In order to test the principle functionality of the Bio-MEMS FPW-sensor, four low-viscous liquids are applied. DI-Water, Isopropanol Alcohol (IPA), Tris buffer and saline solution (4 M NaCl) are used. Here, the viscosity effect is negligible in comparison with the mass loading effect [8]. The densities of the used liquids are listed in . Further, theoretical FPW-sensor considerations according to [3] led to the listed calculated sensor characteristics. The Bio-MEMS FPW-sensor propagates and acoustic wave via a mechanical thin plate. The resonant frequency *f*_{0} of a FPW-sensor membrane is given by ,

$${f}_{0}=\frac{{v}_{p}}{\lambda}\text{\hspace{1em}}\left(1\right)$$( 1 )where λ is the acoustic wavelength and is the phase velocity. The phase velocity *v*_{p,g} in air is given by ,

$${v}_{p,g}=\sqrt{\frac{A}{M}}\text{\hspace{1em}}\left(2\right)$$( 2 )where *A* is the bending stiffness of a homogeneous plate,

$$A={\left(\frac{\lambda}{2\pi}\right)}^{2}\frac{E\cdot {d}^{3}}{12\left(1-{\upsilon}^{2}\right)}\text{\hspace{1em}}\left(3\right)$$( 3 )and where *E* is the Young’s modulus, *ν* is the Poisson’s ratio, *d* is the membrane thickness. M is the mass per unit area of a homogeneous isotropic membrane plate.

The Bio-MEMS FPW-sensor is operated in liquid media. Thus, an additional stiffness effect is introduced by the liquids weight. The corrected phase velocity of the membrane under tensile stress and liquid loading, *v*_{p,l}, is given by ,

$${v}_{p,l}=\sqrt{\frac{{T}_{x}+A}{M+\rho \iota {\delta}_{E}}}\text{\hspace{1em}}\left(4\right)$$( 4 )where *T*_{X} is the component of in-plane tension in x-direction, *ρ*_{l} is the density of the liquid, *δ*_{E} is the evanescent decay length. Because only low viscous liquids are considered in this work, any viscosity effects are neglected.

T**able 1:** Bio-MEMS FPW-sensor modelling for different liquids.

In , the shifts of the resonant frequency of a Bio-MEMS FPW-sensor are shown for injections of the lowviscous liquids. The sequence of injecting each 100 μl of saline solution, IPA and DI-Water was applied twice.

**Figure 2:** Response of a Bio-MEMS FPW-sensor after the injection of each 100 μl 4 M NaCl, Di-water and IPA in Tris.

In the resonant frequencies are plotted against the density. The sensitivity of the Bio-MEMS FPW-sensor is about - 0.39 MHz/g/cm^{3} and has a linear regression coefficient R^{2} of 0.967. The shown frequency shifts are evaluated and compared to the calculated resonant frequencies listed in .

The results obtained in this work are compared with a related FPW device [8]. It has a similar period of the IDT structures (40 μm) and a similar total membrane thickness (2.3 μm). The area of the membrane, however, is much larger compared to this work (11.34 mm^{2} vs. 0.53 mm^{2}). Thus, this FPW device is most likely less affected by microfluidic coupling issues. In this work, the liquid injection is dynamical, whereas the liquid load is applied statically in [8]. In , the results of both works are plotted with calculated and measured frequency shifts. The calculated sensitivity of the reference FPW device is - 0.85 MHz/g/cm^{3} (R^{2} = 0.998) and the measured sensitivity is about - 0.60 MHz/g/cm^{3} (R^{2} = 0.813).

The comparison of both FPW-sensors shows that the Sensor of this work is designed to show a much higher sensitivity. While the referred FPW device shows a relatively good agreement to the model, the here presented Bio-MEMS FPW-sensor shows a deviation by a factor of 7.7. A potential reason may be the microfluidic. Injected liquids may not completely fill the cavity upon a Bio-MEMS FPW-sensor membrane, thus replacing the prior liquid only partially. Then, the change in density can become much smaller than theoretically assumed.

**Figure 3:** Sensitivity analysis of the calculated and measured resonant frequencies of a Bio-MEMS FPW-sensor and the density of low-viscosity liquids for a pump rate of 500 μl/min.

**Figure 4:** Comparison of the calculated and measured resonant frequencies of a Bio-MEMS FPW-sensor in this work to a FPW-device in [8].