Determining the validity of slip models for MEMS flows

Matthew McNenly, University of Michigan

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Many fluidic microelectomechanical systems (MEMS) operate in the slip regime where the molecular spacing of the fluid is about 1% of the length scale of the device. The non-equilibrium effects associated with flow in the slip regime are limited to a region near the surface termed the Knudsen layer, which typically has a thickness on the same order as the molecular spacing. Within this layer there are insufficient molecular collisions to achieve thermodynamic equilibrium, and as a consequence, the traditional continuum solutions fail. However, in the slip regime, the non-equilibrium region accounts for only 1% of the flow area, meaning the continuum equations apply throughout most of the flow. The small non-equilibrium region and the advantages in computational efficiency over low speed direct simulation prompt the usage of continuum methods that have corrected boundary conditions to allow for non-equilibrium effects. The correction is often referred to as a slip model because it permits a slip velocity at the boundary. Of the numerous slip models that have been proposed, most trace their origins to Maxwell’s first-order correction to the no-slip boundary condition. Despite the common foundation, there is not a consensus among the models as to the range of applicable flow conditions. The focus of this research is to assess the different slip models using particle, continuum, and theoretical methods to determine when the underlying assumptions break down.

Abstract Author(s): Matthew J. McNenly, Michael A. Gallis, Iain D. Boyd