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Table 1 List of symbols. Dependent variables (Dep. Var.) refer to variables that are defined by or are calculated directly from experimental data

From: Investigating the effects of substrate morphology and experimental conditions on the enzymatic hydrolysis of lignocellulosic biomass through modeling

Symbol Description Value Units
\({b}_{l}\) Biomass loading Dep. Var. [g/cm3]
\({C}_{E,0}\) Initial bulk enzyme concentration Dep. Var. [mol/cm3]
\({C}_{E}^{F}(r,t)\) Enzyme concentration in pores or bulk (r = R) Dep. Var. [mol/cm3]
\({C}_{E}^{S}(r,t)\) Enzyme concentration adsorbed at the cellulose surface per total cylinder volume V(r) Dep. Var. [mol/cm3]
\({C}_{E,max}^{S}(r,t)\) Maximum enzyme concentration adsorbed at the cellulose surface per total cylinder volume V(r) Dep. Var. [mol/cm3]
\({D}_{E}^{eff}(r,t)\) Effective cellulase diffusivity in pores Dep. Var. [cm2/min]
\({\stackrel{-}{D}}_{E}^{pore}\) Average cellulase diffusivity in pores Dep. Var [cm2/min]
\({D}_{E}\) Time independent part of the effective cellulase diffusivity in pores Dep. Var. [cm2/min]
\({e}_{l}\) Enzyme loading in terms of enzyme:initial binding sites molar ratio Dep. Var [molE/molSites]
Hglu Hydrolysis factor for glucose 0.9 [MMcellulose/MMglucose]
\({k}_{ads}\) Cellulase surface adsorption rate [60] \(3 \cdot {10^{10}}\) [cm3/(mol \(\cdot\) min)]
\({k}_{des}\) Cellulase surface desorption rate [42, 43] \(0.068\) [1/min]
\({M}_{p}\) Average moles of glucose liberated in solution per mole of cellulase during one binding-reaction cycle Fitted var. [molglucose/moldesorbing enzyme]
\({MM}_{glu}\) Molar mass of glucose 180 [g/mol]
\(n\) Grid size Dep. Var. [−]
\({n}_{E,0}\) Total number of moles of enzyme in the system Dep. Var. [mol]
\(r\) Radial distance Indep. Var. [cm]
\(R\) Particle radius Dep. Var. [cm]
\({S}_{c}\) Pore cellulose surface Dep. Var [cm2]
\({S}_{cyl}\) Outer particle surface Dep. Var. [cm2]
\(t\) Time Indep. Var. [min]
\({V}_{B}\) Volume of bulk solution Dep. Var. [cm3]
\(\varepsilon (r,t)\) Porosity Dep. Var. [cm3pore/ cm3biomass]
\({\varepsilon }_{0}\) Initial porosity Dep. Var. [cm3pore/ cm3biomass]
\({\rho }_{C}^{IV}\) Density of cellulose including void Dep. Var. [g/cm3]
\(\varphi\) Angular coordinate Indep. Var. [−]
\(\sigma\) Maximum cellulase surface concentration on cellulose [42, 43] \(2.1\cdot{10}^{-12}\) [mol/cm2]
\(\tau\) Tortuosity Fitted var., [−]
z Longitudinal coordinate Indep. Var. [-]