The miniaturization of microphones is of great interest for several fields, such as medical applications (audio implants), or consumer electronics (cell phones). Almost all existing miniature microphones rely on electrostatic transduction and offer good performances (sensitivity, frequency bandwidth). However, their sensitivity, proportional to the membranes area, would be dramatically reduced in case of extreme miniaturization. A new concept of microphones developed by CEA-LETI, which uses membranes moving in the plane of the substrate and inducing strain on piezoresistive Si nano-gauges (M&NEMS technology), seems promising for its miniaturization potential without significant decrease of sensitivity. The design and optimization of such planar piezo-resistive microphone require a deep understanding of its acoustic and vibroacoustic behavior. Regarding the small dimensions of the slits (1-100µm) and the sharp discontinuities in the microphones structure, viscous and thermal effects in the boundary layers and turbulent perturbations are of great importance, and must then be taken into account with high accuracy in device modeling. The aim of the present work is to provide accurate analytical and numerical (FEM) models able to gather all these effects in a consistent manner, and to suggest an experimental method to check their validity.