Predicting influence of membrane properties on filtration performance
This section evaluates the role of membrane properties (i.e., membrane pore size and porosity) in determining the filtration performance of an EMR. As discussed in the section on theoretical simulation, the membrane pore size determines the convective and diffusive hindrance factors (i.e., Kc in eq. (33) andKd in eq. (34)) and thus affects the sieving efficiency of solutes. Figure 5 shows the permeate flux and permeate concentration of an EMR as a function of membrane pore size. It is evident that the tighter membrane (smaller pore size) suffers from more severe concentration polarization leading to lower permeate flux37 (Figure 5a ). The flux difference becomes smaller in the later stage, which is attributed to the reduction of degree of concentration polarization as more products passed through the membrane. Since the tighter membrane rejects more dextran, it has a low permeate concentration compared to the membrane with larger pore size at the same operation time in the initial stage (Figure 5b ). Although the membrane with large pore size has a higher filtration efficiency, the membrane with small pore size benefits from prolonged retention time which enables sufficient hydrolysis of substrate and in turn produces more uniform and smaller oligodextran molecules10. However, further increase in operation time leads to decrease of permeate concentration (Figure 5b ) because substrate concentration decreases with increase of the operation time under the water feeding mode.
The membrane porosity is also of particular significance because, on one hand, it affects the relationship between the convection and diffusion transportation of solutes (i.e, Pem in eq. (29)) and, on the other hand, it determines the membrane intrinsic resistance (i.e, Rm in eq. (3)) and retention time that relate to separation efficiency. Figure 6 presents the variations of permeate flux and permeate concentration at different membrane porosities. The membranes with different porosities present a similar filtration performance in the initial filtration process. However, as more oligodextran products are collected in the permeate, the concentration polarization decreases and the role of membrane resistance in the total filtration resistance is enhanced. A higher membrane porosity causes a decrease of the membrane resistance (i.e. smaller Rm in eq. (3)). As a result, the membrane with higher porosity has larger permeate flux in the later filtration process, which leads to decrease of the permeate concentration (Figure 6 ). This result is explained by the increase in oligodextran rejection due to the dilution effect at higher flux38. The developed model elaborates the inherent relationship between membrane properties and reaction-separation efficiency and shows that selection of a membrane with large porosity and uniform pore size distribution in an EMR is beneficial for the improvement of filtration efficiency and quality of products.
Figure 5. Simulation investigation of the effect of the pore size of membrane on (a) permeate flux and (b) permeate concentration with membrane porosity of 0.8. Substrate concentration: 50 g/L, enzyme concentration: 0.05 g/L, operating pressure: 3 bar, agitation speed: 1000 rpm, and feeding mode: water feeding.
Figure 6. Simulation investigation of the effect of membrane porosity on (a) permeate flux and (b) permeate concentration with membrane pore size of 10 nm. Substrate concentration: 50 g/L, enzyme concentration: 0.05 g/L, operating pressure: 3 bar, agitation speed: 1000 rpm, and feeding mode: water feeding.