Numerical Simulation of an Electroosmotic Micromixer

We present a micromixer fabricated using MEMS technology which takes advantage of electroosmosis to mix fluids. A time dependent electric field is applied and the resulting electroosmosis perturbs the low Reynolds number flow. It is shown that the electric field can be deemed quasi-steady and the electroosmotic slip boundary condition can be applied when the incompressible Navier Stokes equation is solved. Both the electric field and the electroosmotic flow are simulated numerically. Study of the particle traces shows folding and stretching of material lines, and a positive Lyapunov exponent is found which indicates chaotic-like mixing. INTRODUCTION The ability to mix two or more fluids thoroughly and in a reasonable amount of time is critical to the creation of fully integrated “on-chip” micro-electromechanical fluid processing systems. But mixng in micron sized channels is difficult due to the low Reynolds numbers that characterize these flows. The flow is restricted to the laminar flow region and there is no turbulence which could assist the mixing. If we rely only on molecular diffusion to mix the fluids, the mixing channel must be extended to be extremely long. To achieve fast mixing, several passive micromixers have been developed and studied, such as the T-type [1], L-shaped [2], Address all correspondence to this author. serpentine pipe [3], flow splitting [4], ridged-floor mixer [5] and so on. They do not improve mixing significantly, and need to be fabricated delicately. A few active micromixers have also been demonstrated. A mixing chamber mimicking a source/sink system [6] is designed to stir fluids effectively using microfabricated valves and phase-change liquid micropumps. Pressure disturbances from side channels have also been added to microchannel flows to enhance mixing [7,8]. Encouraging progress in enhancing mixing has been reported. In the past two decades it has been demonstrated that chaos can be used to mix fluids in laminar flows [9], and the chaotic regimes are associated with stretching and folding of material lines [10]. Chaos may arise in a nonlinear dynamical system provided that the system has at least three dimensions. Adding a time dependent external perturbation to a two dimensional flow provides the third dimension, and chaotic mixing may arise. Here we present a silicon microfabricated mixer with no moving parts, which makes use of time dependent electroosmotic flow to mix two fluids. Numerical simulation is carried out to help understand the mixing of fluids in this micromixer. DESCRIPTION OF THE MIXER The geometry of our electroosmotic micromixer is shown in Figure 1. It takes two fluids from different inlets and combines them into a single channel which is 10μm wide. The fluids then enter the central loop with the inner and outer radii being 1 5μm and 15μm respectively. Four microelectrodes are positioned on the outer wall of the central loop at angular positions 45 , 135 , 45 , and 135 . These microelectrodes impose a spatially varying electric field, and the fluids are manipulated via the electroosmotic slip boundary condition before they enter the outlet channel. Electric potentials on the microelectrodes are also time dependent, which adds the third dimension necessary for chaotic mixing. The aspect ratio (channel depth over channel width) is 5 : 1, which validates our 2-D assumption in the numerical simulation. Figure 1. Geometry of the micromixer FABRICATION The micromixer is built on a silicon wafer using lithographic and deep etching technique. A Scanning Electron Microscope (SEM) picture of the micromixer is shown in Figure 2. To obtain a sufficiently high aspect ratio of the microelectrodes, heavily Boron doped silicon is used as the fabrication material. SOI (Silicon On Insulator) wafer is used to isolate the device from the substrate bulk material. The surfaces are thermally grown silicon dioxide (quartz), and exhibit a zeta potential when brought into contact with the fluid. The gap between the electrode and the wall is also filled by the thermally grown silicon dioxide. MATHEMATICAL MODEL The fluid motion is governed by the incompressible Navier Stokes equation ρ ∂V ∂t V ∇ V ∇p μ∇2V ρeE (1) where ρe is the electric charge density, and E is the electric field intensity. E is related to the electric potential Φ by Figure 2. SEM picture of the micromixer