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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