Adsorption, Ion Exchange, and Chromatography
= concentration of species i in the mobile phase (mass volume-1) or (mole volume-1)
= empirical constant for species i for isotherms (units vary)
= adsorption equilibrium constant for species i
= internal parameter for isotherms (units vary)
= partial pressure of species i (pressure)
= amount of species i adsorbed per unit mass of adsorbent at equilibrium (mass mass-1) or (mole mass-1)
= amount of species i adsorbed per unit mass of adsorbent at maximum loading, where maximum loading corresponds to complete surface coverage (mass mass-1) or (mole mass-1)
Modeling Differential Chromatography
= average partitioning of species i between the bulk fluid and sorbent (unitless)
= sorbent porosity, ranges from 0 to 1 (unitless)
= inclusion porosity, accounts for accessibility of sorbent pores to species i (unitless)
= sorbent tortuosity factor, usually approximately 1.4 (unitless)
= fraction of solute in the mobile phase, relative to sorbed solute, at equilibrium (unitless)
= cross-sectional area of the column (area)
= concentration of species i in the mobile phase (mass volume-1) or (mol volume-1)
= effective diffusivity of species i within the sorbent pores (length2 time-1)
= coefficient that accounts for axial diffusion of species i and non-uniformities of flow (length2 time-1)
= height of theoretical chromatographic plate for species i (length)
= kinetic rate constant of adsorption of species i to the sorbent (time-1)
= mass transfer coefficient of species i in the mobile phase (length time-1)
= overall mass transfer coefficient of species i (length time-1)
= equilibrium distribution coefficient of species i between the mobile phase and sorbent (unitless)
= length of column (length)
= amount of solute i fed to column (mass) or (mol)
= resolution of species 1 and 2 in the proposed operating condition (unitless)
= radius of sorbent particles (length)
= variance of the Gaussian peak of the distribution of species i along the column length (time)
= elapsed time since loading of the column (time)
= mean residence time of species i in the column (time)
= actual fluid velocity through the bed (length time-1)
= superficial fluid velocity through the bed (length time-1)
= position along the length of the column, in the direction of flow (length)
= mean position of species i along the length of the column as a function of time (length)
calculated by 15-61 or 15-62, Seader
1.0 g of species A is added to a chromatography column of cross-sectional area 1.0 m2 and length 1.0 m. Mobile phase is added at a flowrate of m3/s. Species A has a mass transfer coefficient of m/s in this solvent. The selected sorbent has a porosity of 0.40 m and average particle radius of m. For species A in this sorbent, the inclusion porosity is 0.80, , m2/s, s-1 and the effective diffusivity is m2/s.
(a) When is mean expected elution time for species A?
(b) Plot the concentration profile for species A at 0.05 m increments along the column length in 10-minute increments, until all of the solute has eluted.
(c) Find the variance of the peak for species A in the proposed operating condition.
(d) The column feed also contains 1.0 g of species B. Species B has a mass transfer coefficient of m/s in the mobile phase, inclusion porosity of 0.50, , m2/s, effective diffusivity of m2/s and s-1. What is the resolution of these two species in the proposed operating condition?