Transient Slip Flow in Microchannels

Abstract

The assumption usually made of spatially fully developed flow during

: transient establishment is revised here. A computational model for transient two­

dimensional Navier-Stokes equations has been used to study both time and space development of flow due to a sudden pressure rise. Two kinds ••of • boundary conditions are used, the no-slip condition as well as the slip condition encountered in microchannels. Compressibility effects are however neglected in order to concentrate on slip effect. Microchannel of height 100 11m and 750 11m length was investigated at different pressure drop values (400, 575, 750, 900 Pa) for both slip and no slip conditions. Also the case ofpressure difference 750 Pa was studied at different slip lent,rth values ranging from 1 to 4 11m The flow rate, velocity profile, pressure distribution along the channel, and the developing length were obtained as a function of time. Also, the velocity profile was obtained at different locations during the developing region. The results show that flow rate, velocity profile, pressure distribution, and developing length depends to a great extent on the pressure difference across the microchannel for both slip and no slip conditions, in such away that increasing the pressure difference increases the discharge and the developing length. For all investigated values of pressure drop, the developing length for slip conditions is higher than that for no slip conditions in the fully developed region. The results also show that the developing length reaches about 1.1 of the hydraulic diameter, which