Eddy diffusion term

Figure 5.6 Van Deemter curves relating H to linear flow velocity. A, eddy diffusion term ...

The eddy diffusion term, o, describes the change in pathway and velocity of solute molecules in reference to the zone center. If the molecules are in a "fast" channel they can migrate ahead of the zone center, if in a "slow" channel they can lag behind the zone center. To quantify the eddy diffusion term, we must describe the step length and the number of steps taken in a specified period of time. The void or channel between particles would be expected to be in the order of one particle diameter, d. As molecules move from one channel to another, their velocity will be of the order of +d or -d (in respect to the zone center). So on the average, the molecules will take an equivalent step of d. 

A is an eddy diffusion term to account for the various pathways in packed columns which lead to peak spreading V is the tortuosity factor which often has a value close to unity u is the linear velocity of the carrier gas terms Cg and account for radial diffusion in the gas phase and the liquid phase respectively. We have found experimentally on packed columns that the Cg term is negligible (6J. The expression for the C- term may be written as... 

Giddings main criticism of the van Deemter equation was that a finite contribution to the peak broadening by the Eddy diffusion term is predicted even for zero flow velocity. However, at the flow velocities encountered in practical applications, the equation proposed by Giddings reduces to the van Deemter equation, since all other terms remain the same. 

As we will see in Chapter 20, capillary columns are the most widely used in gas chromatography because of their high efficiency due to large numbers of plates. These columns have no packing, and so the eddy diffusion term in the van Deempter equation disappears. For open tubular columns, the modification of the van Deempter equation, called the Golay equation, applies ... 

This is known as the Huber equation. Here, u is the mobile-phase linear velocity. The constant C, is the mobile-phase mass transfer term and Cj the stationary-phase term. The B (longitudinal diffusion) term, except at very low mobile-phase velocities, is nearly zero and can be neglected. It is a function of the mobile-phase viscosity and the analyte molecule. The A (eddy diffusion) term turns out to be small compared with diffusion in the liquid phases and almost a constant value and is, therefore, usually neglected. So, H is estimated as ... 

A eddy diffusion term of Eq. (5-2) for bed HETP versus carrier gas velocity... 

In Equation 5.10, it is assumed that the contributions of all individual terms are independent of flow profile except for the //eddy.diff and //t.diff terms. Because of the plug-like flow velocity profile, the contribution of transchannel diffusion is much smaller in an EOF-driven system (Figure 5.6). The contribution of transchannel diffusion to the total HETP in a packed column is very small owing to the small channel diameter approximately one-sixth of the particle diameter. Flow velocity in the channels between particles determines the magnitude of the eddy diffusion term contribution. In... 

The eddy diffusion term. A, describes the effect of peak broadening caused by the presence of particles in the column. It exists only for packed columns. Because of the particles, the molecules travel different paths thus their elution is carried out at different times, as illustrated in Figure 8.8. It depends on the particle diameter, sphericity, and how the column is packed. Eddy diffusion is independent of the gas velocity vector, HETP = A. The initial peak as it enters the column is narrow and taller. As it exits the column the peak becomes much broader and the height decreases. 

The number of theoretical plates is proportional to the column length and inversely proportional to the particle size. The advantage of using small particles is that they distribute flow more uniformly and, as a result, reduce the eddy diffusion, term A in the Van Deemter equation. However, the smaller particles increase the diffusional resistance of the solvent as well as the pressure drop (for a given flow rate). Choosing the flow rate is a critical parameter in developing an HPLC method. Low flow rates allow the analyte sufficient time to interact with the stationary phase and will affect both the B and C terms of the Van Deemter equation. 

They introduced a coupling term that causes the Eddy diffusion term to vanish if the flow velocity approaches zero. In contrast to van Deemter and Giddings, the resistance to mass transfer in the mobile phase is described by an additional term D However, this factor resembles the coupling term proposed by Giddings both in its physical interpretation and in its dependence on the flow velocity. 

Eddy Diffusion Term, In this term, 2Xdp, A. is a dimensionless packing term, expressing the uniformity with which a packed column is filled and dp is the diameter of a support particle. Eddy diffusion is also referred to as the multiple-path effect it is minimized by using small particles of support materials. A support of 100/120 mesh produces a more efficient column than 60/80-mesh particles and should be used whenever possible. A support of lower mesh (e.g., 80/100 or 60/80) should be selected to avoid a high pressure drop within a long column. This term is also independent of linear velocity (u) and flow rate, Fc. 

Gritti, F. and G. Guiochon. 2011. Measurement of the eddy diffusion term in chromatographic columns, i. Applications to the first generation of 4.6 mm i.d monolithic columns./. Ghromatogr. A 1218 5216-5227. 

Here H is the theoretical plate height, a parameter that characterizes the effectiveness of the chromatographic separation. The smaller the H the more powerful is the separation. A is the Eddy diffusion term (or multipath term), B relates to longitudinal diffusion, C represents the resistance of sorption processes (or kinetic term), and u is the linear flow rate. For a given chromatographic system. A, B, and C are constants, so the relationship between H and u can be plotted as shown in Fig. 6. 

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