Dispersion in Chromatography Columns - Dispersion Processes that take Place in an LC Column > Longitudinal Diffusion > The Diffusion Process > Page 14

Longitudinal Diffusion

If a local concentration of solute is placed at the midpoint of a tube filled with either a liquid or a gas the solute will slowly diffuse to either end of the tube. It will first produce a Gaussian distribution with a maximum concentration at the center and, finally, when the solute reaches the end of the tube, 'end' effects occur and the solute will continue to diffuse until there is a constant concentration throughout the length of the tube. The process is illustrated in Figure 5.

Figure 5. Longitudinal Diffusion

Before dispersion due to longitudinal dispersion is discussed some basic principles of diffusion need to be considered.

The Diffusion Process

Diffusion processes play important parts in peak dispersion. The process not only contributes to dispersion directly (i.e., longitudinal diffusion), but also helps to reduce the dispersion that results from solute transfer between the two phases. Consider the situation depicted in figure 6.

Figure 6. The Diffusion Process

Consider a sample of solute is introduced in plane (A), (plane (A) having unit cross-sectional area). Solute will diffuse according to Fick's law in both directions (x) and, at a point (x) from the sample point, according, the mass of solute transported across unit area in unit time (mx) according to Fick will be given by,