Shirazi number

The degree of agreement between the ideal and the equilibrium-dispersive models depends on the value of the effective loading factor, a dimensionless number which is also known as the Shirazi number [1] ... 

The analysis of Equation 10.10 indicated that the loading factor and the plate number are the essential parameters—besides the type of the isotherm—to control the band profile arising from column overload. The Shirazi number connects those two terms and can be regarded as a universal quantity that controls the band profile. 

The Shirazi number combines parameters of fundamentally different origins. Therefore, it combines the effects of thermodynamics and kinetics on the sharpening of the bands. Eigure 10.2 illustrates the effect of overload on the shape of the band at two different column efficiencies. 

The local equilibrium curve is in approximate agreement with the numerically calculated profiles except at very low concentrations when the isotherm becomes linear and near the peak apex. This occurs because band-spreading, in this case, is dominated by adsorption equilibrium, even if the number of transfer units is not very high. A similar treatment based on local eqnihbrinm for a two-component mixture is given by Golshau-Shirazi and Gniochou [J. Phys. Chem., 93, 4143(1989)]. 

In this chapter another dimensionless number is used to represent the injection time, namely the loading factor LFi which was first introduced by Guio-chon and Golshan-Shirazi (1989a) and is defined as... 

When Dapp is not very large (number of stages N (see Section 6.2.9) >100 Guiochon, Golshan-Shirazi, and Katti, 1994), the solution of the equilibrium-dispersive model for small injections can be approximated by a symmetrical Gaussian distribution ... 

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