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For a packed column, the cross-sectional area of the column exit flow path is usually taken as 0.6 times the cross-sectional area of the column. Alternatively, the linear velocity can be taken as the ratio of the column length to the dead time. If the mobile phase is a gas, then the pressure correction must be applied.
Random column packing is the practice of packing a distillation column with randomly fitting filtration material in order to optimize surface area over which reactants can interact while minimizing the complexity of construction of such columns. Random column packing is an alternative to structured column packing.
It is simply a hypothetical equilibrium stage. However, the theoretical plate in packed beds, chromatography and other applications is defined as having a height. The empirical formula known as Van Winkle's Correlation can be used to predict the Murphree plate efficiency for distillation columns separating binary systems. [4]
Proper column packing is important for maximum resolution: An over-packed column can collapse the pores in the beads, resulting in a loss of resolution. An under-packed column can reduce the relative surface area of the stationary phase accessible to smaller species, resulting in those species spending less time trapped in pores.
Where HETP is the height equivalent theoretical plate, A is the eddy-diffusion parameter, B is the longitudinal diffusion coefficient of the eluting material in the longitudinal direction, C is the resistance to mass transfer coefficient of the analyte between mobile and stationary phase, and u is the linear velocity of the column flow.
An a × b rectangle can be packed with 1 × n strips if and only if n divides a or n divides b. [15] [16] de Bruijn's theorem: A box can be packed with a harmonic brick a × a b × a b c if the box has dimensions a p × a b q × a b c r for some natural numbers p, q, r (i.e., the box is a multiple of the brick.) [15]
where: = (), = = (), is the modified Reynolds number, is the packed bed friction factor,; is the pressure drop across the bed,; is the length of the bed (not the column), is the equivalent spherical diameter of the packing,
For example, if the feed is a saturated liquid, q = 1 and the slope of the q-line is infinite (drawn as a vertical line). As another example, if the feed is saturated vapor, q = 0 and the slope of the q-line is 0 (a horizontal line). [2] The typical McCabe–Thiele diagram in Figure 1 uses a q-line representing a partially vaporized feed.