Low Mach number slip flow through diverging microchannel

Abstract

This paper presents experimental and three-dimensional numerical study of gaseous slip flow through diverging microchannel. The measurements are performed for nitrogen gas flowing through microchannel with different divergence angles (4°, 8°, 12° and 16°), hydraulic diameters (118, 147 and 177 μm) and lengths (10, 20 and 30 mm). The Knudsen number falls in the continuum and slip regimes (0.0005 ⩽ Kn ⩽ 0.1; Mach number is between 0.03 and 0.2 for the slip regime) while the flow Reynolds number ranges between 0.4 and 1280. The static pressure drop is measured for various mass flow rates; and it is observed that the pressure drop decreases with an increase in the divergence angle. The viscous component has a relatively large contribution in the overall pressure drop. The numerical solution of the Navier–Stokes equations with the Maxwell’s slip boundary condition shows absence of flow reversal (due to slip at the wall), larger viscous diffusion and lower kinetic energy in the diverging microchannel. The centerline velocity and wall shear stress decrease with an increase in the divergence angle. The numerical results further show three different flow behaviors: a nonlinear pressure variation with rapid flow deceleration in the initial part of the microchannel; uniform centerline velocity with linear pressure variation in the middle part, and flow acceleration with nonlinear pressure variation in the last part of the microchannel. A characteristic length scale for diverging microchannel is also defined. The location of the characteristic length is a function of the Knudsen number and shifts toward the microchannel inlet with rarefaction. Mass flow rate and pressure distribution along the channel are also obtained numerically from the direct simulation Monte Carlo (DSMC) method and compared suitably with the experimental data or Navier–Stokes solutions. Empirical relations for the mass flow rate and Poiseuille number are suggested. These results on gaseous slip flow through diverging microchannels are considerably different than their continuum counterparts, and are not previously available.