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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