Slip-flow Pressure Drop in Microchannels of General Cross-section

In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross-section microchannels. An averaged firstorder Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to the Poisson’s equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. Bahrami et al.’s model, which was developed no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model is a function of geometrical parameters of the channel: crosssectional area, perimeter, polar moment of inertia and the Knudsen number. The model is successfully validated against existing numerical and experimental data from different sources in the literature for several shapes, including: circular, rectangular, trapezoidal, and double-trapezoidal cross-sections and a variety of gases such as: nitrogen, argon, and helium. NOMENCLATURE Cross-sectional area, Hydraulic diameter, . Complete elliptic integral of the second kind Poiseuille number Polar moment of inertia, Dimensionless polar moment of inertia, / Knudsen number Characteristics length, Pressure, / Reynolds number √ Square root of area, Axial velocity, / Local slip-velocity, / Average slip-velocity, / Relative velocity, / Greek symbols Perimeter, Aspect ratio Molecular mean free path, Viscosity, . / Tangential momentum accommodation factor Averaged wall shear stress, / Local shear stress, / Φ reduction of friction coefficient in slip condition,