April 27, 2001 15:1 WSPC/156-IJCES 00023 International Journal of Computational Engineering Science Vol. 2, No. 1 (2001) 1–15 c  Imperial College Press ARBITRARY LAGRANGIAN EULERIAN ANALYSIS OF A BIDIRECTIONAL MICRO-PUMP USING SPECTRAL ELEMENTS ALI BESKOK Mechanical Engineering Department, Texas A&M University, College Station, TX-77843, USA E-mail : abeskok@mengr.tamu.edu TIMOTHY C. WARBURTON Division of Applied Mathematics, Brown University, Providence, RI 02912, USA E-mail : timw@cfm.brown.edu Performance analysis of a reversible micro-pump system is obtained by numerical sim- ulations. The unsteady incompressible Navier–Stokes equations are solved in a moving micro-pump system using a spectral h/p element algorithm, employing an arbitrary Lagrangian Eulerian (ALE) formulation on structured/unstructured meshes. The per- formance of the micro-pump is evaluated as a function of the Reynolds number and the geometric parameters. The volumetric flowrate is shown to increase as a function of the Reynolds number. The unsteady traction forces on the pump membrane and the vorticity dynamics within the pump cavity are presented. Keywords : Bidirectional Micro-Pumps; CFD for MEMS; ALE; Spectral H/P Methods. 1. Introduction Micro-pump systems delivering volumetric flow rates in the order of 10 -8 ∼ 10 -12 m 3 /s can be used in various biofluidic, drug delivery, mixing and flow con- trol applications. Most of the micro-pump systems are actuated by a vibrating membrane in a chamber with hanging-beam-type (Cantilever beam) inlet and exit micro-valves. 1– 3 Since the Cantilever-type micro-valves only open in a preferred flow direction, designs utilizing such valves are strictly unidirectional. Bidirectional micro-pumps have also been proposed, where a rotating cylinder is located asym- metrically within a micro-channel, and it propels the fluid due to the viscous action while turning with a prescribed angular speed. 4,5 This “novel micro-pump” works well for low Reynolds number flows. However, its efficiency rapidly diminishes with increased Reynolds number, as fluid inertia takes over. Also for gas flows the small dimensions of this device, required to maintain small Reynolds numbers, create a further complication. When the local Knudsen number defined as the ratio of mean freepath λ to the channel width h, approaches Kn ≃ 0.01 the “velocity slip effects” 1