Diffusion, eddy chromatographic

Dominant eddy diffusion For chromatographic systems with negligible mass transfer resistance the eddy diffusion is the dominant effect. Thereby, HETP values are constant and independent of the interstitial velocity ... 

Hindered diffusion, the primary transport mechanism in porous solids, can be qualitatively described as a series of hops by the analyte, via gas-phase diffusion, from one surface site to the next. Thus, hindered diffusion is composed of two main components a pure diffusion-related term, often Fickian in nature, associated with movement of the analyte in the gas phase and a term describing the noninstantaneous equilibration between gas-phase analyte and the solid surface at each point where the analyte touches down (adsorbs). In extended porous solids (e.g., a chromatographic column tightly packed with porous beads), transport is often more complex, requiring the consideration of such factors as eddy diffusion and Knudsen effusion. This is important if there is a significant pressure drop along the path of the analyte [109]. Finally, the presence of any external fields (thermal, electric, etc.) must be considered as well. 

In this equation the first factor is called the eddy diffusion, the second and third are molecular diffusion, and the last two are called resistance-to-mass-transfer terms. All the terms include the mobile-fluid velocity as a variable that is proportional to the flow rate in some, and inversely proportional in others. The overall relation between plate height and flow velocity of the mobile phase is the statistical resultant of the five terms and is usually depicted in the form of a Van Deemter plot. ° Such a diagram shows that an optimum flow velocity for minimum band spreading exists for a given chromatographic column. 

Broadening of Chromatographic Bands as a Resuit of Eddy Diffusion and Resistance to Mass Transfer... 

The most characteristic feature of chromatographic bands is that the longer the development time and the greater the distance from the start, the greater become their surface areas. This phenomenon is not restricted to planar chromatography—it occurs in all chromatographic techniques. Band broadening arises as a result of eddy and molecular diffusion, the effects of mass transfer, and the mechanism of solute retention. 

Those who prepare and/or manufacture LC columns must use the above methods to limit the effects of eddy diffusion on the chromatographic separations. However, there are practical limitations. Column and stationary-phase particle diameters can only be reduced to points that are compatible with the pressure limitations of the pumps used in chromatographic instruments and the required sample capacities of the columns. The degree of training and experience of those who pack the columns may also limit the quality of the procedure used in packing the column. Nevertheless, most commercial manufactur-... 

Three mechanisms produce dispersion of a band of solute in a chromatographic system as it passes through the separation column 1) eddy diffusion 2) longitudinal diffusion and 3) mass transfer effects. These effects are discussed, in some detail, in this article. 

Eddy diffusion Diffusion of solutes that contributes to broadening of chromatographic bands, the result of differences in the pathways for solutes as they traverse a column. 

For preparative liquid chromatographic processes the HETP equation can be simplified further by taking a closer look at the axial dispersion coefficient, D j, which is generally described as the sum of the contributions of eddy diffusion and molecular diffusion... 

In chromatographic systems with relatively large effective mass transfer coefficients kefy (i.e. low mass transfer resistance) the influence of axial dispersion, especially eddy diffusion, dominates the concentration profile. HETPj and Nj is then independent of the interstitial velocity. 

The A term corresponds to the eddy diffusion which describes the irregular flow through the packed particles in a column causing different pathways and different exit times for the solute molecules. The B term is the longitudinal molecular diffusion or random diffusion along the column. The last term C, corresponds to the mass transfer in the stationary phase. This mass transfer occurs between the mobile and stationary phase of the chromatographic system and is dependant on several factors such as particle size, column diameter and diffusion coefficient. 

The van Deemter rate theory identified three major factors that cause band or zone broadening during the chromatographic process the eddy diffusion or the multi-path effect (A-term), longitudinal diffusion or molecular diffusion of the analyte molecules (B-term), and resistance to mass transfer in the stationary phase (C-term). The broadening of a zone was expressed in terms of the plate height, H, and was described as a function of the average linear velocity of the mobile phase, u. 

The simple theory of eddy diffusion assumes that solute molecules are fixed in given flow paths. In practice, however, this is not true. The solute molecules may pass laterally by diffusion and by convection from one flow path into another where the flow velocity may be quite different. This coupling of lateral mixing with the normal process of eddy diffusion results in a decrease in the amount of band broadening and hence an increase in efficiency of the chromatographic process. 

Note that D, the dispersion coefficient, is not the molecular diffusivity, but a measure of combined dispersive effects inherent in packed bed operations, of which molecular diffusivity is a minor component. As pointed out by Kramers and Alberda (24), eddy diffusivity involves fluctuations of a statistical nature, and should not be applied to macroscopic effects, such as by-passing and mixing. This equation is important because it allows the modeling of chromatographic results using the dispersion coefficient as a free parameter. 

Obviously, the aim is for a chromatographic separation in which peak width is narrow relative to the time of elution (wi/Vr is minimized), i.e., the number of theoretical plates is maximized. There are three main factors that give rise to band broadening (1) multiple path effect (eddy diffusion), (2) axial (longitudinal) diffusion, and (3) mass transfer—slow transfer/equilibration between mobile and stationary zones. 

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