Three dimensional effects in compressible, rarefied gas flow in bent microchannels

Numerical investigation of pressure-driven gas flow in three-dimensional (3D) bent microchannel is carried out by the Navier – Stokes equations coupled with first order slip boundary condition. Several facets of the problem are investigated, including the influence of geometrical details such as channel aspect ratio and bend radius of curvature, as well as the impact of rarefaction and compressibility. Pressure nonlinearity, Mach number distribution, slip velocity profiles and mass flow rate are computed and commented. The results show that the additional losses induced by the bend, with respect to the straight channel, are almost negligible at high rarefaction levels. Actually, for higher values of Kn the mass flux through the bent microchannel can even be slightly larger than that through a straight microchannel of the same length and subjected to the same pressure gradient. Moreover, this increase in mass flow rate for 3D case is larger than for 2D one. Smoothed bend further reduce the effect of the bend, with respect to sharp corner geometries. Rarefaction effect on mass flow is smaller at smaller radius, nevertheless compressibility effect compensates the rarefaction resulting in a lower increase in mass flow at higher pressure ratio. Compressibility effect increases pressure losses, thus partially compensating the increase in the mass flow due to the rarefaction, at least for higher pressure ratio. For large aspect ratios flow distributions, as expected, get closer to some 2D limit lines.