Plate columns phase inversion

On a perforated plate the liquid side mass transfer coefficient kLa and gas side mass transfer coefficient k( a, based on the column volume, vary linearly with the dispersion height. The true liquid- and gas-side mass transfer coefficients and first increase with the dispersion height and then go through a maximum and decrease slightly (123). Sharma and Gupta (124) attribute this to different behavior of the density of dispersion and the average bubble size with increase in gas flowrate, which leads to a phase inversion point. These authors correlate their experimental data for 10 cm i.d. perforated plates without downcomers by the following expressions... 

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. 

The plate theory assumes that the solute is in equilibrium with the mobile and stationary phases. Due to the continuous exchange of solute between the two phases as it progresses down the column, equilibrium between the phases can never actually be achieved. To accommodate this nonequilibrium condition, a technique originally introduced in distillation theory is adopted, where the column is considered to be divided into a number of cells or plates. Each cell is allotted a finite length and, thus, the solute spends a finite time in each cell. The size of the cell is such that the solute is considered to have sufficient residence time to achieve equilibrium with the two phases. Thus, the smaller the plate, the more efficient the solute exchange between the two phases and, consequently, the more plates there are in the column. As a result, the number of theoretical plates contained by a column has been termed the column efficiency. The plate theory shows that the peak width (the dispersion or peak spreading) is inversely proportional to the square root of the efficiency and, thus, the higher the efficiency, the narrower the peak. Consider the equilibrium that is assumed to exist in each plate then... 

Relative retentions..the a values..usually vary Inversely with column temperature, but are most strongly affected by the choice of liquid phase. In packed column chromatography, the choice of liquid phase Is usually the most effective route by which separation efficiency Is Influenced. In capillary GC, however, there Is normally such an abundance of theoretical plates that the choice of liquid phase Is a relatively unimportant parameter for many analyses. In some cases however. It does become desirable (or even necessary) to select a liquid phase in which the relative retentions of certain solutes Is larger. Until quite recently, this posed a real problem with the fused silica capillary column, because the more polar liquid phases, l.e. those In which relative retentions are usually greater, coated fused silica only reluctantly, and produced columns whose useful lives were quite limited. The development of stable bonded phase columns ( ) eventually overcame this difficulty (vide Infra). 

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. 

It is seen from equation (26) that the optimum velocity is determined by the magnitude of the diffusion coefficient and is inversely related to the particle diameter. Unfortunately, in LC (where the mobile phase is a liquid as opposed to a gas), the diffusivity is four to five orders of magnitude less than in GC. Thus, to achieve comparable performance, the particle diameter must also be reduced (c./., 3-5 p) which, in turn, demands the use of high column pressures. However, the minimum plate height is seen to be controlled only by the particle diameter, the quality of the packing and the thermodynamic properties of the distribution system. 

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