## 3 Results and Discussion
Therefore, the FEA modeling also confirmed that both density and viscosity variations affect the SPMF\({}^{3}\) deflections. However, the FEA results have confirmed that the viscosity and density effects are opposite to each other. Figure 5: \(Cont.\)  
As explained earlier, viscosity and density are coupled in influencing the structural behavior and a comprehensive parameter would be helpful to capture their influence on microcantilever deflection. Hence, kinematic viscosity--which absorbs the combined effects of dynamic viscosity and density--is used to represent the fluid in order to capture the variation of dynamic viscosity and density. To address this issue here, the simulation results are presented with kinematic viscosity (Figure 5c) over a wide range, covering possible engineering applications. This shows how these two parameters--dynamic viscosity and density--can represent the fluid property under study when coupled together as a single parameter. The kinematic viscosity range is chosen to represent a variety of fluids from simple Newtonian fluids, such as water, to non-Newtonian fluids, such as milk and blood. Using design parameters of the SPMF\({}^{3}\), the theoretical prediction (Equation (7)) is compared with FEA results and shown in Figure 5c. These parameters are microchannel hydraulic diameter, (a = 133 \(\upmu\)m), velocity difference at nozzle sides, (\(\Delta V\) = 0.002 m/s), microcantilever stiffness, (\(k_{m}\) = 0.035 N/m) which is calculated based on E = 700 kPa [34], mass flow rate, (\(\dot{m}\) = 8.33 \(\times\) 10\({}^{-7}\) kg/s), and nozzle length, (\(l\) = 300 \(\upmu\)m). The parameters are substituted into the derived theoretical formula which can be simplified as \(v=k\delta-S\) where \(k\) is the resultant cantilever stiffness. The theoretical formulation can be used to design any SPMF\({}^{3}\) for required kinematic viscosity measurements. In other words, any variation in fluid concentration cannot exactly be predicted with only density or dynamic viscosity since both are changing and each parameter has a different effect on the static behavior of suspended microfluidics. The proposed suspended microcantilever has a unique response to changes in kinematic viscosity as is shown here, thus validating the SPMF\({}^{3}\) as an appropriate tool for measuring fluid property through kinematic viscosity. In a similar way, prediction has been continued for other fluids such as acetone, DI water, blood, milk and the results are presented against kinematic viscosity in Figure 6. These fluids were selected to basically cover a reasonable range of the fluids, representing both Newtonian and non-Newtonian fluids together. In order to validate the SPMF\({}^{3}\) platform for kinematic viscosity measurements, the experimental results with water-salt solutions and milk, in Table 1, are compared with finite element analysis and simplified prediction formulation in Figure 6. As is shown here, there is a good agreement among the theoretical, finite element and experimental results. These results are shown in the logarithmic format in order to represent fluid properties in equally expanded regions. As is shown,  
Figure 5: Finite element analysis results of microcantilever deflection when fluid density or viscosity was changed, (**a**) against density at constant viscosity, \(\mu\) = 0.89 cP, (**b**) against viscosity at constant density, \(\rho\) = 997 kg/m\({}^{3}\), (**c**) finite element analysis (FEA) and theoretical results of microcantilever deflection against kinematic viscosity. kinematic viscosity can be employed for studying variation in fluid properties specifically in a more comprehensive way. The error bars of experimental results were calculated according to the geometrical scheme of the laser deflection measurement system. There are three main sources of error--laser angle, Photo Sensitive Detector (PSD) angle and microcantilever position--that should be considered in this experiment.