Treatments of flows through micro-channels based on the Extended Navier-Stokes-Equations

Abstract

The paper briefly refers to the present treatments of micro-channel flows that are based on the existing Navier-Stokes-Equations and the employment of wall-slip boundary conditions. The Maxwell slip velocity is employed for this purpose. This theoretical treatment is questioned. It is shown by the authors that the existing Navier-Stokes-Equations are incomplete. They do not contain terms for the self diffusion of mass. Introducing these terms yields the extended Navier-Stokes-Equations that allow micro-channel flows to be treated without the assumption of Maxwellian slip velocities at the wall. A pressure driven slip velocity occurs at the wall and it results as part of the solution for flows in micro-channels by the “Extended Navier-Stokes Equations”. Using these equations, analytical treatments of micro-channel flows are presented. Good agreement with existing experimental results is obtained.