The sensing element consists of a thin piezoelectric bulk acoustic wave (BAW) plate that operates in the thickness shear mode of vibration (TSM). As shown in the figure, the displacement profile is throughout the thickness of the plate and maximum at the surfaces. Because the displacement is parallel to the surface of the plate, and the fluid interface, it makes the TSM BAW sensing element an ideal solution for measuring the viscosity of a fluid. Just like many other lab based methods of viscosity measurement, motion applied to the fluid is shear; however, unlike many other methods of viscosity measurement, the displacements are atomic scale and at a frequency of 5.25 million cycles per second. The sensing element is packaged to allow one surface to interact with the fluid under test (Figure 1b).

Figure 1. SenGenuity BAW viscosity sensing element. (a.) Cross-sectional view of the sensing element and the displacement profile. (b.) Packaged sensing element to allow one surface of the sensor to interact with the target fluid.

The importance of these acoustic sensors lies in the distinctly different measurement principle. Whereas one class of mechanical devices measures kinematic (flow) viscosity and the other class measures intrinsic (friction) viscosity, the AW sen¬sors measure acoustic impedance, (ωρη)^½, where ω is the radian frequency (2ττf), ρ is the density and η is the intrinsic viscosity.

The viscosity measurement is made by placing the BAW TSM resonator in contact with liquid. The liquid's viscosity determines the thickness of the fluid hydro-dynamically coupled to the surface of the sensor. The sensor surface is in uniform mo¬tion at frequency, ω=2ττf, with amplitude, U. The frequency is known by design and amplitude is determined by the power level of the electrical signal applied to the sensor. As the shear wave penetrates into the adjacent fluid to a depth, d, determined by the frequency, viscosity and density of the liquid as d=(2η/ωρ)^½, as depicted in Figure 3.

Figure 3. Hydro-dynamically coupled fluid layer on the surface of the BAW viscometer with a shear wave penetration defined by the penetration depth d.

Acoustic viscosity is calculated using power loss from the piezoelectric resonator into the fluid. The unit of measure is acoustic viscosity (AV), also known as Andle's Viscosity, and is equal to ρη, (g/cm3 • cP) or ρ²ν, ((g/cm3 )2• cSt). Acoustic viscosity is thus equal to density times the dynamic viscosity or density-squared times the kinematic viscosity.

The acoustic wave resonator supports a standing wave through its thickness. The wave pattern interacts with electrodes on the lower surface (hermetically sealed from the liquid) and interacts with the fluid on the upper surface. The bulk of the liquid is unaffected by the acoustic signal and a thin layer (on the order of microns or micro inches) is moved by the vibrating surface. As shown in Figure 4, for the SenGenuity bulk acoustic wave viscometer operating at 5.25MHz, the penetration depth into the fluid is ideal for measuring the viscosity of homogeneous fluids like lubricants and the viscosity measurement will not be susceptible to large particles or debris because the small penetration depth makes them virtually unnoticeable.

Figure 4. AW penetration depth (um) vs. kinematic viscosity. This graph assumes an operating frequency of 5.25MHz and a constant density of 0.850g/cm3.

Generating Correlation Functions for a Specific Lubricant Type:
As mentioned in the section above, AW viscometers measure acoustic impedance, (ωρη)½ and are calibrated to report acoustic viscosity (ρη) referenced to a laboratory method taken at a very low frequencies of measurement. To achieve this calibration, SenGenuity uses Galden® perfluoropolyether fluids characterized with an Anton Paar Stabinger Viscometer and Density Cell; the Galden® fluids are very homogeneous and Newtonian. Because lubricants vary considerably in their molecular and chemical compositions, the viscosity, η, at 5.25MHz can sometimes be very different than the viscosity at lower frequencies typically given by laboratory grade viscosity measurements. Because of this and other factors including shear rate dependence and Maxwellian effects, the translation of the measured acoustic impedance, (ωρη)½ into acoustic viscosity may be fluid dependent resulting in a systematic error in reported acoustic viscosity when compared to acoustic viscosity calculated from reference lab measurements. As shown in Figure 5, a measurement of our Galden HT-270 calibration fluid will result in a one for one correlation of the reported sensor acoustic viscosity and the acoustic viscosity calculated from lab measurements.