Static micromixers based on large-scale industrial mixer geometry

Abstract

Mixing liquids at the micro-scale is difficult because the low Reynolds numbers in microchannels and in microreactors prohibit the use of conventional mixing techniques based on mechanical actuators and induce turbulence. Static mixers can be used to solve this mixing problem. This paper presents micromixers with geometries very close to conventional large-scale static mixers used in the chemical and food-processing industry. Two kinds of geometries have been studied. The first type is composed of a series of stationary rigid elements that form intersecting channels to split, rearrange and combine component streams. The second type is composed of a series of short helix elements arranged in pairs, each pair comprised of a right-handed and left-handed element arranged alternately in a pipe. Micromixers of both types have been designed by CAD and manufactured with the integral microstereolithography process, a new microfabrication technique that allows the manufacturing of complex three-dimensional objects in polymers. The realized mixers have been tested experimentally. Numerical simulations of these micromixers using the computational fluid dynamics (CFD) program FLUENT™ are used to evaluate the mixing efficiency. With a low pressure drop and good mixing efficiency these truly three-dimensional micromixers can be used for mixing of reactants or liquids containing cells in many μTAS applications.

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1. Introduction

Traditionally, mixing has been achieved by stirring, and a wide range of mixing devices is used in the chemical, pharmaceutical, petroleum, waste treatment, plastic industries and food processing industries. However, mixing by stirring becomes more and more difficult and ineffective when dimensions are scaled down. In micro-channels and micro-reactors, the Reynolds number (Re) is usually lower than 100, which is representative of laminar flow profiles and excludes the possibility of turbulent mixing. At the micro-scale, mixing can only be accomplished through diffusion, and the most favorable alternative to stirring is the static mixer approach.

Static mixers do not require any moving parts, and mixing is not obtained by external agitation, but by the natural motion of the fluid as it flows through the mixing elements composing the static mixer. Static mixers are widely used at the macro-scale^1,2 when the mixing task must be performed in a continuous fashion, when liquids are extremely viscous such that turbulent stirring effects do not exist to aid the mixing, or when excessive mixing has to be prohibited (for example, biological material can be damaged by the shear forces in stirred reactors and mixing can cause segregation of solid particles in powder mixtures). Two main types of static mixers are used in industry to mix liquids or gases at the macro-scale: the first type, sold by Sulzer™ and Koch™, is based on a series of rigid elements that form intersecting channels to split, rearrange and combine the component streams. The second type, commercialized by Kenics™ is made of right-handed and left-handed short-helix shaped mixing elements arranged alternately in a pipe, which stretch and fold the fluid.

The micromixers described in this paper are based on the same mixing principles and have similar geometries to large-scale mixers previously cited. The microstereolithography technique has been used to shrink the size of the conventional macromixers while maintaining similar geometries.

2. Geometry

The geometry of the micromixers that were built and studied was generated with a CAD program (Autocad 2000) in 3D mode by performing Boolean operations on simple volumic primitives. Both kinds of mixers are in-line devices consisting of mixing elements inserted into a pipe. A Y-shaped structure was added at the end of the pipe to allow an easy connection with the tubes carrying the different fluids to be mixed.

2.1 Structure made of intersecting channels

The structure of the micromixer based on intersecting channels is presented in Fig. 1a. Four mixing elements of 1200 μm in length are inserted into a 1200 μm diameter tube. Each mixing element is made of 24 rectangular bars placed at ±45° that form intersecting channels. The mixing elements are arranged in the pipe so that each element can be generated by a reflection and a 90° rotation of its neighbor.

2.2 Structure made of helical elements

The structure of micromixer made of right- and left-handed helical elements is presented in Fig. 1b. It contains 6 small-helix structures, each 900 μm long, inserted into a 1200 μm diameter pipe. Each helix element is aligned at 90° from the previous one and has a twist angle of 90° with right-hand and left-hand elements alternately arranged in the pipe.

Fig. 1 Cut-out view of the micromixer structures and connector obtained by a CAD step with Autocad 2000. (a) Micromixer made of intersecting channels. (b) Micromixer made of helical elements.

3. Manufacturing process

Different types of micromixers designed for microfluidic applications have already been produced by conventional microfabrication technologies. Those mixers can be grouped into three areas: static mixers,³ nozzle arrays,⁴ and active mixers.⁵ In general a piezoelectric element is used in active mixers to oscillate a membrane and aid in mixing. Static mixers, in contrast, use the divide and conquer approach, where the liquid to be mixed is divided into smaller streams. These streams are interwoven in such a way as to reduce the distance that molecules need to diffuse and, therefore, to reduce the mixing time. The micromixers presented in this paper fall into the category of static mixers; they are fully three-dimensional and cannot be obtained directly by silicon-based technologies. The microstereolithography process has been used to obtain the complex shape of these small components.

Microstereolithography is a relatively new microfabrication process that has evolved from rapid prototyping technologies.^6–8 This process allows complex objects to be manufactured by a layer-by-layer light-induced polymerization of a liquid resin. This technique is not yet commercially available, but different academic research institutes are investigating this domain.

The microstereolithography apparatus used to manufacture the micromixers in this study has been developed at the Swiss Federal Institute of Technology in Lausanne, Switzerland (EPFL). It is based on the ‘integral method’ with which one complete layer of the object is built in one irradiation only, whatever its shape may be. The manufacturing principle of such microstereolithography machines is described in detail in many publications.^{6, 9}

Even though the resolution of microstereolithography is not as good as conventional microfabrication processes, this technique has nevertheless many advantages: the manufactured micro parts are complex in shape, truly three-dimensional and made of a large number of layers (up to 1000 or even more). The manufacturing times are short; typically the microstereolithography machine at EPFL can produce from one to five layers per minute, and the time needed to build one layer is the same whatever the pattern. Its typical resolution is 5 µm in the 3 directions of space.

4. Manufactured micromixers

To manufacture the objects with the microstereolithography process, 3D file formats like those used in conventional rapid prototyping technologies are used. One of the most common file formats is the STL format, which describes the objects by triangles and their normals. It is now widely used and can be generated by most CAD programs. A slicing subroutine is used to make the pattern for the successive layers to be built in the fabrication step.

When manufacturing a micromixer, the microstereolithography process allows the mixing elements, the pipe and the connectors to be built at the same time. Fig. 2a shows a scanning electron microscope (SEM) picture of a micromixer made of intersecting channels, and Fig. 2b presents the micromixer made of helical elements. These objects were obtained by superimposing respectively 1807 and 1868 layers of 5 μm in thickness. Their manufacturing time is approximately 5 h.

Fig. 2 Cut-out view of the micromixer structures built by microstereolithography. (a) Micromixer made of intersecting channels. (b) Micromixer made of helical elements.

5. Experimental results

The pressure drop of the two micromixers presented in the previous paragraph has been evaluated. The mixers were used in experiments for Reynolds numbers between 1 and 500.

5.1 Pressure drop

The experimental setup used to measure the flow rate of the micromixers for different pressure differences is known as the gravimetric method: The flow rate across the device is calculated by monitoring the temporal evolution of the weight of water that travels through it with a high resolution scale. The pressure of nitrogen that pushes the water into the micromixers is measured by a pressure gauge (Bioblock Scientific MP 340 A, 0–2000 mbar). The water used for these experiments has been previously filtered (by a 0.2 μm pore filter), de-ionized and de-gassed in a vacuum of −800 mbar for approximately 15 min.

Before their connection to the experimental setup, the micromixers are primed: they are immersed in water and de-gassed in vacuum so that the water fills their structure and the air bubbles are removed. For each pressure interval, multiple values of the flow rate are recorded, and their average is plotted in Fig. 3.

Fig. 3 Measurement of the pressure drop in the micromixers made by microstereolithography and using water as fluid.

The Haagen–Poiseuille relation (eqn. (1)) shows a linear dependence of the flow, Φ, with the pressure drop, Δp, in a pipe:

where μ is the viscosity, A is the pipe section, L is the length of the canal, and C_r is a geometric coefficient depending on the shape of the pipe.

Such a linear dependence of the pressure drop can be observed, as presented in Fig. 3, in the case of both types of studied micromixers. The pressure drop in the micromixer made of helical elements is lower than the one made of intersecting channels, and intuitively this result is easy to understand: the numerous interwoven structures that split and recombine the flow have a much bigger influence on the pressure drop than the simple helical elements.

5.2 Mixing efficiency

The mixing efficiency of the micromixers has been visually evaluated by injecting colored fluids in the structures. Fig. 4 shows a picture of such an experiment in the case of a micromixer made of intersecting channels. The two different colored liquids can be seen on the left of the picture in the connector part of the structure. Of course this kind of visual evaluation is only qualitative, but it gives clear indications of the micromixers behavior: the mixing efficiency of the micromixer made of intersecting channels seems better than the micromixer made of helical elements (not shown) where the different colored flows are still not completely mixed at the output. Nevertheless, the mixing gets better with the number of helical elements inserted in the pipe.

Fig. 4 Experimental visualization of the mixing of two fluids of different colors.

6. Numerical simulation

As the experimental evaluation of the mixing efficiency of the different micromixers was only qualitative, numerical simulations have been performed with FLUENT-5, a commercially available CFD (computational fluid dynamics) software to get quantitative indications of the micromixers behavior.

The simulation of the three-dimensional static mixing of large-scale devices is described in many publications and has been validated experimentally.^10–14 The same approach used in the case of large-scale mixers has been used to simulate the micromixers.

The FLUENT-5 software package was chosen because it is widely used for solving fluid dynamics problems in many disciplines. The software suite provided by FLUENT facilitate geometry modeling and grid refinement and is relatively straightforward to use. The micromixers geometries were laid out using the GAMBIT preprocessor with the geometry specifications described in Table 1. The meshing of surfaces and volumes and the specification of boundary conditions was also undertaken with GAMBIT.

Table 1 Simulation of the micromixers: geometrical characteristics, fluid properties and mesh properties

Micromixer type	Intersecting channel	Helical element
Geometry:
Diameter	1200 μm	1200 μm
Length per element	1200 μm	900 μm
Number of elements	4	6
Entrance length	10000 μm	10000 μm
Entrance exit	10000 μm	10000 μm
Overall length	24800 μm	25400 μm
Fluid:
Density	998.2 kg m^−3	998.2 kg m^−3
Viscosity	1.003 × 10^−3 Pa s	1.003 × 10^−3 Pa s
Mesh:
Tetrahedral cells	910094	877532
Nodes	179457	168447

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The 3D meshes were imported in FLUENT-5. In addition to the mixing elements, entrance and exit sections for the micromixers were also simulated. They were modeled as an open tube with the same diameter as the mixer elements. The boundary conditions used at the system inlet was a uniform velocity profile in the axial direction with v_x = 1 cm s⁻¹, v_y = v_z = 0. A constant outlet pressure outlet (P [double bond, length half m-dash] 0) was used and the ‘no-slip’ boundary condition was used at all solid/liquid interfaces.

6.1 Velocity field

The experimental investigations on the manufactured micromixers were undertaken in non-creeping flow conditions, with Reynolds numbers between 1 and 100. The numerical simulations were undertaken in equivalent flow conditions, with water as fluid and Re = 12.

The description of the velocity field within a single mixer element is shown using two dimensional cross sectional contours plots. The top part of Fig. 5 shows the micromixer made of intersecting channels and the bottom part of Fig. 5 shows the micromixer made of helical elements.

Fig. 5 Cross sectional profiles of velocity computed for flow with Re = 12 at regularly spaced locations of one element of each type of micromixer (from top left to bottom right). The top part corresponds to the 3rd element of the micromixer made of intersecting channels. The bottom part corresponds to the 4th element of the micromixer made of helical elements.

In the case of micromixer made of intersecting channels, the flow field is intricate, with important velocity gradients near the rectangular bars composing the mixing elements.

In the case of micromixer made of helical elements, the persistence of entrance and exit effects over more than one fourth of the flow field within a single element can be observed. This effect is well known in the case of large-scale mixers.

6.2 Particle distributions

The determination of the efficiency of the micromixers was achieved by calculating the trajectories of fluid particles in the flow field of the micromixer. This method avoids the problem of the excessive numerical diffusion that is observed if the species continuity equations are solved.¹⁵ However, to obtain an accurate global evaluation of the mixing efficiency in the mixer, it is necessary to study the trajectories of a large number of particles.

The basis for this study is the injection of 65000 evenly distributed particles, in the upper half of the pipe, just before the micromixer inlet. The particles trajectories correspond to streamlines. A few percent of particles are ‘lost’ between the inlet and outlet of the micromixer, because particles trajectories are trapped near the walls where the local velocity is close to zero. This phenomenon causes some inaccuracies in the simulated results.

Nevertheless, the particles distributions resulting from this simulation clearly shows how the mixing phenomenon occurs for the different studied geometries of micromixers. Fig. 6 shows the location of the particles at regularly spaced axial locations along both types of micromixers. The upper line shows the cross sections corresponding to the beginning and middle of the first 3 elements of the micromixer made of intersecting channels. The bottom line shows the cross sections of the beginning of each of the 6 elements composing the micromixer made of helical elements. In the micromixer made of intersecting channels (top of Fig. 6), the mixer elements split and rearrange the flow and a relatively good dispersion of the particles is achieved after only two or three mixing elements. In the case of the mixer made of helical elements (bottom line of Fig. 6), the flow is stretched and folded in each successive element and obtaining a good mixing efficiency requires a large number of elements.

Fig. 6 Plots of the locations of 65000 particles computed for flow with Re = 12 at regularly spaced axial locations along the micromixers (from left to right). The left plot corresponds to the beginning of the mixers. The top line corresponds to the micromixer made of intersecting channels, whereas the bottom line corresponds to the micromixer made of helical elements.

7. Conclusion

Downscaling large-scale components to create microdevices is seldom a successful solution, nevertheless, creating micromixers analogous to large-scale mixers already used in chemical, pharmaceutical and food-processing industries leads to interesting results. Microstereolithography has been used to produce the micromixers with a fully three-dimensional geometry. This microfabrication technique is still not wide spread but allows micro-components that are complex in shape to be manufactured with a 5 µm resolution. The pressure drop of the studied micromixers has been measured and it is relatively low compared to most micromixers produced with more conventional microfabrication processes. Their mixing efficiency has also been investigated experimentally by mixing different colored liquids and with a numerical simulation using the FLUENT-5 CFD program. The numerical simulation allows the determination of the velocity field in the micromixers. The calculation of trajectories of the particles gives a clear idea of the way the mixing phenomenon takes place, and allows the comparison of the efficiency of the different manufactured micromixers geometries. The true three-dimensional geometry of the studied micromixers, the low pressure drop and relatively good mixing efficiency shown could be an advantage to achieve, for example, the mixing of liquids containing cells and reactants in µTAS applications.

8.  Acknowledgements

The authors wish to thank Dr M. L. Sawley of the Fluids Mechanics Laboratory at the Swiss Federal Institute of Technology, Lausanne (EPFL) for his help in the computational fluids dynamics part of this work.

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