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)] |
\({k}_{des}\) | \(0.068\) | [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. | [-] |