Simulation of MEMS speakers using the linearized flow equations with Maxwell slip boundary conditions

The acoustic simulation of microstructures in Micro-Electro-Mechanical-Systems (MEMS) usually requires including viscous effects. In the case of channels and gaps in the low μm- to high nm-range, continuum theory no longer holds, and appropriately extended or different sets of equations have to be used. In this contribution, we investigate the influence of using a Maxwell slip boundary condition for the linearized compressible flow equations to extend the usability in the slip flow regime (Knudsen number Kn ≤ 0.1) for acoustic computations. This technique is widely used in fluid dynamics but is uncommon within the acoustic community. Nevertheless, the increased demand for modeling MEMS loudspeakers and other acoustic microstructures poses new requirements for simulation tools, rendering this technique a viable choice to extend currently used acoustic software packages. We compare simulations of a MEMS speaker based on an ultrasound pumping principle (Advanced Digital Sound Reconstruction – ADSR) using different boundary conditions and their effect on the achievable sound pressure. Due to the stress-dependent slip velocity, sealing effects seem to be slightly overestimated for the application example using a classical no-slip boundary condition. Hence, the achievable sound pressure drops slightly, albeit not more than a few percent.