Incompressible Criterion and Pressure Drop for Gaseous Slip Flow in Circular and Noncircular Microchannels

Slip flow in various noncircular microchannels has been further examined, and a simple model for a normalized Poiseuille number is proposed. As for slip flow, no solutions or graphical and tabulated data exist for most geometries; the developed simple model fills this void and can be used to predict the Poiseuille number, mass flow rate, tangential momentum accommodation coefficient, pressure distribution, and pressure drop of slip flow in noncircular microchannels by the research community for the practical engineering design of microchannels. The incompressible flow criterion for gas flow in microchannels is given. A Mach number less than 0.3 is not sufficient to ensure that the flow is incompressible. Compressibility depends on the product of two dimensionless parameters: $L/L(DRe)(DRe)$ and Ma (Arkilic et al., 1997, “Gaseous Slip Flow in Long Microchannels,” J. Microelectromech. Syst., 6(2), pp. 167–178). Some flows where Ma < 0.3 are low speed compressible flows. A fresh general pressure drop model for isothermal low Mach number compressible flow in microchannels is proposed. If the pressure drop is less than 10% of the outlet pressure, the flow can be considered as incompressible for practical engineering applications. This paper improves and extends previous studies on slip flow in noncircular microchannels.