Longitudinal diffusion term

Now, equations (1) and (2) indicate that both the Knox equation and the Van Deemter equation predict a linear relationship between the value of the (B) term (the longitudinal diffusion term) and solute diffusivity. 

Now, at high linear velocities, the longitudinal diffusion term will become insignificant and, equally important, the resistance to mass transfer term that incorporates the inverse function of diffusivity will become large, thus improving the precision of measurement. 

It is seen from equation (7) that the longitudinal diffusion term is a function of (k ) the capacity factor of the solute. While this may be a significant effect in LC capillary column systems, where the film of stationary phase is continuous along the length of the column, it will not be so in a packed column. The stationary phase in a packed column is not only broken into segments between each particle but also between each pore in each particle so free diffusion would be impossible. It follows that the longitudinal diffusion term for packed columns will be independent of the k of the solute or, very nearly so, and the experimental support for this will be discussed in the next chapter. 

In fact, in the original form, equation (1), was introduced by van Deemter for packed 6C columns and consequently, the longitudinal diffusion term for... 

Equation 9.17 can be used to obtain a plate height equation for field-flow fractionation. (The longitudinal diffusion term, Eq. 9.14, is generally negligible in FFF.) We assume that the relative flow dispersion hYIVis approximately unity. Most diffusion processes are limited to paths not much larger than thus we can write d 2(. With these assumptions we get the equation [24]... 

This shows that the secohd term, i.e., the longitudinal diffusion term, is negligible compared to the first Iterm, i.e., the radial diffusion term, if the quantity Re Pr is large. The quantity RePr is termed the Peclet number, Pe. Generally, if the Peclet number is greater t ian 10, the effects of longitudinal diffusion are, indeed, negligible. 

Longitudinal diffusion term, Bin A term in chromatographic band-broadening models that accounts for longitudinal diffusion. Lower control limit, LCL The lower boundai7 that has been set for satisfactory performance of a process or measurement. Luminescence Radiation resulting from photoexcitation (photoluminescence), chemical excitation (chemiluminescence), or theiTnal excitation (thermoluminescence). 

B — longitudinal diffusion term = 2jDm y obstruction factor Dm = diffusion coefficient... 

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 ... 

The Longitudinal Diffusion Term B u. Diffusion is a process in which species migrate from a more concentrated part of a medium to a more dilute region. The... 

The longitudinal diffusion term (B) This term accounts for the spreading of molecules in both directions from the band center along the length of the column as a result of random-walk diffusion. This occurs primarily in the mobile phase in GC, but significantly in both phases in LC (as the analytes... 

Decreasing the retention time is the first step in the speed-up of the separation. The related decrease in viscosity lowers the column pressure and allows for an increase in linear velocity. It was mentioned above that this is actually necessary, to prevent longitudinal diffusion, -term, processes becoming dominant and hence losing separation efficiency. In the example of the alkylphenol separation, it can be seen the potential reduction in analysis times related to a temperature increase from 30 to 80 °C with the following aspects ... 

The continuous elution method is conducted in an open mbe with circular cross section. The carrier gas flow rate is chosen such that the plate height, H, depends mainly on only one of the van Deemter terms, namely the longitudinal diffusion term. For correction reasons, the use of two different length columns is necessary, and the equation for H is ... 

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