## 1 Introduction  
Fluid density and viscosity result in inertia, or resistance to move or flow. If we assume that fluid molecules are located in multiple sheets placed one on top of another, viscosity is defined as the friction force between these sheets. Based on the application and fluid properties, two types of fluid viscosity, called dynamic viscosity and kinematic viscosity, are defined. Dynamic viscosity is mainly used for comparing different fluids based on their flow resistivity. This resistance comes from the Van der Waals force among molecules of fluid layers. The more force which comes from the electron cloud density of atoms, the higher the viscosity effect on fluid flow. The fluid molecules have a specific mass which comes into effect when kinematic viscosity is being employed. The higher the molecule mass is, the more it produces inertia at the molecular level, thus the lower the tendency (or more inertia) to move and transfer momentum to other layers. The fluids with their dynamic viscosity dependent on shear rate are called non-Newtonian fluids and the rest are defined as Newtonian fluids. For example, blood viscosity changes with shear rate which results in lower viscosity in capillaries and higher viscosity in larger veins [1]. In other words, an external force applied to non-Newtonian fluids affects their viscosity and shear rate [2; 3]. In order to interpret this non-Newtonian effect, a deeper understanding of kinematic viscosity is required. The non-Newtonian behavior is mainly due to the structural organization of molecules inside the fluid. For example, in colloidal fluids such as blood, the shear thinning behavior is because of segregation of particles and phases inside the fluid. Thus, connection between phases inside a non-Newtonian fluid will increase the fluid viscosity and density in a control volume, such as a capillary. Here, the definition of kinematic viscosity, \(v=\mu/\rho\), affects the connection among phases inside a fluid in a way that not only changes the distance between them and their interaction forces, but also the fluid density in a control volume. Thus, kinematic viscosity varies with shear stress in non-Newtonian fluids. Any variation in fluid substances during a process affects both density and viscosity, therefore another comprehensive parameter which considers both is required in order to identify and study the fluid in a more comprehensive way during different processes. In order to measure fluid parameters, there has been lots of interest towards employing microelectromechanical systems (MEMS) based viscometers due to their accuracy, simplicity and compatibility with different industries. There are three types of microsensors that have been used mostly in dynamic viscosity measurement: vibrating microcantilever [4] and plate, quartz crystal resonators [5] and microfluidic systems [6]. The governing equations of these micro-viscometers--vibrating microcantilever, Equation (1); quartz crystal resonators, Equation (2); and transduction principle of the microfluidic sensors--are as follows. \[\textbf{Vibrating microcantilever},\ \frac{\mu}{\rho}=\pi b^{2}\Gamma_{r}(\omega_{R})/4(( \frac{\omega_{vac}}{\omega_{R}})^{2}-1) \tag{1}\]  
\[\textbf{Quartz crystal resonator},\ \mu\rho=\pi E_{Q}\rho_{Q}(\Delta f)^{2}/f_{o}^{3} \tag{2}\]  
\[\textbf{Microfluidic sensors},\ \text{transduction principles are pressure difference, image}\] \[\text{processing, and impedance variation}\]  
where \(\mu\) is fluid dynamic viscosity, \(\rho\) is fluid density, \(\omega_{vac}\) is frequency response in a vacuum, \(\omega_{R}\) is frequency in fluid medium, \(b\) is microcantilever width and \(\Gamma_{r}\) is hydrodynamic function in the governing function for microcantilevers. In quartz crystal resonators, \(E_{Q}\) is elastic modulus, \(\rho_{Q}\) is density of the quartz crystal, \(\Delta f\) and \(f_{o}\) are frequency shift and natural frequency of free crystal, respectively. Quartz resonators employ piezoelectric surfaces which can make high frequency vibrations with low amplitude.