A visco-thermal model for a novel type of electrostatic micromachined in-plane ultrasound transducer

The acoustic fields within the microchannels of an in-plane electrostatic ultrasound transducer are analysed in this work by means of the Low Reduced Frequency (LRF) approximation of the Navier–Stokes equations. This device is composed primarily of two kinds of structures that can be described in rectangular coordinates – a prismatic slit and a cavity with curved walls –, for which a solution of the LRF equations is presented. The interaction between these two elements in an actual device is solved by an approximate model whereby the propagation modes are transmitted from one component to the other without energy losses. The solution of the LRF equations in the isolated components offered results that were in good agreement with equivalent finite-element simulations of the Full Linearised Navier–Stokes (FLNS) equations, whereas the approximate model of the complete structure slightly overestimates the output pressure in comparison to the corresponding simulation. The predictions of the analytic and finite-element models of the device were compared against an actual measurement, finding an approximate correspondence, although certain effects remain to be predicted by a more accurate analysis of the radiation pattern of the device.