nike-swoosh” relationship between the peak height and pumping rate. The excellent coherence of theoretical and experimental peak shapes confirms that the temporal distortion effect is the dominating reason to explain the peak asymmetry in flow injection analysis.