## 3 Results and Discussion
### Simulation of Continuous Mode MFC  
#### 3.3.1 Effect of Influent Substrate Concentration and Dilution Rate  
When MFC reactors were operated in continuous mode, the operating variables that might have pronounced effects were dilution rate (\(D\)) and influent substrate concentration (\(S_{in}\)). These two variables controlled the substrate inflow rate and biomass washout rate, and therefore would eventually impact MFC power generation and energy efficiency at steady state. So in the simulation, the dilution rate was varied between 0.1 to 2 d\({}^{-1}\). The upper limit was chosen to be less than the maximum microbial specific growth rate (2.4 d\({}^{-1}\)) to prevent biomass washout. The influent substrate \begin{table}
\begin{tabular}{c c c c} \hline \hline
**External Resistor** & **Peak Power** & **Energy Recovered** & \(\eta_{overall}\) \\ \hline
10 \(\Omega\) & 0.0142 mW & 1.96 J & 0.87\% \\
300 \(\Omega\) & 0.0998 mW & 37.1 J & 16.4\% \\
1000 \(\Omega\) & 0.0882 mW & 47.3 J & 20.7\% \\
2200 \(\Omega\) & 0.0685 mW & 40.0 J & 17.7\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulated peak power and energy recovery from an external resistor, and overall energy efficiency (\(\eta_{overall}\)) at different external resistors. Figure 5: Simulated batch performance of MFC with 100 mg L\({}^{-1}\) initial substrate at different external resistors. (**A**) substrate concentration; (**B**) suspended biomass concentration; (**C**) external voltage; and (**D**) power generation. (HAc) concentration was between 10 to 2400 mg L\({}^{-1}\). The results, including the substrate concentration, suspended biomass concentration, attached biomass concentration and overall energy efficiency, were plotted in Figure 6. Please note that the external power (\(P_{ext}\)) was not considered in the simulation of varying \(S_{0}\) and \(D\), because it was found that when assuming the attached biomass was fully grown at steady state, the external power was a function of the external resistor, rather than a function of these two operating variables. It should be noted that little effort in MFC studies of varying these operating parameters was found in continuous mode, so literature data for comparison were not available. At a given level of the influent substrate concentration, the steady state substrate concentration went up with the increasing dilution rate, basically due to the increased substrate inflow to the reactor (Figure 6A). When the influent substrate concentration was higher than 500 mg L\({}^{-1}\), the concentration did not have much impact on the steady state substrate concentration at a given dilution rate. But when the influent concentration was lower than 500 mg L\({}^{-1}\) and the dilution rate was greater than 1.5 d\({}^{-1}\), the steady state concentration increased along with the influent concentration. The suspended biomass concentration obviously increased with the influent substrate concentration in a linear manner at any dilution rate (Figure 6B). The dilution rate between 0.5 and 1 d\({}^{-1}\) resulted in a maximum suspended biomass at a given influent substrate concentration, because a lower rate caused substrate limitation and a higher rate could partially wash out suspended biomass. The attached biomass was more stable and could generally achieve its maximum in most cases (Figure 6C), except for the cases of \(S_{in}\), which were much lower than 100 mg L\({}^{-1}\) and were too low to provide enough carbon sources for supporting the bacterial growth and attachment. As to the overall energy efficiency, it could be concluded that a higher influent substrate concentration reduced the efficiency (Figure 6D). The only exception was the case with about 10 mg L\({}^{-1}\) of influent substrate and 0.1 d\({}^{-1}\) of dilution rate, under which condition the attached biofilm was not fully mature, due to substrate deficiency,  
Figure 6: Process variables and MFC performance predicted at steady state under different dilution rates and influent substrate concentrations.