## 3 Results and Discussion
### Various Flow Rate Patterns of Pure Liquid Controlled with Syringe Pump
The minimum value of \(\beta\) decreased substantially when \(T\) increased from \(T\) = 120 s to \(T\) = 360 s. The minimum value of \(\beta\) did not show a difference between \(T\) = 360 s and \(T\)= 480 s. Based on temporal  
Figure 3: Quantitative comparison of pressure and shear stress for both streams at the same flow rate of two fluids. 1\(\times\) PBS was selected as reference fluid. While the flow rate of each fluid increased stepwise from 0.2 mL/h to 1.6 mL/h, both fluids were supplied into the microfluidic device at the same flow rate (\(Q_{r}=Q_{l}\)). (**A**) Temporal variation of \(\beta\) as well as flow rate (\(Q_{r}\), \(Q_{l}\)) with respect to \(C_{glycerin}\) = 10%, 20%, and 30%. (**B**) Variation of viscosity of test fluid (i.e., \(C_{glycerin}\) = 10%, 20%, and 30%) with respect to \(Q_{l}\). (**C**) Variations of \(P_{r}\) and \(P_{t}\) and ND between both pressures with respect to \(C_{glycerin}\). (**D**) Variations of \(\tau_{r}\) and \(\tau_{t}\) for each stream and ND between both shear stresses with respect to \(C_{glycerin}\). variations in \(\beta\) over time as shown in Figure 5A(a), variations in \(P_{r}\) (\(L_{c}\)) were obtained with respect to \(T\) and \(\beta\). As shown in Figure 5A(b), \(P_{r}\) tended to increase gradually with respect to \(\beta\). Four trajectories (i.e., \(P_{r}\) vs. \(\beta\)) overlapped well with respect to \(T\). The minimum values of \(P_{r}\) and \(\beta\) tended to decrease with decreasing \(T\). Figure 5A(c) showed the variations in \(\tau_{r}\) with respect to \(T\) and \(\beta\). \(\tau_{r}\) showed remarkably similar behaviors to \(P_{r}\) with respect to \(T\). According to Equations (2) and (4), \(P_{r}\) and \(\tau_{r}\) were proportional to \((1-\beta)^{-1}\). From Figure 5A(b,c), it was impossible to determine the relationship between \(P_{r}\) and \(\beta\) with respect to \(T\). To quantify the contribution of \(T\) to \(P_{r}\) or \(\tau_{r}\), the other parameter (i.e., work = pressure \(\times\) volume or shear stress \(\times\) volume) was proposed by analyzing \(P_{r}\) or \(\tau_{r}\) with respect to \(\beta\) for each period. As shown in Figure 5B(a), to construct the X-Y plot, \(P_{r}\) (or \(\tau_{r}\)) and \(\beta\) were graphically represented on the Y-axis and X-axis, respectively. According to the definition of work, the pressure-volume work (\(W_{P}\)) was calculated as \(W_{P}=\int_{V_{1}}^{V_{2}}P_{r}dV\). The infinitesimal volume (\(dV\)) becomes \(dV=L\times h\times(W\ d\beta)\) as shown in Figure 1C. The \(W_{P}\) was then calculated as \(W_{P}=V\times\int_{\beta_{1}}^{\beta_{2}}P_{r}d\beta\). As the volume of the coflowing channel (\(V=L\times h\times W\)) remained constant, the pressure unit volume work (i.e., \(w_{p}=W_{P}/V\)) was then calculated as \(w_{p}=\int_{\beta_{1}}^{\beta_{2}}P_{r}d\beta\). Here, \(\beta_{1}\) and \(\beta_{2}\) represent the minimum and maximum values of \(\beta\) obtained for a single period, respectively. Similarly, using the same procedure for calculating \(w_{p}\) as above, the shear stress-volume work (\(W_{i}\)) was derived as \(W_{t}=V\times\int_{\beta_{1}}^{\beta_{2}}\tau_{r}d\beta\). The shear stress-unit volume work (i.e., \(w_{\tau}=W_{t}/V\)) was calculated as \(w_{\tau}=\int_{\beta_{1}}^{\beta_{2}}\tau_{r}d\beta\). As shown in the inset of Figure 5B(a), \(w_{p}\) and \(w_{\tau}\) are represented graphically by means of an X-Y plot (i.e., \(P_{r}\) vs. \(\beta\), \(\tau_{r}\) vs. \(\beta\)). Figure 5B(b,c) showed variations in \(w_{p}\) and \(w_{\tau}\) with respect to \(T\). \(w_{P}\) tended to increase with respect to \(T\). As shown in Figure 5A(a), the minimum value of \(\beta\) (i.e., \(\beta_{1}\)) decreased at higher values of \(T\). Integration of \(P_{r}\) from \(\beta_{1}\) to \(\beta_{2}\) increased at higher values of \(T\). Similarly, \(w_{\tau}\) tended to increase with respect to \(T\). The variations in \(w_{\tau}\) were remarkably similar to \(w_{P}\) with increasing \(T\).