## 2 Materials and Methods
### Mathematical Representation of Pressure and Shear Stress of Each Stream in Coflowing Channel  
To determine analytical expressions of pressure and shear stress, the coflowing channel filled with the test fluid and reference fluid was analytically modeled with discrete fluidic circuit elements (i.e., flow rate and fluidic resistances). As shown in Figure 1C(a), the coflowing channel consists of two streams (i.e., reference fluid stream [r] and test fluid stream [t]). Each stream was represented mathematically by fluidic discrete elements, such as fluidic resistance (\(R_{t}\), \(R_{r}\)) and fluid rate (\(Q_{r}\), \(Q_{t}\)). \"Ground\" indicated zero pressure as the reference value. As the coflowing channel (channel length [\(L\)]) had a straight and rectangular channel, both streams had the same pressure (i.e., \(P_{t}\approx P_{r}\)). Although the analytical expression of pressure was reported in a previous study [55], the measurement accuracy deteriorated significantly when the interface moved to each wall from the middle plane [56]. Instead of the previous analytical model, a simple discrete circuit model was suggested using the virtual wall concept. As shown in Figure 1C(b), each stream was separated mathematically using a virtual wall. The coflowing channel was partially filled with the test fluid stream (\(\beta\times W\)) and the reference fluid stream (\([1-\beta]\times W\)). According to a previous study [30], a correction factor for pressure (\(C_{P}\)) was included to compensate for the difference in boundary conditions between the real physical model and discrete circuit model. For a rectangular channel with a lower aspect ratio of 0.08 [57], the analytical expression of the pressure for each fluid stream was derived as  
\[P_{t}=\frac{12\;\mu_{t}L}{C_{P}\;\beta\;W\;h^{3}}\times Q_{t},\text{ for the test fluid stream} \tag{1}\]  
\[P_{r}=\frac{12\;\mu_{r}L}{(1-\beta)\;W\;h^{3}}\times Q_{r}\text{ for the reference fluid stream}, \tag{2}\]  
respectively. Here, \(\mu_{r}\) and \(\mu_{t}\) are the viscosities of the reference and test fluids, respectively. Using the same pressure condition (\(P_{t}=P_{r}\)), the viscosity of the test fluid was derived as follows:  
\[\mu_{t}=\mu_{r}\times\frac{\beta}{1-\beta}\times C_{P}\times\left(\frac{Q_{r} }{Q_{t}}\right) \tag{3}\]  
Based on the force balance between the shear stress and pressure along the test fluid stream (i.e., \(\oint\tau_{r}dS=\iint P_{r}dA\)), the relationship between shear stress and pressure was given as \(\tau_{r}\times(2\beta W\times L)=P_{r}\times(\beta W\times h)\). Here, it was assumed that the shear stress acted along the top and bottom surfaces. Using Equation (1), the shear stress of the reference fluid stream (\(\tau_{r}\)) was calculated as:  
\[\tau_{r}=\mu_{r}\times\frac{6Q_{r}}{(1-\beta)\times W\times h^{2}} \tag{4}\]  
Using a procedure similar to that discussed as above, the shear stress of the test fluid stream was derived as follows:  
\[\tau_{t}=\mu_{t}\times\frac{6Q_{t}}{C_{P}\times\beta\times W\times h^{2}} \tag{5}\]  
From Equations (3)-(5), both streams in the coflowing channel had the same shear stress (i.e., \(\tau_{r}=\tau_{t}\)).