Indications of Segmental Flow in Straight Pipes by Flow Injection with Spectrophotometric Detection

Abstract

A procedure of spectrophotometric analysis of fluid flow in pipes is described and its performance is tested on three different dye compounds. The procedure follows measurement and mathematical de-convolution of the signal with an exponential function that is associated with molecular diffusion. Evidence is provided for the presence of segmental flow and the three dye compounds, used as tracer molecules, indicate that the solute molecules gain velocity, predominantly in the streamwise direction, from the solvent flow rate. The additional velocity, as gained from the solvent flow rate, depends on a kinetic-diffusion constant and the internal friction of the system. The model allows a calculation of the flow-injection signal and serves as a tool for the investigation of properties of fluid dynamics.

Signal convolution indicates chromatographic pulse flow and open-end flow

“…The optimum conditions of peak shape with respect to chromatographic separation are described by the Van Deemter equation [23], which is widely used for purposes of optimization [35]. Very large injection volumes produce long segments when injected into narrow pipes, and the resulting 'square distribution' of the concentration of solute molecules is pulse-like [11,25,36] rather than Gaussian shaped [11,37]. The chromatographic peak is observed not as a square signal, but as a signal that is smoothed by the response function of the detector, extra-column band broadening [38,39] and column-only band broadening [40].…”

Evaluation of the van Deemter equation in terms of open‐ended flow to chromatography

“…Similarly, upon the interaction beginning again, the signal rises again proportionally to (1 − exp[β ⋅ ]). In the following analysis, it is assumed that these two events occur simultaneously, which leads to the characteristic response function, R(t), of the system, as described previously [26,35,38].…”

“…Most frequently, deconvolution in chromatography refers to a decomposition of the signal into linear combinations of Gaussian functions [39]; however, the present investigation employs a different type of deconvolution, referred to as "response deconvolution" [26,35]. Accordingly, a response convolution is a mathematical convolution of a proposed theory by means of a response function [26,35,38] or another function that is time dependent. To simplify the calculations and obtain algebraic formulae, this latter approach is chosen.…”

“…To simplify the calculations and obtain algebraic formulae, this latter approach is chosen. Further, to perform investigations in the present work, the simplest case of the flow profile was considered: the flow-concentration profile of a pulse flow [22,26,38]. In this flow regime, the front of the injected pulse reaches the detector at time t 0 and exits the detector compartment at time t 1 .…”