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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 |
---|---|---|---|

a_{i}(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 |

a_{o, i}, x_{i}
| 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) |

b_{i}(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 |