A Refined Modeling for the Liquid Loading Effect in Microacoustic Sensors

The liquid loading effect on microacoustic sensors can be modeled using an acoustic impedance boundary condition. A rigorous expression for the acoustic impedance tensor is derived for isotropic linear elastic layers backed by a defined impedance. This formulation is generalized to enclose viscous liquids. Furthermore, the impedance tensor is also applied to the half-space, free surface and rigid backing boundary conditions and is compared to the one dimensional expressions of bulk impedance for the half-space and the transmission line equations for layers of finite thickness. In contrast to these 1D expressions, the coupling of pressure- and shear-wave propagation is considered which results in interesting phenomena for viscous liquid layers. For example, it is found that also for liquid layers much thicker than the decay length of the shear waves (e.g., hundreds of nanometers for a QCR in the lower MHz range), the boundary affects the shear impedance, due to pressure and shear wave coupling.