Kowarsch Robert, Suhak Yuriy, Eduarte Lucia Cortina, Mansour Mohammad, Meyer Frederick, Peschel Astrid, Fritze Holger, Rembe Christian, Johannsmann Diethelm
Institute of Electrical Information Technology, Clausthal University of Technology, Leibnizstr. 28, D-38678 Clausthal-Zellerfeld, Germany.
Institute of Energy Research and Physical Technologies, Clausthal University of Technology, Am Stollen 19B, D-38640 Goslar, Germany.
Sensors (Basel). 2020 Apr 29;20(9):2535. doi: 10.3390/s20092535.
The operation of the quartz crystal microbalance (QCM) in liquids is plagued by small flexural admixtures to the thickness-shear deformation. The resonator surface moves not only in the transverse direction, but also along the surface normal, thereby emitting compressional waves into the liquid. Using a simple analytical model and laser Doppler vibrometry, we show that the flexural admixtures are stronger on the fundamental mode than on the overtones. The normal amplitude of motion amounts to about 1% of the transverse motion on the fundamental mode. This ratio drops by a factor of two on the overtones. A similar dependence on overtone order is observed in experiments, where the resonator is immersed in a liquid and faces an opposite planar wall, the distance of which varies. Standing compressional waves occur at certain distances. The amplitudes of these are smaller on the overtones than on the fundamental mode. The findings can be rationalized with the tensor form of the small-load approximation.
石英晶体微天平（QCM）在液体中的运行受到厚度剪切变形中微小弯曲混合效应的困扰。谐振器表面不仅在横向移动，还沿表面法线方向移动，从而向液体中发射压缩波。通过一个简单的分析模型和激光多普勒振动测量，我们表明弯曲混合效应在基模上比在泛音上更强。在基模上，法线方向的运动幅度约为横向运动的1%。在泛音上，这个比例下降了一半。在实验中也观察到了对泛音阶数的类似依赖关系，其中谐振器浸入液体中并面对一个相对的平面壁，其距离可变。在特定距离会出现驻波压缩波。这些波在泛音上的幅度比在基模上小。这些发现可以用小负载近似的张量形式来解释。
