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Table 1 Notation Table of All Variables

From: Standing-wave Design of Three-Zone, open-loop non-isocratic SMB for purification

Notations Description Notations Description
ai(pH) Equilibrium distribution coefficient as a function of pH value of component “i” in a linear system, or Langmuir “a” value as a function of pH value of component “i” in a non-linear system. L C Column length
ao, i, xi Adsorption equilibrium constant in Example 2 Eq. (20) L j Length of Zone j
a, b, c Coefficients in quadratic formula in Eq. (12) n pH dependent equilibrium order in Example 1 Eq. (18)
bi(pH) Langmuir “b” value as a function of pH value in a non-linear system. P Phase ratio, \( P=\frac{1-{\varepsilon}_b}{\varepsilon_b} \)
\( {C}_1^{II} \) Concentration of component 1 in the make-up solvent in Zone II pH j pH in Zone j
\( {C}_2^I \) Concentration of component 2 in the desorbent in Zone I pH ref Reference pH in Example 1 Eq. (18)
C E, i Average concentration of component “i” in the Extract Q f Feed flow rate
C R, i Average concentration of component “i” in the Raffinate Q j Flowrate in Zone j
C f, i Feed concentration of component “i” Q E Extract flow rate
C i Bulk concentration of component “i” in the fluid Q R Raffinate flow rate
C p, 1 Plateau concentration of component 1 (less retained component) in Zone III q i Solid phase concentration on a solid volume basis of component “i”
C p, 2 Plateau concentration of component 2 (more retained component) in Zone II q max Sorbent capacity
C s, 1 Plateau concentration of component 1 after feed port in Zone III R p Particle radius
\( {C}_{s,1}^{\ast } \) Plateau concentration of component 1 in Zone II before mixing with the feed port S Cross-sectional area of the column
C s, 2 Plateau concentration of component 2 after feed port in Zone III t s Step time
\( {C}_{s,2}^{\ast } \) Plateau concentration of component 2 in Zone II before mixing with the feed port \( {u}_o^j \) Zone velocity
D p, i Pore diffusivity of component “i” \( {u}_{w,i}^j \) Wave velocity of component “i” in Zone j
d p Particle diameter Y i Yield of component “i”
\( {E}_{b,i}^j \) Axial dispersion coefficient of component “i” in Zone j \( {\beta}_i^j \) Decay coefficient of component “i” in Zone j.
K A Association equilibrium constant in Example 1 Eq. (18) \( {\delta}_i^j \) Retention factor of component “i” in Zone j
K se, i Size exclusion factor of component “i” ε b Bed void fraction
\( {k}_{e,i}^j \) Lumped overall mass transfer coefficient of component “i” in Zone j ε p Particle porosity
\( {k}_{f,i}^j \) Film mass transfer coefficient of component “i” in Zone j ν Port velocity