A calculation of gaseous slip velocity and microscale flow fields from a molecular-continuum matching analysis

Abstract

Small-scale gaseous flows cannot be described as a continuum, especially at boundaries where molecular interactions of the fluid with a wall takes place. Work has been done to match molecular dynamics simulations near a wall to continuum flow away from a wall [S.T. O'Connel, P.A. Thompson, Phys. Rev. E 52, R5792.2.]. Microscale flow fields have also been calculated by solving the Navier–Stokes equations with a Maxwellian slip boundary condition [E.B. Arkilic et al., J. Microelectromech. Systems 6 (2) (1997) 167–178.]. This paper, in two dimensions, calculates microscale flow fields and slip velocities ab initio by matching, with a novel computer algorithm, analysis of molecular interaction with boundaries to continuum flow away from the boundaries for wall-velocity-step-jumped-time-varying Poiseuille flow. Slip velocities are also calculated in the steady-state case for Poiseuille flow. Drift velocities approximately one mean free path from the walls are found to be between 20–30% of the maximum flow field velocity along the length of the channel for transient analysis of helium gas and 5–36% of the maximum velocity for steady-state analysis of various gases. These ratios are consistent with past calculations of flow fields calculated with a prescribed Maxwellian slip boundary condition (E.B. Arkilic et al., 1997.).