## 3 Results and Discussion
### Quantitative Evalution of Blood Flow and Blood Flow Stabilization  
A micropump delivered suspended blood using piezoelectric membrane vibration resulting in the periodic fluctuations in the blood flow [33]. However, to measure the shearing viscosity of the blood or plasma, it was essential to maintain a constant flow rate (or velocity) during the experiment. Therefore, the frequency of micropump was adjusted to reduce the fluctuations in blood flow. Additionally, the effect of the air damper on the stabilization of blood flow was evaluated by changing the length (or cavity) of the air damper. Suspended blood (Hct = 50%) was prepared by adding normal RBCs to autologous plasma.  
To quantify the blood flow delivered by the micropump, the velocity (\(U_{b}\)) and interface (\(\alpha_{\text{b}}\)) were monitored without the addition of an air damper. Figure 3A shows microscopic images of variations in the interface with respect to the operational frequency (\(f\)) ([i] f = 100 Hz, [ii] f = 300 Hz, [iii] f = 400 Hz, and [iv] f = 800 Hz). The excitation voltage of the micropump was fixed at \(v\) = 140 au, where au denotes an arbitrary unit. \(\alpha_{\text{b}}\) showed a tendency to decrease at higher values of the operational frequency. Based on the microscopic images captured over time, temporal variations in \(U_{b}\) and \(I_{b}\) were obtained with respect to the operational frequency. Figure 3(B-i) shows the temporal variations in \(U_{b}\) with respect to \(f\). At \(f\) = 100 Hz, \(U_{b}\) exhibited large alternating blood flow. However, when the frequency was shifted to 300 Hz, the fluctuations decreased substantially. From the results, it was inferred that the resonance frequency of the micropump was close to 100 Hz. To reduce fluctuations in the blood velocity, the operational frequency must be set above 100 Hz. Figure 3(B-ii) shows the variations in \(U_{b}\) and coefficient of variance (COV) (COV = standard deviation/mean) with respect to \(f\). \(U_{b}\) showed a tendency to gradually decrease with respect to operation frequency. Additionally, the COV had a minimum value at \(f\) = 300 or 400 Hz. Figure 3(B-iii) shows the temporal variations in \(\alpha_{\text{b}}\) with respect to \(f\); the value of \(\alpha_{\text{b}}\) gradually decreased at higher frequencies. The fluctuation in \(\alpha_{\text{b}}\) is very small with respect to \(f\), which implies that it remained constant with respect to the operational frequency. Figure 3B-iv shows the variations in \(\alpha_{\text{b}}\) and COV with respect to the operational frequency; \(\alpha_{\text{b}}\) decreased linearly with respect to \(f\), and the COV was less than 1%. From the results, it can be concluded that the blood velocity (\(U_{b}\)) was significantly influenced by the operational frequency when compared with the interface (\(\alpha_{\text{b}}\)). Based on the experimental results, the operational requirement was set to \(f\) = 300 Hz during the subsequent experiments.  
To reduce periodic fluctuations in the blood flow, an air damper was connected to inlet (a). To substantially increase the air compliance effect, the air cavity inside the air damper was adjusted by increasing the length of the polyethylene tubing (\(L_{t}\)). Figure 3(C-i) shows a schematic of the air damper connected to the inlet (a) of the microfluidic device. The flow rate of the reference fluid (1 \(\times\) PBS) was set to 1 mL/h using a syringe pump. The control parameters of the micropump were set to \(f\) = 300 Hz and \(v\) = 140 au. Figure 3(C-ii) shows the temporal variations in \(U_{b}\) with respect to \(L_{t}\) = 0, 20, 40, and 60 mm. The air damper contributed to the decrease in periodic fluctuations of \(U_{b}\). Figure 3(C-iii) shows the variations in CV with respect to \(L_{t}\); CV decreased significantly from 3% to 1% with the addition of the air damper. From the results, the length of the air damper was set as \(L_{t}\) = 40 mm during the subsequent experiments.