An Extended Langhaar’s Solution for Two-Dimensional Entry Microchannel Flows with High-Order Slip
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 So, no-slip velocity assumption on the boundaries of channel is no longer valid, and a slip velocity needs to be defined.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.
KeywordsMicrochannel flow High-order slip Langhaar’s solution
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