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 |