A MEMS Microfluidic Mixer with Electrostatic Actuation

Xi Kang1, Chengxin Zhang2, Xingguo Xiong3, Sk Hasan Hafizul Haque4 Department of Electrical Engineering

University of Bridgeport Bridgeport, CT 06604

E-mail1: xikang@my.bridgeport.edu; Email4: shaque@my.bridgeport.edu

Abstract— Bio-MEMS (Bio-Micro-electro-mechanical Systems) have been widely used for disease diagnosis and treatment. In bio-MEMS devices, the mixing of different micro-fluidics is frequently needed. However, such mixing has been very challenging due to the fact that micro-fluidic is generally laminar flow. As a result, MEMS mixers which can enhance the mixing of different micro-fluids are in pressing need. In this paper, the design and simulation of a 3-way pressure disturbance based micro-fluidic mixer for Bio-MEMS (bio-micro-electro-mechanical systems) application is proposed. Three aqueous solutions with different concentrations represented by different colors (sea blue, sky blue and red) are introduced through six inlets. The mixing of micro-fluid in the proposed mixer is analyzed. The parameters of the mixer are decided through the theoretical analysis. Based on results of the experiment simulation, almost 100% mixing can be finished within a mixing distance x equal to3.24mm of outlets for flow rates ranging in 1000um/s, and when the micro-fluids (3 kinds of liquids) near the outlets, the mixing degree is better. More or less than this velocity, the micro-fluids cannot get a good mixing. ANSYS simulation is used to verify the effectiveness of the MEMS mixer device. Compared with passive mixer, the pressure disturbance design with the straight channel diffusion model mixer is easier to fabricate and it makes device smaller and cheaper. The fabrication flow of the MEMS mixer is also suggested in this paper. The proposed MEMS mixer can be used for lab-on-a-chip, digital micro-fluidics, PCR amplification, DNA analysis, cell manipulation, cell separation and other applications. Keywords— Microfluidic, Electrostatic Actuation, Micro Mixer, ANSYS

I. INTRODUCTION

A Micro-fluidic device can be confirmed the fact that it has one or more channels and at least one size less than 1 mm. Common liquid used to micro-fluidic devices include whole blood samples, bacterial cells suspension, protein or antibody solution and various buffer. Micro fluidic devices have had a considerable impact on the fields of biomedical diagnostics and drug development, and are extensively applied in the food and chemical industries. The diminutive scale of the flow channels in micro fluidic systems increase the surface to volume ratios, and is therefore advantageous for many applications [14]. Micro fluidic devices can be used to obtain a variety of interesting measurements including molecular diffusion coefficients [1], fluid viscosity, pH, chemical binding coefficients and enzyme reaction kinetics [2]. Mixing

is not only a ubiquitous natural phenomenon accompanying geophysical, ocean and atmospheric flows, but it is also an important step in many technological processes [3]. Effective mixing underlies the operation of chemical and fermentation reactors, combustion engines and other processes; it is required to make glasses, polymer blends and pharmaceutical formulations. The majority of these industrial processes are carried out on macroscopic scales, and it has only been in the recent years that mixing of small quantities of liquids has become technologically relevant in the context of micro-fluidics and micro total analysis systems [4].

The aim of micro fluidic mixing schemes is to enhance the mixing efficiency such that a thorough mixing performance can be achieved within shorter mixing channels, which can reduce the characteristic size of micro fluidic devices. Furthermore, the development of efficient mixing schemes is essential for increasing the throughput of micro fluidic systems and to realize the concept of micro-total-analysis systems and lab-on-a-chip systems. Mixing on microscopic scales is, however, difficult. Although diffusion on the micro-scale is fast the Reynolds numbers are usually low (Re ~ 0(1)), and the flows are laminar [5]. In the absence of turbulence, it is hard to increase the interfacial area of contact through which the molecules diffuse. Increasing the contact area between the species to be mixed is one of the most efficient means of enhancing the diffusive mixing effect .In this paper a design is proposed of a micro fluidic mixer with electrostatic actuation.

II. MICRO-FLUID MIXER Mixing is not only a ubiquitous natural phenomenon accompanying geophysical, ocean and atmospheric flows, but it is also an important step in many technological processes [3]. Effective mixing underlies the operation of chemical and fermentation reactors, combustion engines and other processes; it is required to make glasses, polymer blends and pharmaceutical formulations. The majority of these industrial processes are carried out on macroscopic scales, and it has only been in the recent years that mixing of small quantities of liquids has become technologically relevant in the context of micro-fluidics and micro total analysis systems [4].

Numerous and often ingenious micro-mixing devices have been developed that overcome the limitations imposed by the laminar of micro-flows. Before discussing the architectures and principles of these micro-mixers in detail, a few words are in order to clarify certain nomenclatural nuances. Thus, both the process of mixing itself and the mixing devices are classified as either passive or active—these terms, however, have very different meanings in each of the contexts. Specifically, passive mixing refers to processes in which the interfaces between the substances being mixed follow the flow and have no back-effect on it, while active mixing refers to processes in which the interfaces interact with the flow and modify it [6].

Passive mixers, on the other hand, are those that have no moving parts and achieve mixing by virtue of their topology alone that are designed to increase either the contact area or the contact time or both of the multiple species, while active mixers enhance the mixing performance by stirring or agitating the fluid flow using some form of external energy supply such as either do have moving parts or they use externally applied forcing functions such as pressure or electromagnetic fields [7]. In principle, one can have active mixing in a passive mixer or vice versa.

Passive mixers (see Figure 1) use the channel geometry to either laminate the flowing fluids in-plane or out-of-plane to promote chaotic advection in these fluids. Both approaches lead to an increase in the interfacial area and, consequently, to better mixing. Although the lack of moving parts makes passive mixers free of additional friction and wear effects, their intricate channel topologies are often hard to micro fabricate, and they are generally not switchable: once incorporated in a fluidic system, they perform their function whenever fluids pass through them.

Figure 1. Two examples of the passive mixer in which fluids are mixed by chaotic adection[17]

In contrast, active mixers (see Figure 2) can be controlled externally, which makes them suitable components of reconfigurable micro-fluidic systems: that is, systems that can perform several different functions given different states of external controls. The advantage of controllability is

somewhat offset by the complicated micro fabrication that is often needed to make active mixing micro devices.

Figure 2. Integrated drug reconstitution and delivery system

with integrated fluidic components[15]

III. DESIGN OF MICRO-FLUIDIC MIXER WITH ELECTROSTATIC ACTUATION

A micro fluid mixer combines small amounts of two or more fluid species into a single stream where the intake components are evenly distributed. Micro fluid mixers have advantageous properties such as compactness, and miniscule fluid consumption. These traits make micro mixers very attractive for use in chemical, biological, and medical micro-systems. In this paper, we design a novel active two-dimensional micro mixer with electrostatic actuation. The mixing performance was investigated using CFD (ANSYS) for computational fluid dynamic (CFD) analysis and using experiments for flow visualization.

Figure 3. Coordinates and dimensions of the micro mixer model

Computational fluid dynamics (CFD) simulations were applied to guide the design of the electrostatic based micro mixer using ANSYS. The coordinates and dimensions of electrostatic based mixer model are shown in Fig.3. Two aqueous solutions with different concentrations represented by different color (blue and red) are introduced through two inlets. The Density is 1.0g/cm3 for blue and 1.8g/cm3 for red solution. The two solutions are mixing in the chamber under

electrostatic force. Compared with passive mixers, this designed mixer has a smaller size and high efficiency. The mixing chamber is 580µm long and 190µm wide. It comes with four resonant beams and four electrodes to increase the fluidics mix. The two inlets are 20µm wide and 60µm long. The resonant beams are 250µm long and 1µm thick. The basic principle of Micro fluidics is the flow of a fluid through a micro-fluidic channel can be characterized by the Reynolds number, defined as:

….. (1)

The electrostatic force q(x) between the resonant beam and the electrode depends on the deflection of the beam at any distance x, along the beam. Assuming a square-law curvature for the beam deflection, the load distribution along a beam of length L is given by[8]:

Using the conventional beam theory[9], the trip deflection under partial loading is given by:

….. (3)

Combining equations (2) and (3) we can obtain:

The integral in equation (4) can be solved for the voltage[10] to obtain:

Therefore, the driving voltage for any tip displacement can be calculated from the equation (5). In this project, E=169GPa, w=500µm, g=20µm, =8.85*10-12C2/N m2, =1 C2/N m2 for air.Consider of this relationship and the device size, mix efficiency purpose, we choose L=250µm as the length of resonant beam and 1µm as it thickness. Driving voltages for a silicon beam of length L=250µm at various beam thicknesses between 1-2µm are shown in Figure 3.2. From it we can get that the driving voltage get binger with the normalize tip deflection increase, but it drops from the point ∆=0.7. The normalized loads greater than 0.7 cannot be realized as it exceeds the snap-through voltage[11].

Figure 4. Driving voltage versus the deflection for various beam thicknesses

The angular natural frequency of the resonant beam can be defined as[12]:

Figure 5. Resonant frequency versus the length of the beam

The curve shows this relationship between the resonant frequency and the length of the beam. It is easy to see that the resonant frequency drops sharply as the length of the beam is increased. In this project, we set the length of the cantilever beam as 250µm. Based on above analysis, a set of optimized design parameters of the proposed electrostatic mixer are obtained, as show in Table 1.

Design parameters values

Mixer channel length 580µm

Mixer channel width 180µm

Inlet length 60µm

Inlet width 20µm

Outlet length 60µm

Outlet width 40µm

Cantilever beam length 250µm

Cantilever beam width 500µm

Cantilever beam thickness 1µm

Electrode length 240µm

Electrode width 500µm

Electrode thickness 10µm

Gap between beam and electrode

20µm

Table 1. The optimized parameters

IV. ANALYSIS IN ANSYS AND SIMULATON RESULT The mixer design is considered in ANSYS (see Figure 6) and its performance is vibration of the cantilever beam in the mixing chamber. The mixer is analyzed under continuous fluid flow under the electric force. The proposed design of the mixer is attempt to enhance the mixing process by disrupting the laminar flow as much as possible.

Figure 6. The micro mixer model

The maximum beam displacement sensitivity is 1.0 µm/g (see Figure 7)

. Figure 7. Vibration of the cantilever beam

Figure 8. Vibration mode in ANSYS

Figure 9. Vibration of the cantilever beam The Figure 8 shows the vibration mode under 30kHz in ANSYS simulation. The Figure 9 shows the resonant frequency is about 23 kHz, which match the resonant frequency we get from chapter 3. The amplitude of the beam’s deflection increase around the resonant frequency. This working frequency is far away from the 90 kHz which means it can work properly.

V. DENSITY VARIATIONS IN ANSYS

In this paper, I use two different liquids which have two kinds of different density. The density of Liquid 1 is 1.0 g/cm3 and the density of Liquid 3 is 1.8g/cm3. We put the two kinds of liquid in two different inlets and make them mixed. By ANSYS, we get the density variations in ANSYS as below:

Figure 10. Density variations of mixer

Figure 10 shows us the density variations of mixer without perturbing the interface by resonant beam. They are almost did not mix because of the laminar flow in micro scales. As we know, the different behavior between micro fluidics and macro fluidic is not because traditional physical laws (e.g. Newton’s laws) are not valid for micro fluidics anymore. Instead, it’s because the force playing dominant role (e.g. gravity force or surface tension force) is different for micro fluidics. To achieve mixing purpose, we can either increase the mixing time or increase the contact area between species.

Figure 11. Density variations of mixer with four resonant beams The program simulate it as three separate layers so when two species meet together, the diffuse to each other a little bit at the lower layer but we designed it to be a chamber which have four resonant beams inside that can vibrate with electric force to increase the mixing. It should be a whole chamber and the mixing should increase because of the vibration causes turbulence and the turbulence can increase the areas of the contact species. But because we cannot define two totally different materials at the same time in the chamber, we can only get the vibration results in air instead of species.

VI. VELOCITY VECTOR IN ANSYS

The flow velocity vector plot of the micro-fluid along MEMS mixer without perturbing the interface by resonant beam is shown in Figure4.7. Two species go into the inlet with a specific speed and they slow down in the chamber. As we see, the two fluidics diffuse in the chamber but do not meet together until near the outlet. The velocity is almost zero near the sides of the chamber because of the resistance.

Figure 12. ANSYS fluid velocity vector plot

Figure 13. ANSYS fluid velocity vector plot with resonant beams

Figure 13 shows us the velocity vector of the fluid with four resonant beams in the mixing chamber. It is clearly to see that the fluid is flows slowly without vibration. It is hard for species to mix for laminar flows.

VII. THE FABRICATION FLOW OF MICRO-FLUID MIXER

According to the mentioned above, According to the mentioned above, the DRIE fabrication technology, Photolithography and Thermal oxidation used in this Micro-fluid-mixer research. From Figure 14 to illustrates the fabrication flow.

Figure 14. Fabrication flow

After fabrication above, the MEMS micro-mixer device fabrication is completed.

VIII. FUTURE WORK In the future, we will further analyze how other micro-fluid properties affect the mixing result of the mixer, such as changed the concentration of micro-fluids. And keep working on the ANSYS simulation to get the more significant results for the mixing simulation. We also try to find a more effective fabrication process to reduce material consumption and save money.

IX. CONCLUSION

In this project, the design and analysis of a micro-fluid mixer with electrostatic actuation is proposed. The MEMS mixer utilizes electrostatic force to improve the mixing efficiency of laminar micro-fluid flows. The mixing of micro-fluid in the proposed mixer is analyzed. Based on the theoretical analysis using the MATLAB, we found relationship between mixing index and driving voltage, the length, thickness and angular natural frequency of the resonant beam. We got a set of optimized parameters for the mixer. Because of the 2D simulation, we only get the resonant beams vibration results in air and the mixing species without vibration of beams in mixing chamber. But we still can see that the theoretic analysis would work properly. Compared with passive mixers, this design should mix fluidics effectively. In the last chapter, I also suggest that a fabrication flow for this device.

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