Mixing Principles for Microstructured Mixers - American Chemical

Chapter 21

Downloaded by KTH ROYAL INST OF TECHNOLOGY on September 15, 2015 | http://pubs.acs.org Publication Date: August 9, 2005 | doi: 10.1021/bk-2005-0914.ch021

Mixing Principles for Microstructured Mixers: Active and Passive Mixing Volker Hessel* and Holger Löwe Institut für Mikrotechnik Mainz GmbH, Carl-Zeiss-Str. 18-20, D-55129 Mainz, Germany *Corresponding author: [email protected]

Microstructured mixers have two major application fields. They are used for mixing operations in theframeworkof con ventional chemical processing as part of ordinary industrial field equipment, i.e. use of multi-scale technology. On the other hand, these tools may be integral part of miniaturised analytical devices like lab-on-a-chip. Mixing is here part of an entire microflow process and orients on a new means of analysis. These two application fields have totally different requirements on their devices: in the first case, capacities range from 11/h to several m /h flow for watery systems. In contrast, analytical tests typically demand for consumption of minute sample volumes, which correspond to flows in the μl/h to ml/h range. Especially at such low flow velocities, the often applied pressure-driven or electroosmotic flow mixing, the so -called passive mixing, is not adequate. Here, active mixing principles which rely on external energy are better suited and may be used over periods of several minutes. Examples for both types of mixing principles are given below. 3

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© 2005 American Chemical Society

In Microreactor Technology and Process Intensification; Wang, Y., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2005.

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In the following, only the mixing of miscible fluids, mostly liquids, in mi crostructured mixers is considered. No reference is given to mixing of immis cible fluids generating multi-phase systems, i.e. to emulsification and foaming. In addition, only the mixing principles themselves and sometimes their design issues are explained. No details on the respective devices, their characterization and applications are given for reasons of limited space and consistency within this chapter. Here, selected major references provide further information.

Active Mixing Electrokinetic Instability Mixing Fluctuating electric fields can be used for liquid mixing (1). This results in rapid stretching and folding of material lines or sheets, having a similar impact as stirring. Flow instability achieved by oscillating electroosmotic flows are referred to as electrokinetic instability (EKI) (1). A preferred type of oscillation of electric fields is to apply a sinus wave. EKI mixing does not rely on moving parts and is applicable for mixingflowsat very low Reynolds number (-1). Full-field images of the entire mixing chamber of an EKI mixer device, yielded by injection of afluorescencetracer, prove that rapid stretching and folding is indeed given (1). Mixing times of about 2.5 s were deduced from time-resolved images showing the point when a randomly distribution of a fluorescence tracer is achieved (I). Image power spectra provide further details on the EKI mixing . If no A C field is turned on, an unmixed state is given characterised by a slightly elongated frequency band (I) (see Fig. 1). This is indicative of higher spatial frequencies transverse to the interface and corresponds well to the initial horizontal orientation of the interface. Advectivefluxarises when EKI mixing is set on and leads to high spatial frequency gradients in the power spectra. New, undiffused fluid interface lengths occur. These high-frequency bands are dampened in the final, mixed state, yielding thus isotropic power spectra indicative for good stirring. The mixing times of the 1 generation EKI device were determined by analyzing the flow patterns viafluorescenceimaging. After a period of 2 s, the flow becomes unstable and transverse velocities stretch and fold material lines in the flow (1). The initial seeded / unseeded interface becomes rapidly deformed. Finally after about 13 s, a random distribution of the tracer transverse to the applied AC field is achieved. EKI action is visible throughout the whole channel length of 7 mm. The mixing time of a 2 generation EKI, being 2.5 s, is even superior to the performance of the prototype device. st

nd

Chaotic Electroosmotic Stirring Mixing A temporal modulation by non-uniform ζ potentials along a micro charmers walls can be achieved by superposition of electroosmotic flows. In this way, chaotic advection can be induced leading to a material transport simi lar to mixing by stirring (see Fig. 2) (2). Non-uniform ζ potentials can be ob tained by coating the channel's walls with different materials or by using differ-



Fig. i

Power spectra obtainedfor an electrokinetic mixer (reproduced from (1); Copyright: ACS).



337 ent buffer solutions. For one concept investigated in detail, such electric fields were achieved by a series of electrodes located under the channel's floor. Both spatial and temporal control of the ζ potential was so achieved by imposing an electric field perpendicular to the solid-liquid interface. As an alternative means, the light charging of photosensitive surfaces has been proposed (2). So far, the chaotic electroosmotic stirring concept has not been transferred into a physical device. Hence, there are no experimental proofs to report. Nonetheless, simulations give first evidence on the mixing efficiency of such devices. In one such simulation study, a square material blob was placed in the center of the channel (2) (see Fig. 2). This is equivalent to inserting a drop of a dye in the channel. Rapid stretching and folding processes, characteristic of chaotic advection, arise when periodically switching between flow fields. Eventually, the blob is spread over the entire cell's area. Hence efficient stirring is given. Magneto Hydro Dynamic M i x i n g The use electric fields for liquid mixing can be extended by combination to a magnetic field (3). For this purpose, a micro channel was equipped with an array of electrodes. A complex electric field with currents in various directions was generated by alternate potential differences. This electric field was then coupled to a magnetic field. By induction of Lorentz body forces for fluid mix ing, a cellular motion was achieved which stretches and deforms material lines. Simulations were performed for the magneto hydro dynamic mixing to predict to which extent and by which pattern the interfaces are stretched which is a qualitative measure of mixing efficiency (3). The evolution of the interface was given as a function of the dimensionless time. An initial bi-layered system forms a vortex-type structure with increasing spiral winding upon time. A quantitative analysis shows that the interface increases slightly faster than a linear function of time (3). This is better than when having diffusion only, but is inferior to the performance of chaotic advection. These predictions have been corroborated by dye-visualization experiments. Owing to the dc potential difference, a visible flow was clearly induced in a water-filled chamber with a central dyed line by magneto hydro dynamic action (3). Upwards and downwards fluid motion in a rotating fashion was observed. Air-Bubble Induced Acoustic M i x i n g Air-bubble acoustic mixing is a method to mix liquids in micro chambers of comparatively large internal volume (4). An air bubble in a liquid medium can act as actuator and thus achieve liquid mixing. When stimulated by an acoustic field, the bubble surface vibrates. The bubble vibration induces friction forces at the air/liquid interface. In this way, a bulk fluid flow around the air bubble is achieved, termed cavitation microstreaming or acoustic microstreaming. Circul atory flows lead to global convection flows of "tornado"-type pattern. The bubble resonance characteristics govern the bubble actuation (4). An insonation frequency equalling the resonance frequency for pulsation has to be set. The frequency of acoustic microstreaming is, as to be expected, strongly dependent on the bubble radius and vice versa.



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Fig. 2 Streamline patternsfor various electroosmoticflows,showing the transition to chaoticflow(reproducedfrom (2); Copyright: ACS). T: periodicity offlow switching; the x- andy-axes denote dimensionless numbers for the respective axes ofthe mixing volume.



339 The bubbles are favorably fixed at a solid boundary in specially designed pockets (4). By use of a commercially available piezoelectric (PZT) disk, liquid mixing times of a few seconds were realized. Mixing of comparable volumes solely by diffusion would require several hours. Initial dye imaging mixing experiments by multiple-bubble microstreaming yielded complete mixing of the micro chamber within 105 seconds (5 kHz; 5 V) (4). Mixing based on pure diffusion in the same volume would have taken about 6 hours. By increasing the peak-to-peak amplitude further optimization of mixing was performed. Now, a mixing time of only 6 seconds results (5 kHz; 40 V) (4). Mixing based on pure diffusion in the same volume would have taken about 8 hours. The method of multiple-bubble microstreaming has been proven to be particularly suitable for mixing of relatively large mixing chambers. Bubbles with radii of 0.5 mm can stir fluid volumes in a distance with a radius smaller than 2 mm (4). Thus, any micro chamber is suitable for acoustic microstreaming with a depth

Mixing Principles for Microstructured Mixers - American Chemical

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