An extended Langhaar’s solution for two-dimensional entry microchannel flows with high-order slip

Abstract

The tremendous advances in micro-fabrication technology have brought numerous applications to the field of micro-scale science and engineering in recent decades. Microchannels are inseparable part of microfluidic technology which necessitate knowledge of flow behavior inside microchannels. For gaseous flows, the mean free path of a gas is comparable with characteristic length of a microchannel due to the micro-scale dimension of the channel. So, no-slip velocity assumption on the boundaries of channel is no longer valid, and a slip velocity needs to be defined. Although rigorous modeling of rarefied flows requires molecular solutions, researchers proposed use of slip models for applicability of the continuum equations. In slip-flow regime (i.e. Knudsen numbers up to 0.1), well-known Maxwell’s first-order slip model is applicable. For higher Knudsen numbers, higher-order slip models can be implemented to extend the applicability limit of the continuum equations. In the present study, Langhaar’s assumptions for entrance region of two-dimensional microchannels (microtube, slit-channel and concentric annular microchannel) have been implemented using high-order slip models. Different slip models proposed in the literature have been used and velocity profile, entrance length and apparent friction factor have been obtained in integral forms.