## 5 Results and Discussion
### Influence of Electrolyte Flow Hydrodynamics on \(\mu\)DSSC Cell Performance  
The equivalent circuit of DSSC can be represented as in Figure 20[56]. In this equivalent circuit, a constant current source J\({}_{\text{cell}}\) in which electrons are generated by dye molecules is in parallel with an impedance \(Z_{1}\) associated with electron transfer at the TiO\({}_{2}\)/dye/electrolyte interface [57]. The main source of power loss in DSSC is the series resistance, which is the sum of the resistances of photoanode R\({}_{1}\), electrolyte R\({}_{2}\), counter electrode R\({}_{3}\), and transparent conducting oxide (TCO) R\({}_{8}\). Resistance R\({}_{2}\) and capacitance C\({}_{2}\) are elements of Nernst diffusion impedance \(Z_{2}\), relating to the carrier transport of ions within the electrolyte, while the resistance R\({}_{3}\) and capacitance C\({}_{3}\) are elements of impedance \(Z_{3}\) due to redox reaction at the platinum counter electrode. The shunt resistance R\({}_{\text{sh}}\) is responsible for back electron transfer across the TiO\({}_{2}\)/dye/electrolyte junctions, which is mainly caused by the leakage of current in the case of impurities or defects in the cell manufacturing process. In perfectly manufactured cells, this resistance is large compared to other resistances, which prevents current loss in DSSC. Under short circuit conditions, the injected electrons flow through the TCO layer to the counter electrode via the external circuit. The resistance of TCO mainly contributes to the series resistance of a cell, so the R\({}_{8}\) should be reduced in order to improve the efficiency of DSSC. Although R\({}_{8}\) can be decreased with low sheet resistance of TCO, the transmittance of TCO will be reduced at the same time [57]. We have prepared several FTO glass electrodes to investigate the influence of R\({}_{8}\) on the DSSC performance. In Figure 21, the experimental results of the surface distribution of resistances of FTO glass with or without silver path are compared. Silver paths with a thickness of several micrometers reduce the electrical resistance of DSSC electrodes by almost four times and lead to an even distribution of current density on the surface (Figure 21a,c,e,g). Important for the scale-up process is that the resistance of the electrode with silver paths is not dependent on its size, as the silver paths resistance is below 0.1 \(\Omega\)/cm\({}^{2}\) and the current is not limited by the resistance of the electrode. [PERSON] at al. [57] have found that, in a standard DSSC under short circuit conditions, electron transport was predominately affected by the series resistance Rs in TCO and R\({}_{3}\) at the electrolyte/Pt-TCO interface. They found that, compared with R\({}_{8}\) and R\({}_{3}\), the diffusion resistance R\({}_{2}\) influences both the electron transfer and charge transport. R\({}_{2}\) not only limited the electron extraction from the TiO\({}_{2}\) layer to the external circuit under the short circuit conditions but also influenced the electron transfer from the TiO\({}_{2}\) film to tri-iodide in the electrolyte. The diffusion resistance of the electrolyte R\({}_{2}\) is relatively small and equals approximately 1.6-3.4 \(\Omega\) when the thickness of the electrolyte layer is about 60 \(\upmu\)m. At the  
Figure 20: Circuit model of a DSSC connected to a load. J\({}_{\text{cell}}\) is a constant current source; R\({}_{8}\) is the TCO resistance; Z\({}_{1}\) is the impedance for electron transfer across the TiO\({}_{2}\)/dye/electrolyte interface; R\({}_{1}\) is the electron transfer resistance; C\({}_{1}\) is the capacitance of TiO\({}_{2}\); Z\({}_{2}\) is the diffusion impedance of redox species in the electrolyte associated with diffusion capacitance C\({}_{2}\) and diffusion resistance R\({}_{2}\); Z\({}_{3}\) is the impedance of electrolyte/Pt-TCO interface associated with the electron transfer resistance R\({}_{3}\) and capacitance C\({}_{3}\); R\({}_{\text{sh}}\) is the shunt resistance.