A Novel Expression for the Effective Viscosity to Model Squeeze-Film Damping at Low Pressure

The Navier-Stokes equation is currentlyconsidered for modelling of squeeze-film damping in MEMS devices, also when the fluid flow associated to it is rarefied.In order to include rarefaction effects in such equation, a common approach consists of replacing the ordinary fluid viscosity with a scaled quantity, known as effective viscosity.The literature offers different expressions for the effective viscosity as a function of the Knudsen number (Kn). Such expressions were shown to work well whenKn<1, but theyresulted to be lessaccurate in case ofKn>1. In this paper a new expression is proposed to evaluate the effective viscosity for 1<Kn<40with increased reliability. Such anexpression was derivedfrom an optimized numerical-experimental procedure,developed in MATLAB® environment, using a finite element code and experimental data extracted from the literature. A comparison is finally reported and discussed between the results, in terms of damping coefficient, obtained considering previously reported effective viscosity expressions and the novel one,with reference to different squeeze film damping layouts, for which experimental data are already available.