## 5 Results and Discussion
### The Results of Analysis of Microflows by the \(\mu\)PIV Method  
In Figures 17-19, the velocity distributions in microchannels experimentally determined by the \(\mu\)PIV method are presented and compared with the results of the LBM simulations and with the S&M model. The normalization of \(\mu\)PIV velocity data follows the same procedure as described for simulation data, except that \(u_{m\_min}\) was calculated as an average value of experimental data for profile 3 (Figure 15). The calculated values of \(u_{m}\) [m/s], used for normalization, were: 1.78 \(\times\) 10\({}^{-3}\), 2.28 \(\times\) 10\({}^{-4}\), and 1.57 \(\times\) 10\({}^{-4}\), respectively, for serpentine, hexagonal, and circular channels.  
The consistency of the experimental results with the simulation results is satisfactory in all cases. For the serpentine channel, the velocities in the bend region (Figure 17c) seem not to be properly determined by our \(\mu\)PIV system configuration. This can be caused by the too low tracer particles concentration in flowing fluid in this region caused by the inertial particle separation phenomena or by the high curvature of the bend geometry, which, combined with high fluid velocities, prevented the proper recognition of tracer particles displacement. Except for this small discrepancy, our simple configuration of the \(\mu\)PIV measuring system properly predicted regions with high and low velocities (dead zones) and the shape of velocity profiles.  
The higher fluctuations (noise) of experimental results presented in Figures 18 and 19, compared to the results in Figure 17, come from the increased microscope magnification. The algorithm of the PIV method uses the interrogation regions in which the mean values of tracer particle velocity are determined. With the same size of interrogation regions and the same picture resolution used, the results presented in Figure 17 are more averaged by the PIV algorithm. We have found that the primary source of observed discrepancies between measured and modeled velocity profiles come from the PIV measurement noise and the fluctuations of concentration of tracer particles.  
The S&M model is not applicable for the prediction of velocity distributions in the hexagonal and circular microchannels, where the contractions highly influence the velocity profiles, making them highly variable (Figures 18 and 19). For the straight sections of the serpentine microchannel, the S&M model's compliance with experimental and simulation data is satisfactory (Figure 17d), which allows for its use for the scale-up of the serpentine microchannels of flow-by industrial-scale DSSC-RFB system when the straight sections are much longer than the bend sections.  
Figure 17: Comparison of the normalized y-mean velocity profiles experimentally determined by the \(\upmu\)PIV method in the serpentine microchannel with the S&M model and with the results of numerical simulations: (**a**) Velocity vectors distribution from \(\upmu\)PIV; (**b**–**e**) Velocity profiles along the lines 1–4 (Figure 15). A,B,C—the same-positioned profiles for the consecutive periodic channel sections.  
Figure 18: Comparison of the normalized y-mean velocity profiles experimentally determined by the μPIV method in the hexagonal microchannel with the S&M model and with the results of numerical simulations: (**a**) Velocity vectors distribution from μPIV; (**b–f**) Velocity profiles along the lines 1–4 (Figure 15).  
Figure 19: Comparison of the normalized y-mean velocity profiles experimentally determined by the \(\upmu\)PIV method in the circular microchannel with the S&M model and with the results of numerical simulations: (**a**) Velocity vectors distribution from \(\upmu\)PIV; (**b–f**) Velocity profiles along the lines 1–4 (Figure 15).