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Table 4 The model symbols

From: A novel film–pore–surface diffusion model to explain the enhanced enzyme adsorption of corn stover pretreated by ultrafine grinding

Parameters

Description

Units

Value

Sources

SGCS

UGCS

V L

Total volume of the liquid phase

mL

5

5

This study

C 0

Initial concentration of the enzyme in the bulk solution

mg/mL

0.133

0.133

This study

C L

Enzyme concentration in the bulk solution

mg/mL

Dep. var.

Dep. var.

C P,r|r=R

Enzyme concentration at the particle surface

mg/mL

Dep. var.

Dep. var.

C P,r

Enzyme concentration in the particle pores at position r

mg/mL

Dep. var.

Dep. var.

q b

Equilibrium amount of solid-phase bound enzyme

mg/g substrate

Dep. var.

Dep. var.

q m

Maximum solid-phase bound capacity

mg/g substrate

Indep. var.

Indep. var.

K a

Affinity constant

mL/mg

Indep. var.

Indep. var.

C f

Equilibrium concentration of free enzyme in solution

mg/mL

Indep. var.

Indep. var.

t

Adsorption time

min

Indep. var.

Indep. var.

A

Total outer surface area of all the particles

cm2

Dep. var.

Dep. var.

R

Radius of the particle

cm

2.18 × 10−2

0.18 × 10−2

This study

m

Mass of all the particles

g

0.1

0.1

This study

r

Radial position in the particle

cm

Indep. var.

Indep. var.

ρ a

Apparent density of the particle

g/cm3

Dep. var.

Dep. var.

ρ s

Solid density of the particle

g/cm3

Indep. var.

Indep. var.

V pa

Pore volume accessible to the enzyme

cm3/g

Indep. var.

Indep. var.

V p

Pore volume

cm3/g

Indep. var.

Indep. var.

φ

Ratio of the pore volume accessible to the enzyme to the total pore volume

Dep. var.

Dep. var.

K L

External-film mass transfer coefficient

cm/min

Indep. var.

Indep. var.

D p

Pore diffusion coefficient of the enzyme

cm2/min

Indep. var.

Indep. var.

D s

Surface diffusion coefficient of the enzyme

cm2/min

Indep. var.

Indep. var.

D e

Effective diffusion coefficient in the internal pore

cm2/min

Dep. var.

Dep. var.

q r

Solid-phase enzyme adsorption amount at position r

mg/g substrate

Dep. var.

Dep. var.

q a

Average enzyme adsorption amount in the solid particles

mg/g substrate

Dep. var.

Dep. var.

ε

Porosity

Dep. var.

Dep. var.

M c

Mass percentage of cellulose in the particles

%

33.44

33.38

This study

M h

Mass percentage of cellulose in the particles

%

17.58

17.47

This study

M l

Mass percentage of lignin cellulose in the particles

%

25.21

24.35

This study

M o

Mass percentage of other compositions such as ash in the particles

%

23.77

24.8

This study

ρ c

Cellulose density

g/cm3

1.52

1.52

[44]

ρ h

Hemicellulose density

g/cm3

1.56

1.56

[44]

ρ l

Lignin density

g/cm3

1.39

1.39

[44]

ρ o

Density of other compositions such as ash

g/cm3

2.50

2.50

[45]

  1. Dependent variables are listed as Dep. var. and can be calculated from one of the equations while independent variables are listed as Indep. var