## 3 Results and Discussion
### Various Flow Rate Patterns of Pure Liquid Controlled with Syringe Pump
The flow rate of the test fluid increased stepwise from 0.2 mL/h to 1.6 mL/h at intervals of 0.2 mL/h. As shown in Figure 4A, the temporal variations in \(\beta\) were obtained with respect to glycerin and \(Q_{t}\). The value of \(\beta\) increased gradually at higher flow rates and higher concentrations of the glycerin solution. The viscosity of the glycerin solution was then calculated by substituting \(\beta\) and \(Q_{t}\) into Equation (3). Figure 4B showed the viscosity of the glycerin solution with respect to \(Q_{t}\) as well as \(C_{glycerin}\). Above \(Q_{t}\) = 0.4 mL/h, the viscosity of the test fluid remained constant with respect to \(Q_{t}\). The corresponding viscosity of each glycerin solution was obtained as (a) \(\mu_{t}\) = 1.357 \(\pm\) 0.016 cP for \(C_{glycerin}\) = 10%, (b) \(\mu_{t}\) = 1.891 \(\pm\) 0.029 cP for glycerin = 20%, and (c) \(\mu_{t}\) = 2.425 \(\pm\) 0.074 cP for glycerin = 30%. When compared with the viscosities obtained under the same flow rate condition (\(Q_{r}=Q_{l}\)), the viscosity of the test fluid showed substantially similar values with respect to \(C_{glycerin}\). To determine the correlation of viscosities obtained under two different flow rate conditions, a linear regression analysis was conducted using experimental data as shown in Figures 3B and 4B. As a result, the linear regression was obtained as \(\mu\) (\(Q_{r}\
eq Q_{l}\)) = 1.026 \(\times\)\(\mu\) (\(Q_{r}=Q_{l}\)) (\(R^{2}\) = 0.9685). From the quantitative study, the present method quantified the viscosity of the test fluid consistently, without respect to flow rate condition (i.e., \(Q_{r}=Q_{l}\), \(Q_{r}\
eq Q_{l}\)). Figure 4C showed the variations of \(P_{r}\) and \(P_{t}\) with respect to glycerin concentration and \(Q_{l}\). Both pressures tended to increase linearly with respect to \(Q_{l}\). In addition, there was little difference between \(P_{r}\) and \(P_{t}\) (\(P_{r}\approx P_{t}\)). Figure 4D showed the variations in \(\tau_{r}\) and \(\tau_{t}\) with respect to glycerin concentration and \(Q_{l}\). Both shear stresses tended to increase linearly with respect to \(Q_{l}\). Namely, higher concentrations of glycerin solution resulted in higher shear stress values. Furthermore, there was little difference between \(\tau_{r}\) and \(\tau_{t}\) with respect to \(Q_{l}\). On the other hand, when compared with the pressure and shear stress as shown in Figure 3C,D, the shear stress and pressure which are represented in Figure 4C,D decreased substantially because the flow rate of the reference fluid remained constant at 1 mL/h. Third, to induce a sinusoidal flow in the test fluid, glycerin solution (\(C_{glycerin}\) = 30%) as test fluid was supplied at a flow rate of \(Q_{l}\) = 0.9 + 0.7 sin (2 \(\times\)\(\pi\)\(\times\)\(t/T\)) mL/h. Here, the period (\(T\)) set to \(T\) = 120, 240, 360, and 480 s. The reference fluid was supplied at a constant flow rate of 1 mL/h. Variations in the pressure and shear stress (i.e., \(P_{r}\) and \(\tau_{r}\)) were obtained with respect to \(T\). Here, it was impossible to obtain the flow rate (\(Q_{l}\)) and viscosity (\(\mu_{t}\)) of the test fluid in advance. In the coflowing channel, it was already validated that both streams had the same pressure and shear stress (i.e., \(P_{r}\approx P_{t}\), \(\tau_{r}\approx\tau_{t}\)). Both properties of the test fluid could be then obtained indirectly by quantifying the pressure (\(P_{r}\)) and shear stress (\(\tau_{t}\)) of the reference fluid because three vital properties (i.e., \(\mu_{r}\), \(Q_{r}\), and \(1-\beta\)) of the reference fluid were obtained over time. Figure 5A(a) showed the temporal variations of \(\beta\) with respect to \(T\). As \(T\) increased, the maximum value of \(\beta\) remained unchanged with respect to \(T\).