Micromixers—a review on passive and active mixing principles

Chemical Engineering Science 60 (2005) 2479–2501

www.elsevier.com/locate/ces

Micromixers—a review on passive and active mixing principles

Volker Hessel∗, Holger Löwe, Friedhelm SchönfeldInstitut für Mikrotechnik Mainz GmbH, Carl-Zeiss-Straße 18-20, D-55129 Mainz-Hechtsheim, Germany

Received in revised form 19 October 2004; accepted 2 November 2004

Abstract

A review on microstructured mixer devices and their mixing principles concerning miscible liquids (and gases) is given. This issupplemented by the description of typical mixing element designs, methods for mixing characterisation, and application fields. Themixing principles applied can be divided in two classes relying either on the pumping energy or provision of other external energy toachieve mixing, termed passive and active mixing, respectively. As far as passive mixing is concerned, devices and techniques such asY- and T-type flow-, multi-laminating-, split-and-recombine-, chaotic-, jet colliding-, recirculation flow-mixers and others are discussed.Active mixing can be accomplished by time-pulsing flow owing to a periodical change of pumping energy or electrical fields, acousticfluid shaking, ultrasound, electrowetting-based droplet shaking, microstirrers, and others.� 2005 Elsevier Ltd. All rights reserved.

Keywords:Micromixers; Active mixing; Passive mixing; Chemical microprocess engineering; Microreactors; Mixing principles

1. Mixing principles, design elements and mixingefficiency analysis of microchannel mixers

In the following, only the mixing of miscible liquids (andgases) is considered; the same micromixers, however, canusually be used for making liquid/liquid and gas/liquid dis-persions which is out of the scope of this article.

1.1. Application fields and types of microchannel mixers

Generally, application fields of microchannel-based mix-ers encompass both modern, specialised issues such assample preparation for chemical analysis and traditional,widespread usable mixing tasks such as reaction, gas ab-sorption, emulsification, foaming, and blending (Bayeret al., 2003; Ehrfeld et al., 2000; Hessel et al., 2004;Jensen, 1998; Löwe et al., 2000) (see alsode Mello andWootton, 2002; Fletcher et al., 2002; Gavriilidis et al.,2002; Haswell and Watts, 2003; Hessel and Löwe, 2003;

∗ Corresponding author. Tel.: +49 613 19 90; fax: +49 613 1990X305.E-mail address:[email protected](V. Hessel).

0009-2509/$ - see front matter� 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2004.11.033

Jähnisch et al., 2004; Jensen, 2001; Pennemann et al.,2004a–c). In the first case, credit-card-sized fluidic chipsare typically equipped withmicromixer elementsas parts ofthe integrated system. Chip-like micromixer components,shortly micromixers, are employed for the more conven-tional chemical and chemical engineering applications at thelaboratory scale. Glass interdigital micromixers of cheque-card size are one example for this type of devices (seeFig. 1). At pilot- or even production-scales, much biggercomponents are applied for the same mixing tasks, typicallycomprising microstructures in a large housing, therefore be-ing more correctly termedmicrostructured mixers. Arraysof several tens and hundreds of stacked star-shaped plateletsare inserted in apparatus of fist-type size and larger withthroughputs up to the m3/h-range for liquids (seeFig. 1andScheme 1).

Micromixer elements, micromixers, and microstructuredmixers typically have flows in the sub-ml/h, ml/h–l/h and10–10,000 l/h ranges, respectively, thus covering the wholeflow range up to the conventional static mixers and beingamenable to analysis and chemical production as well (seeScheme1andFig. 2). When used at the upper flow limit, mi-crostructured mixers can act as process-intensification (PI)equipment.

http://www.elsevier.com/locate/ces

mailto:[email protected]

2480 V. Hessel et al. / Chemical Engineering Science 60 (2005) 2479–2501

Fig. 1. Slit-type interdigital micromixer made in glass for laboratory-scaleapplications, typical liquid flows 10–1000 ml/h.Source: Hessel et al.,2003; mgt mikroglas chemtech GmbH, Mainz/Germany (top). StarLami-nator StarLam3000 made in stainless steel for pilot- and production-scaleapplications, typical liquid flows 100–10,000 l/h (bottom).Source: Werneret al., 2005; IMM, Mainz/Germany.

1.2. Drivers for mixing at small-sized internal volumes

In the past, micromixers and microstructured mixers wereused to initiate and optimise fast reactions which in turnrequire even faster mixing (for the latter see e.g.Oroskaret al., 2000). This has been applied to fast liquid reactions,e.g. in the field of organometallic synthesis, or to fast gas-phase reactions, e.g. the ethylene oxide formation (Hesselet al., 2004). Besides in the field of chemicals synthesis,processing of fast reactions is used in the quench-flow anal-ysis (< 1 ms), e.g. to study rapid biological transformations(Bökenkamp et al., 1998). Since microflow mixing is typi-cally done in the laminar regime, laminar mixing of viscousmedia is a further example of use (Schönfeld et al., 2004).Besides their fastness of mixing and their suitability towardsone flow regime (Hardt and Schönfeld, 2003), microstruc-tured mixers benefit from their small internal volumes. Thisis particularly useful for handling of hazardous chemical re-

actions (Haas-Santo et al., 2001; Kestenbaum et al., 2000a,b;Veser, 2001) as well as rare, precious samples or numeroussamples on a small format in chemical and biological anal-ysis which requires mixing of small-sized volumes (a verylarge number of papers are available for such MicroTotalAnalysis Systems(� TAS) applications, among them see,Auroux et al., 2002; Ehrnström, 2002; Knapp et al., 2001;Manz and Becker, 1998; Ramsey, 1996; Reyes et al., 2002;van den Berg and Bergveld, 1995; van den Berg andLammerink, 1998). Some microstructured mixers provide aflow with high regularity, i.e., leading to periodic or otherspatially ordered concentration profiles when feeding mis-cible liquids (Hessel et al., 2003). A corresponding usage ofsuch structured streams is not evident in the case of immis-cible liquids; however, highly structured immiscible liquidsform fluid cylinders in a continuous medium and theyfragment via hydrodynamic instabilities to regularly sizeddroplets (Hardt et al., 2001a,b). In a similar way, gas–liquiddispersions such as foams (Pennemann et al., 2004a) andpolymer capsules via droplet solvent extraction (Freitaset al., 2003) may be created via periodical arrangements ofimmiscible liquid compartments in microstructured mixers.Concerning the latter, particles can be generated as well byprecipitation or crystallisation using miscible liquids routes,benefiting here in a complex way from the relationshipbetween mixing and seed formation/growth (Schenk et al.,2002, 2004).

Lastly, the mixing in small volumes bears the safety as-pect, both for thermal and mechanistic reasons (Veser, 2001).Hence microstructured mixers were placed upstream of re-action zones which were fed with explosive or otherwisehazardous substances (Haas-Santo et al., 2001; Kestenbaumet al., 2000a,b).

1.2.1. Mixing principlesDue to the absence of turbulence in microfluidic devices,

mixing relies solely on molecular interdiffusion (Gravesonet al., 1993). The diffusive flux, e.g. of a solute, equalsD · A · ∇c, i.e., diffusion coefficient times the interfacialsurface area times the gradient of species concentration. Ac-cordingly, diffusive mixing can be optimised by maximisa-tion of the constituting factors. Leaving an enhancement ofthe diffusion coefficient, e.g. by an appropriate temperaturerise, aside one is left with the maximisation ofA · ∇c. So,basically ‘the art of micromixing’ translates to an efficientmaximisation of interfacial surface area and concentrationgradient. Above all convective diffusion enhancementis commonly employed in mixing devices. For instancesecondary-flow patterns superposed to the main flow orrecirculation patterns within liquid plugs of segmented liq-uid/liquid flows are known to be effective mixing means.The maximum possible interfacial area generation is how-ever related to the viscous dissipation. Thus, efficient mix-ing and viscous dissipation, i.e., energy consumption, areinvoluntarily interlinked.

V. Hessel et al. / Chemical Engineering Science 60 (2005) 2479–2501 2481

Element in Lab- planar <ml/h Silicon, glass, polymeron-a-Chip system

Components Construction Flow Materials

Micro mixer 3-D ml/h – l/h Steel, silicon, glass, polymer

Microstructured 3-D 10 l/h – 10 m3/h Steelmixer/PI apparatus

Scheme 1.

Figure 2. Micromixers (laboratory-scale) and microstructured mixers (pilot-scale) close the gap to static mixers, yielding apparatus for a multi-scaleconcept. Today’s microstructured devices achieve mixing up to about 1 m3/h liquid throughput.Source: Bayer et al., 2003.

Besides the Reynolds number(Re = U · d/�), the Peclétnumber,Pe=Ud/D, and the Fourier number,Fo=Tr/Tm,are commonly used as dimensionless groups to characteriseconvective/diffusive problems. HereU, d, � denote the aver-age velocity, the hydraulic diameter or the transverse diffu-sion distance which are assumed to be of the same order ofmagnitude, and the kinematic viscosity.Tr , Tm denote the av-erage residence time and the diffusive mixing time, definedasTr =L/U andTm=d2/D, whereL denotes the longitudi-nal length. For laminar uniaxial flows the mixing lengthLm

is found to be proportional toPe times the channel width.Convective diffusion enhancement is achieved by deforma-tion of lamellae arrangements into tendril, whorl or striation-like shapes and thereby increasing interfacial area and theconcentration gradient due to reduction of the striation thick-ness (Ottino, 1989). In this way the mixing length can beconsiderably reduced. In case of a linear reduction of stri-ation thickness with the flow path a sub-linear dependence

of the mixing length as function ofPe is achieved which caneven be reduced down toLm ∼ ln(Pe) for chaotic flows inthe limit of largePe (Stroock et al., 2002a).

1.2.2. Means to induce mixingTwo basic principles are followed to induce mixing at

the microscale. First, energy input from the exterior is used,termedactive mixing. These external energy sources areultrasound (Yang et al., 2001), acoustic, bubble-inducedvibrations (Liu et al., 2003, 2002), electrokinetic instabil-ities (Oddy et al., 2001), periodic variation of flow rate(Glasgow and Aubry, 2003; Niu and Lee, 2003; Qian andBau, 2002), electrowetting-induced merging of droplets(Palk et al., 2003), piezoelectric vibrating membranes(Woias et al., 2000), magneto-hydrodynamic action (Westet al., 2002), small impellers (Lu et al., 2001), integratedmicrovalves/pumps (Voldman et al., 1998), and others(Scheme 2).


Ultrasound

ACTIVE MIXING – external energy input

Acoustically induced vibrations

Electrokinetic instabilities

Periodical variation of pumping capacity

Electrowetting induced joint of droplets

Magneto-hydrodynamic action

Small impellers

Piecoelectrically vibrating membrane

Integrated micro valves / pumps

Scheme 2.

Interdigital multi-lamellae arrangements

PASSIVE MIXING – Energy input by pumping power

Split-and-Recombine concepts (SAR)

Chaotic mixing by eddy formation and folding

Nozzle injection in flow

Specialties, e.g. Coanda-effect

Collision of jets

Scheme 3.

As a second means, the flow energy, e.g. due to pump-ing action or hydrostatic potential, is used to restructurea flow in a way which results in faster mixing. This isknown aspassive mixing. Thin lamellae are created in spe-cial feed arrangements, termed interdigital (Bessoth et al.,1999; Branebjerg et al., 1996; Drese, 2003; Ehlers et al.,2000; Ehrfeld et al., 1999; Floyd et al., 2000; Hardt andSchönfeld, 2003; Hessel et al., 2003; Löb et al., 2004; Zechet al., 2000). A serial way of creating multi-lamellae canbe achieved by Split-and-Recombine (SAR) flow guidance(Branebjerg et al., 1996; Schönfeld et al., 2004; Schwesingeret al., 1996). Chaotic mixing creates eddy-based flow pat-terns which provide high specific interfaces, albeit bearingthe danger of being spatially inhomogeneous (Jen et al.,2003; Jiang et al., 2004; Lee et al., 2001; Liu et al., 2001; Niuand Lee, 2003; Qian and Bau, 2002; Solomon and Mezic,2003; Stroock et al., 2002a,b). Different from the first threeexamples, where two flows are contacted, a further concept

Interdigital- and bifurcation flow distribution structures

Focusing structures for flow compression

Flow obstacles within micro channels

Multi-hole plates

Specialty flow arrangements

Tiny nozzles

Repeated flow division- and recombination structures

T- and Y-flow configurations

Meander-like or zig-zag channels

Typical microstructure designs employed for passive mixing

Scheme 4.

relies on the injection of many substreams, e.g. via nozzles,into one main stream (Miyake et al., 1993). Collision of jetsprovides a means for turbulent mixing (Penth, 1999; Werneret al., 2002). Finally, a number of specialty flow guidanceshave been described as e.g. the Coanda effect, relying on amicrostructure for redirecting the flow (Hong et al., 2001)(Scheme 3).

1.2.3. Microstructures used in micromixer elements anddevices

Experts in microtechnology and in computational fluid dy-namics “transform” the above-mentioned micromixer meansinto physical objects, i.e., the microstructures which thenperform the mixing (Scheme 4). Some typical generic de-signs of such microstructures are given inFig. 3 .

Bi-lamination can be achieved in T- and Y-flow structures(Bökenkamp et al., 1998; Gobby et al., 2001), in their outershape similar to conventional mixing tees. Multi-laminationis done via structures with alternate feeds. The latter are re-alised either by interdigital (Branebjerg et al., 1996; Drese,2003; Ehlers et al., 2000; Ehrfeld et al., 1999; Floyd et al.,2000; Hardt and Schönfeld, 2003; Hessel et al., 2003; Löbet al., 2004; Zech et al., 2000) or bifurcation (Bessoth et al.,1999) structures. To speed up mixing, thinning of the multi-lamellae flow via hydrodynamic focusing can be utilised.(Branebjerg et al., 1996; Drese, 2003; Ehrfeld et al., 1999;Floyd et al., 2000; Hardt and Schönfeld, 2003; Hesselet al., 2003; Löb et al., 2004). Several types of flow dividingand recombining structures were developed for SAR-typemixing (Branebjerg et al., 1996; Schönfeld et al., 2004;Schwesinger et al., 1996). Chaotic mixing was, amongother later solutions (Jen et al., 2003; Jiang et al., 2004;Lee et al., 2001; Liu et al., 2001; Niu and Lee, 2003; Qianand Bau, 2002; Solomon and Mezic, 2003), first achievedby placing microstructured objects, such as herringbonestructures, into a microchannel (Stroock et al., 2002a,b).


Contacting

High energy collision

Injection into a mainstream

Injection of substreams

Decrease ofdiffusion path

Splitting andrecombination

Forced masstransport

Periodic injection

Contacting

High energy collision

Injection into a mainstream

Injection of substreams

Decrease ofdiffusion path

Splitting andrecombination

Forced masstransport

Periodic injection

Figure 3. Schematic drawings of selected passive and active micromixing principles.Source: Löwe et al., 2000.

Meander-like or zig-zag channels are also known to inducesecondary flows, e.g. recirculation, which at certain flowvelocity, is efficiently promoting mixing (Mengeaud et al.,2002). Several sub-streams may be injected into one mainstream via multi-hole plates (Miyake et al., 1993).

Mixing through turbulent collision can be achieved by themerging of two jets which are formed via nozzles (Penth,1999; Werner et al., 2002). Specialty flow arrangementspresent other solutions for passive mixing, e.g. to combinediffusion and convection mixing in analogy to the perfor-mance of packed beds in chromatography (He et al., 2001).

1.2.4. Determination of mixing efficiencyThe most common and simplest way to judge on mix-

ing in micromixer structures is done by flow visualisationvia dilution-type experiments(seeFig. 4) usually by the aidof microscopic-, photo-, video- or high-speed camera tech-niques (see e.g.Hessel et al., 2003for some details on thevisualisation technique). This is done by contacting dyedand transparent liquid streams (passive mixing) or standingvolumes (active mixing) in a type of photometric experi-ment. In fluorescence experiments, visualisation is achievedby fluorescent streams; in a commonly applied reaction vari-ant, mixing is proven by quenching of fluorescent streams.Reaction-type experiments(seeFig. 4) underlay the mix-

ing with a very fast reaction so that mixed regions sponta-neously indicate the result of the reaction (see e.g.Hesselet al., 2003). The simplest outcome of a reaction, again, isthe formation of a coloured species such as observed by theiron rhodanide reaction, introduced by Löwe inHessel et al.(2003), for flow visualisation in the microscale or the ylideformation (Skelton et al., 2000) in the framework of theWittig synthesis. Acid–base reactions with a pH-sensitivedye are also known as extremely fast reactions that sponta-neously induce colour changes. More detailed informationis given bycompetitive reactions, i.e., two parallel reactions,

e.g. introduced byRoessler and Rys (2001)or Villermauxet al. (1991). These reactions develop differently under vary-ing pH, solvent, etc. The latter parameters can be influencedvia mixing; they are different for the mixed state and the un-mixed state with temporally, spatially varying features. De-pending on the time required for reaching the mixed state,the ratio of the products of the competing reactions can con-siderably differ as a consequence of different reaction envi-ronments (pH, solvent, etc.) and, in turn, be used as a mea-sure of the mixing efficiency.

One frequently applied competitive approach for the char-acterisation of micromixer devices is the Dushman reaction,by which iodine is formed via an acid catalysed redox re-action between iodide and iodate (Villermaux et al., 1991).This reaction was first applied for determining mixing ef-ficiency in stirred batch reactors and then adapted to theneeds of micromixer devices (Ehrfeld et al., 1999). Later,an optimised protocol was developed for the Dushman re-action giving more accurate and better reproducible results(Loebbecke et al., 2004).Concentration profiling(seeFig. 5) uses on- or in-line

measurements of optical properties, typically not done forthe whole volume, but along lines such as the projectedchannel cross-section (see e.g.Hessel et al., 2003). Mea-suring several cross-sectional profiles at varying distancein a flow-through mixing channel gives the temporal evo-lution of the mixing at detailed spatial information. Con-centrations are accessible by photometric or fluorescencemeasurements. Electrode-based concentration detection, asroutinely used for the impeller-in-tank mixing characterisa-tion, may be used as well, albeit there are at present hardlyany reports (Tatterson, 1994). Especially miniaturised elec-trochemical sensors, available already today for other means,may perform this task in-line.

Besides using photometric techniques, vibrational anal-ysis such as IR and Raman can be used for following the


Figure 4. Multi-lamination flow patterns of a split-and-recombine mixer visualised by a dilution-type experiment, using the dye water blue (top).Multi-lamination flow patterns of a split-and-recombine mixer visualised by a reaction-type experiment, using the iron rhodanide reaction (bottom).Source: Schönfeld et al., 2004. In this way, complementary information on the course of mixing is yielded.

mixing course in a micromixer device (Loebbecke et al.,2000, 2002). Using an IR microscope, FTIR spectraat various channel sites can easily be monitored, if anIR-transparent construction material such as silicon is used(see alsoFig. 9, below).

2. Passive mixing: exemplary principles and devices

2.1. Y-type flow configurations

Y-type flow configurations are simple mixing structures,but have been applied both for gas and liquid mixing (Gobbyet al., 2001). Assuming a laminar flow and neglecting detailsof the flow field, e.g. entrance flow effects, the mixing lengthin these channels can be approximated byPe·w,Pebeing thepeclet number andw being the channel width. Despite thesimplicity of the concept, details of theY-type structure havea considerable impact on the mixing efficiency. This wasshown in a CFD study with regard to the mixing of gaseousoxygen and methanol, giving their mass fractions along thechannel path (inlet velocities= 0.3 m/s; Pe= 8.08, w =0.5 mm) (seeFig. 6).

The mixing length of a+45◦-oriented Y-mixer was2.03 mm; it amounts to 2.12 mm when using an inverseY-mixer (−45◦ orientation of the inlets). The−45◦ Y-mixerhas stagnant zones with reduced mixing, however, is lessfoot-print consuming compared to the+45◦ Y-mixer (seeFig. 6). The highest reduction of the mixing length of all

investigated Y-type mixer designs is given for a throttle(Venturi-type) Y-mixer. Oxygen/methanol mixing is com-pleted after only 0.5 mm flow passage for a throttle of100�m diameter which implies a pressure drop of about20 Pa for the inlet velocity given above.

The use of double T-type flow configurations for quench-flow analysis was demonstrated using fast acid–base neu-tralisation with colour change (Bökenkamp et al., 1998).Liquid mixing times in the ms range are achieved by highlyturbulent flows.

2.2. Multi-laminating flow configurations

Multi-laminating flow configurations can be realised bydifferent types of feed arrangements. Bifurcation-type feedscreate an alternate arrangement of feeds (Bessoth et al.,1999). Such a laminated feed stream passes into an inversebifurcation structure and a subsequent folded delay-loopchannel where mixing takes place. The multi-lamination pat-tern was confirmed by fluorescence flow visualisation. Byfluorescence quenching experiments quantitative informa-tion on the course of mixing at different locations was gath-ered. Mixing of liquid solutions was completed in less than100 ms; 95% mixing needs about 40 ms.

Another, so far more widely used feed concept is basedon parallel-flow interdigital feed arrangements (Branebjerget al., 1996; Drese, 2003; Ehlers et al., 2000; Ehrfeld et al.,


0

1

2

3

4

5

6

0 200 400 6000

1

2

3

4

5

6

0 200 400 600

0

1

2

3

4

5

6

0 200 400 600 0 200 400 6000

1

2

3

4

5

6

0

1

2

3

4

5

6

0 200 400 600 0 200 400 6000

1

2

3

4

5

6

c (w

ater

blu

e) [

g/l]

c (w

ater

blu

e) [

g/l]

c (w

ater

blu

e) [

g/l]

c (w

ater

blu

e) [

g/l]

c (w

ater

blu

e) [

g/l]

c (w

ater

blu

e) [

g/l]

6 ml/h : 6 ml/h

100 ml/h : 100 ml/h

Channel cross section [µm]


Channel cross section [µm] Channel cross section [µm]



10 ml/h : 10 ml/h

300 ml/h : 300ml/h

500 ml/h : 500ml/h 1000 ml/h : 1000ml/h

Figure 5. Axial concentration profiles in a focusing interdigital micromixer. At high flow rates, the regular multi-lamination patterns change to morecomplex super-positions of such patterns owing to lamellae tilting and winding.Source: Hessel et al., 2003.

1999; Floyd et al., 2000; Hardt and Schönfeld, 2003;Hessel et al., 2003; Löb et al., 2004; Zech et al., 2000).Basically, the flow outlet of these feed arrays is the sameas for the bifurcation-type feeds; however, the way toachieve it is based on pressure-loss triggered flow equipar-tition rather than relying on flow symmetry. Interdigitalfeeds with parallel (Branebjerg et al., 1996; Drese, 2003;Ehlers et al., 2000; Floyd et al., 2000; Hardt and Schönfeld,2003; Hessel et al., 2003; Löb et al., 2004; Zech et al.,2000) or counter-oriented flows (Ehrfeld et al., 1999)have been described as well as special types for handlingparticle-generating reaction systems (Schenk et al., 2002,2004). The channel width of the feeds of most interdigitalarrangements is chosen in a way that the width of the corre-sponding liquid lamellae is rather thick (e.g. 100�m), i.e.,diffusion is not very effective. Therefore, a second momen-

tum for speeding up mixing is employed. In analogy to thewell-known hydrodynamic focusing concept (seeKnightet al., 1998for a single stream andVeenstra et al., 1998fortwo streams), the multi-laminated flows are focused by pos-ing geometric constraints (typically a triangular focusingchamber), thereby compressing the lamellae (Branebjerget al., 1996; Drese, 2003; Floyd et al., 2000; Hardt andSchönfeld, 2003; Hessel et al., 2003; Löb et al., 2004).The benefit of the geometrical focussing can be easily seenlooking at the Fourier number, which in case of a straightrectangular channel comprising two fluid lamellae equalsFo=Tr/Tm =4·(hL/w) ·(D/�). Here,h, L, w, denote thechannel height, length width and� denotes the volumetricflow rate. Thus a reduction of the channel width leads toan increase ofFo implying an advanced diffusion. In thisway, diffusion distances are reduced by compressing the


Figure 6. Methanol mass fraction contours for the mixing of gaseousoxygen and methanol (0.3 m/s;Pe = 8.08). +45◦-oriented Y-mixer (top);−45◦-oriented Y-mixer (middle); throttle (Venturi-type) Y-mixer, 160�mdiameter (bottom).Source: Gobby et al., 2001.

fluid lamellae to a few micrometres, corresponding to liq-uid mixing in the milliseconds range. Two iodide solutionsfed by large excess, for example, compress a fluorescentlamellae in this hydrodynamic way until quenching of thefluorescence is achieved by fast diffusion (seeFig. 7).

Similarly, geometric compression, i.e., reduction of theflow cross-section, can lead to lamellae thinning, amenable

Figure 7. Hydrodynamic focusing by compressing a central stream bytwo outer streams at much larger flow rate. Mixing is visualised in areaction-type experiment. The internal fluorescent solution is quenchedby mixing with the excess external solution.Source: Knight et al., 1998.

especially to multi-lamellae systems. This has been theoret-ically predicted and experimentally confirmed by integratedphotometric analysis (Hardt and Schönfeld, 2003; Hesselet al., 2003). Concerning the latter, cross-sectional concen-tration profiles providing detailed spatial information wererecently measured. Among other information on the fluiddynamics, the existence of highly regular, periodical multi-lamination patterns could be confirmed for liquid flows, be-fore and after focusing. In addition, it was thereby shownthat liquid lamellae can tilt and, at high Reynolds numbers,spirally wind and form recirculations, if the focusing angleis set too large. In the case of gas mixing in an interdigitalmicrostructured mixer (Schubert et al., 1994, 2001) similarperiodic multi-lamination patterns were determined by a tinygas-collecting nozzle which was moved within the mixingchamber of interdigital mixers (Zech et al., 2000). At highvelocities of the gas streams, anomalously high mixing ef-ficiencies were found at a certain axial distance along themixing chamber. This observed faster mixing was explainedwith additional turbulent mixing due to the collision of gasstreams owing to the tilted injection via the interdigital feed.It was found that the mixing energy of these microstructuredmixers normalised by the volume for a given mixing task islower than that of an industrially employed jet mixer.

A special liquid focusing interdigital mixer with paral-lel feed flows, termed SuperFocus, was optimised by semi-analytical calculations and first realised as a glass versionwith 128 nozzles (8 l/h at 3.5 bar) and later as a steel version(350 l/h at 10 bar) with 138 nozzles (Drese, 2003; Hardt andSchönfeld, 2003; Hessel et al., 2003; Löb et al., 2004). Bothversions yield 4�m thin liquid lamellae. While the glass


Figure 8. Multi-lamination pattern fed by 138 microchannels in a Su-perFocus mixer made of stainless steel and equipped with an inspectionwindow (flow: 350 l/h at 3.5 bar).Source: Löb et al., 2004.

mixer has a focusing ratio of 40, the steel mixer provides aratio of 200 for reasons of larger throughput and less sen-sitivity of fouling. Since the final lamellae width was fixed,the number of lamellae and hence the throughput was con-siderably increased for the steel mixer (seeFig. 8). A mix-ing time (for 95% completion of mixing) of 4 ms, exclud-ing the time needed for passing the focusing chamber, wasconfirmed by photometric measurement for the SuperFocusmixer, corresponding to some cm mixing length at mostpractical throughputs. Recently, a design optimisation studyon the dimensions of the triangular focusing chamber wasmade to reduce the residence time within this flow passageto shorten the overall mixing time (Drese, 2003).

Earlier versions of counter-flow interdigital mixers werecharacterised for their mixing efficiency using the Dushmancompeting reaction, discussed above (Ehrfeld et al., 1999).By photometric analysis it was evident that the mixing effi-ciency is superior to that of stirred vessel and conventionalmixing tees. Moreover, the analysis method allowed one todraw detailed conclusions on the impact of small designchanges and paved the way for a comparison of different mi-crostructured mixers, facing throughput or energetic issues.The mixing efficiency of the earlier designs was influencedby a secondary mixing mechanism based on jet mixing in-ducing eddies in the surrounding liquid. The flow in thisoutlet region is not entirely laminar anymore. So it must betaken into account that results for determination of mixingefficiency (as well as for performing chemical reactions) canbe strongly influenced by the flow behaviour outside the mi-crostructured region and may lead to a misinterpretation ofexperimental results.

For an unfocused parallel-flow interdigital mixer FTIR-monitoring of the reacting flows was achieved, yielding alarge number of interferograms and consequently detailedinformation on the course of mixing and reaction (seeFig. 9)

Stop flow

Abs

orba

nce

1900 1800 1700 1600 1500 1400 1300 1200 1100 1000

0.050

0.025

∆t(6

5 m

sea

ch)Stop flow

Wavenumber / cm-1

Figure 9. Stack plot of FTIR spectra obtained from a time resolved runof the reaction of methyl monochloroacetate and sodium hydroxide (timedelay between spectra amounts to 65 ms).Source: Kakuta et al., 2003a.

Figure 10. Flow patterns in a cyclone micromixer made of glass, CFDsimulations (left) and experimental patterns by a dilution-type experiment(right). 30 ml/h: 20 ml/h (top images), 64 ml/h: 42 ml/h (bottom images).Source: Hardt et al., 2002.

(Kakuta et al., 2003a). As an example for a fast reaction theneutralisation of an acid/base reaction was chosen; as a slowprocess, the saponification of an ester was investigated. ForNMR-monitoring by micromixers seeKakuta et al. (2003b).

Cyclone mixers are a further type of multi-laminatingmixers (Böhm et al., 2001; Hardt et al., 2002). Respec-tive flow patterns were confirmed by microscopy analysisand resemble the predictions made by CFD analysis (seeFig. 10).


0

1

2

3

4

5

6

7

8

9

10

0 1000 2000 3000 4000 5000 6000

Total flow rate [l/h]

Pre

ssu

red

rop

[b

ar]

StarLam 1st version with 50 µm plates (2 x 140)

StarLam300 with 100 µm plates (2 x 65)

ditto - extrapolated

StarLam3000 with 250 µm plates (2 x 113)

ditto - extrapolated

Caterpillar mixer version 1 R1200/8, milled

Figure 11. Achievable throughputs for large-capacity microstructured mix-ers of theStarLamseries.Source: Werner et al., 2005.

StarLaminators are large-capacity microstructured de-vices with a stack of plates which have star-like openings(Ehrfeld et al., 2000; Werner et al., 2005; Löwe et al.,2000). Their fluid feed generically resembles an alternating(interdigital) flow injection. Owing to the large internalopening and the typically applied large volume flows, theflow regime, however, is turbulent so that a pre-layered flowis consecutively mixed by eddy formation. Since the platescan be manufactured at low cost and a large number ofplates, e.g. several hundreds, can be stacked, extremely largethroughputs can be achieved already for devices of smallexternal volume. TheStarLam300andStarLam3000appa-ratus were operated at nearly 1000 l/h (3 bar) and 3.5 m3/h(0.7 bar) liquid throughput, the latter can be extrapolated to5 m3/h (about 3 bar) (seeFig. 11). The determined mixingefficiencies reach the limits which are usually be attributedto good mixing in micro and microstructured mixers.

2.3. Split-and-Recombine flow configurations

Split-and-Recombine (SAR) mixers create sequentiallymulti-laminating patterns, different from the parallel ap-proach of the interdigital feeds. For this purpose, basicallythree steps are required, flow splitting, flow recombinationand flow rearrangement (seeFig. 12) (Branebjerg et al.,1996; Ehrfeld et al., 2000;Löwe et al., 2000; Schönfeldet al., 2004; Schwesinger et al., 1996). The designs of SARmixers differ in the exact geometry by which they actuallyachieve this fluidic arrangement. Fork-like- (Schwesingerand Frank, 1995; Schwesinger et al., 1996), ramp-like-(Branebjerg et al., 1996; Löwe et al., 2000) and curvedarchitectures (Schönfeld et al., 2004) with (Branebjerget al., 1996; Schönfeld et al., 2004) and without (Löweet al., 2000; Schwesinger et al., 1996) splitting plane werereported.

It is meanwhile known that the flow splitting in SARmixers is superimposed by secondary recirculation flowpatterns at most practical Reynolds numbers (Re) and formost liquids. This can be, e.g., shown by particle-tracking

Figure 12. CFD simulation of the cross-sectional flow pattern of anoptimised split-and-recombine (SAR) caterpillar microstructured mixer,displaying several stages within one SAR step. At the end, a four-laminatedpattern is achieved, close to the ideal. Only small deviations regarding tothe lamellae width and the lamellae curvature are given.Source: Schönfeldet al., 2004.

simulation which give “diffusive” patterns at highRe (seeFig. 13) (Schönfeld et al., 2004). This makes it difficult tojudge on their real flow-splitting performance. In a recentstudy high-viscosity liquids were mixed in order to work atlow Renumber(< 10). Here, by CFD-based optimisationof a previous SAR design indeed multi-lamination patternswere found. In this way, it was shown that ideal SAR flowsare easily spoiled by inertia or friction forces which areinduced for lamellae having a relative velocity. The forma-tion of the multi-lamellae was proven both by dilution-typeand reactive imaging. It was further noted that SAR flows,although ideally highly regular, have features of chaoticmixing, as they benefit from an exponential increase ininterface similar to the chaotic stretching, as e.g. describedby the Lyapunov exponent.

2.4. Structured packing flow configurations

Some devices have internal 3-D structures, like structuredpackings, for distributive mixing, essentially as given forconventional static mixers (Bertsch et al., 2001; He et al.,2001). This is meanwhile achievable by use of modern 3-D microfabrication techniques such as stereolithography us-ing polymerisation of solutions. Two microstructured mix-ers with intersecting and helical internals were realised inthis way (seeFig. 14). The analysis of cross-sectional ve-locity profiles(Re = 12) shows that the device intersectingstructures has intricate gradient fields near the bars of theinternals, while the helical device displays entrance and exiteffects (seeFig. 14). When judging mixing efficiency byparticle trajectories(Re = 12), it is evident that the inter-secting device performs manifold splitting and recombining


Figure 13. Secondary flows appear in a split-and-recombine caterpillar microstructured mixer at highRenumber, as imaged by particle tracking simulations.Source: Schönfeld et al., 2004.

Figure 14. Images and simulated mixing efficiency, visualised by particle trajectories (atRe = 12) for the intersecting device (top) and helical device(bottom).Source: Bertsch et al., 2001.

of the flow, yielding a fine-dispersed system at the end, i.e.,achieving a good mixing efficiency. In contrast, flow stretch-ing and folding are found for the helical device, resulting ina coarsely textured fluid, which means less efficient mixing.

Besides having additional structures within the wholechannel, they may be placed only on one channel side,yet altering the profile in the complete flow domain (Jenet al., 2003). T-shaped, inclined, oblique, and wavy struc-tures were simulated for their performance for mixing ofgaseous methanol and oxygen. Though an influence of thegeometry was detectable, comparatively similar mixinglengths for mixing completion were found for the differentdesigns. A correlation between mixing performance andperiodicity of the functional elements is given, leading to amaximum-type curve of the mixing efficiency. The shortestmixing length calculated was about one third of the onefound in a basic T-junction.

2.5. Chaotic flow configurations

The salient feature of chaotic advection in the presentcontext is the exponential growth of the interfacial areaaccompanied by a corresponding reduction of the striationthickness. A proper definition of chaotic flows requires acertain mathematical framework which is beyond the scopeof this review. A comprehensive mathematical description

Figure 15. Staggered herringbone micromixer for the generation of chaoticflows with schematic and real flow patterns.Source: Stroock et al., 2002a.

can be found in (Ottino, 1989). Chaotic advection can oc-cur either by two-dimensional unsteady velocity fields orby three-dimensional velocity fields with or without time-dependence. Many of the active mixing principles fall intothe former class. The simplest example is the so-called‘Blinking Vortex Model’, i.e., an alternating agitation vor-tex, mathematically analysed byAref (1984). Steady three-dimensional chaotic flows have been successfully used formicromixing in several contexts (Jen et al., 2003; Jianget al., 2004; Lee et al., 2001; Liu et al., 2001; Niu and Lee,2003; Qian and Bau, 2002; Solomon and Mezic, 2003;


0

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0.00008

0.00009

0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002

Y (m)

Z (

m)

0

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0.00008

0.00009

0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002

Y (m)

Z (

m)

Z (

m)

Z (

m)

0

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0.00008

0.00009

0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002

Y (m)

Z (

m)

0

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0.00008

0.00009

0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002

Y (m)

0

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0.00008

0.00009

0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002

Y (m)

Z (

m)

0

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0.00008

0.00009

0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002

Y (m)

(a) X = 0.00000 m (b) X = 0.00099 m

(c) X = 0.00209 m (d) X = 0.00319 m

(f) X = 0.00539 m(e) X = 0.00429 m

Figure 16. Evolution of the positions of particle tracers along a staggered herringbone micromixer design.Source: Aubin et al., 2003.

Stroock et al., 2002a,b). The first publications on chaoticadvection by micromixers rely on placing microstruc-tured objects within the flow passage on one side of themicrochannels (Stroock et al., 2002a,b). By this means,flow circulations are generated which lead to an exponentialincrease of specific interface, hence to fast mixing. Typicalfor such chaotic flows are circulating fluids with large inter-faces besides quiescent zones with less improved mixing.

One of the pioneering descriptions presents a staggeredherringbone mixer (SHM) (Stroock et al., 2002a,b). High-resolved cross-sectional images of the flow were presented,showing the ongoing folding of the initial lamellae afterpassing the cycles defined by the herringbone pattern (seeFig. 15). The SHM mixing is superior to similar microchan-nels without internal structures or with straight ridges only.Whereas the basic T-mixer requires mixing lengths of about1 m and 10 m at Peclet numbersPe=104 and 105, the SHMmixer performs the same task within 1 and 1.5 cm only, re-spectively. The dependence of mixing efficiency on thePenumber is described as well.

The laminar flow patterns and the mixing performance ofthe comparable mixers with diagonal or asymmetric groovesherringbone grooves was investigated and quantified by CFD(Aubin et al., 2003; Kang and Kwon, 2004). A single helicalflow was generated by the diagonal mixer, whereas the her-ringbone mixer produces a double helical flow, consisting oflarge and small vortices (seeFig. 16). By particle trackingit is confirmed that a low degree of convective mixing takesplace in the diagonal mixer. In turn, the herringbone mixerachieves very good mixing. Further, calculations of the vari-ance of the tracer dispersion and the stretching were made.

A much simpler channel design, based solely on alter-nately curved microchannels, has been proposed later (Jianget al., 2004; Schönfeld and Hardt, 2003). This was set inanalogy to a similar 3-D curved mixer made by conventionalfolded tubing described earlier (Schierholz et al., 1997).While the SHM mixer performs well atRe ∼ 1, this de-sign is suited for Reynolds numbers in the range of a fewhundred. The important dimensionless group for flow de-scription in the curved-channel mixer is the Dean number


0

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0.00008

0.00009

0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002

Y (m)

0

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0.00008

0.00009

0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002

Y (m)

0

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0.00008

0.00009

0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002

Y (m)

0

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0.00008

0.00009

0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002

Y (m)

0

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0.00008

0.00009

0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016 0.00018 0.0002

Y (m)

Inlet Outlet

(a) (b) ( c) (d) ( e) (f) (g) ( h) (i) ( j) (k)

Z (

m)

Z (

m)

Z (

m)

Z (

m)

Z (

m)

(g) X = 0.00649 m (h) X = 0.00759 m

(i) X = 0.00869 m (j) X= 0.00979m

(k) X = 0.01089 m

Figure 16. (continued).

(De = Re(d/R)1/2), taking into account the channel curva-ture R. By triggeringDe, mixing efficiency can be tuned.It was demonstrated that four vortices develop inducinglarge internal interfacial areas forDe > 140; the correspond-ing interfacial stretching rises largely loop per loop (seeFig. 17). By iron rhodanide reactive imaging the course ofmixing could be followed (Jiang et al., 2004). Only a pas-sage of two curves was sufficient to result in a fully colouredsystem, indicating a complete mixing (seeFig. 17).

2.6. Recirculation flow configurations

Zig-zag channels can create recirculation flow patternsin their recesses at sufficiently highRenumber (e.g. 267)(Mengeaud et al., 2002). Then, a slightly curved main flow

passes through the channel diagonal, being encompassed bya number of eddies in the triangles of the zig-zag channels.For low and moderateRe numbers below 100 a constantmixing efficiency is found ifPe is kept fixed(Pe= 2600),only quiescent zones, i.e., dead zones, are observed. In a de-tailed study, it was confirmed that the improvement of mix-ing at highRenumbers is not only owing to the decrease oflamellae width as a result of the reduced extension of theflow into the triangles, but also due to the impact of recir-culation. It was further shown that having a too high peri-odicity of the zig-zag arrangement is not beneficial, as thisultimately resembles the straight channel condition. Whenplotting the mixing efficiency over the periodicity, thus, amaximum is passed; accordingly, the difference between theperformances of the zig-zag to the straight channels is alsomaximal there (seeFig. 18).


Figure 17. Interface stretching in a curved Dean micromixer as a function of the flow passage (number of loops) at two Dean numbers (left). Flow patternsat the two Dean numbers (upper right) and reactive imaging of the mixing by the iron-rhodanide reaction (lower right) are given.Source: Jiang et al., 2004.

Figure 18. Mixing efficiencies for zig-zag channel micromixers of dif-ferent periodicity at twoRe numbers (triangles: 2.67; circles: 267) andcomparison to ‘base cases’ which are linear channels of widths that cor-responds to the inner or outer width of the zig-zag channels.Source:Mengeaud et al., 2002.

2.7. Colliding jet configurations

High-velocity jets can mix fast by turbulence when theyare merged (Penth, 1999, 2000). Even at lower velocity thisconcept can be useful, if there is no other micromixer alterna-tive. Particle-producing solutions usually cannot be handledinside microstructured mixers, but there may be nonethelessreasons for such usage (e.g. with regard to safety). In thesecases, mixing efficiency is not the key function.

A complete system with jet collision at very high veloc-ities is commercially available and versatile in application,i.e., can be used for powder synthesis and emulsification(Penth, 1999, 2000). A low-velocity jet collision device withY-type flow configuration, with free guided jets, i.e., basi-cally a “mixing tee without guiding walls”, has been realised

Figure 19. Y-type jet generated by a jet micromixer.Source: Werneret al., 2002.

for conducting reactions that lead to immediate and heavyprecipitation (seeFig. 19) (Werner et al., 2002). This sys-tem was successfully applied to the quaternisation of ternaryamines and the base-assisted amide formation, which bothare known to be not feasible in other standard microchanneldevices.

2.8. Moving droplets configurations

Droplets can be moved via electrowetting which is thechange of surface energies by applying electric fields (Palket al., 2003). Typically, this is achieved by ground electrodeand a linear electrode array which act as path for the mov-ing droplets. The size of the droplet is chosen so that it is


Figure 20. (a) 2-D image of a packed bed and schematic of a possible mixing of two streams at two discrete zones. (b) A microstructured analogueof the packed bed shown in (A). (c) The same microstructure as displayed in (B), however part of the columns were removed to form a large conduitwhich is fed by many flows through the small interstices. (d) Microstructured mixer developed based on the packed bed mixing concept. A large foldedmain channel and smaller channels serve for dual flow passage.Source: He et al., 2001.

slightly larger than the area of one electrode segment, i.e.,partly overlaps with the adjacent electrodes. In one pioneer-ing study, the electrode gap was set to 800�m and the dropletvolume was 1.9�l. A voltage of 50V was applied (Palket al., 2003).

If mixing is achieved by droplet movement only, this ispassive mixing owing to convections (Palk et al., 2003). Fur-thermore, the droplets can be shaken which is a kind of activemixing (see below). In a passive mixing experiment fluores-cent and non-fluorescent droplets were merged. It was foundthat this did not lead to effective mixing, rather a verticallylayered structure within the droplet is produced. These lay-ers mix only via diffusion and therefore need 1–2 min timefor completion of mixing. Owing to the layered structure, avertical microscopy inspection (‘from the side’) in additionto the normal, horizontal (‘from the top’) is needed. Other-wise, the images suggest mixing, albeit this is actually notthe case.

2.9. Specialty flow configurations

One micromixer design was oriented at the structure ofpacked columns, e.g. for use in chromatography, which haveboth diffusive and convection mixing owing to the presenceof smaller channels and larger conduits, respectively, caused

by imperfect packing or imperfect packing material (seeFig. 20) (He et al., 2001). The latter effect can be exploitedpurposeful using microstructuring techniques. A first gen-eration microdevice was thus equipped with a large mainzig-zag-channel. The tilted channel parts are, in addition,linked via smaller channels to have short diffusion distances,which are expected to result in enhanced diffusive mixing(seeFig. 20).

A passive Coanda effect micromixer relies on the re-direction of a flow by a special guiding structure which cre-ates new interfaces within the flow (Hong et al., 2001). Inthis way the Coanda mixer can also be seen as a specialrealisation of the SAR approach using recycle-flows.

A self-filling micromixer device utilises capillary forcesto insert and hold the liquids in separate chambers whichare connected via a small gap (Seidel et al., 2000). At thisinterface, mixing takes place. Owing to the self-filling natureof the mixer, the tool was also termed auto-mixing device.

3. Active mixing: exemplary principles and devices

3.1. Periodic flow switching

One of the most obvious ways to achieve active mix-ing in microstructured devices is by alternating, preferably


Figure 21. Numerical simulation results obtained for two inlet flows pulsed at 180◦ phase difference. (a) Mean velocity as a function of time in thein-line (dashed) and perpendicular (solid) inlets; contour levels of the liquid mass fraction in theYZ-plane cross-section at various times correspondingto the previous graph. Finger-shaped folds are found. (b) Contour levels of the liquid mass fraction in theXY-plane at half the channel depth at varioustimes corresponding to the previous graph. Alternate puffs of the liquids travel downstream.Source: Glasgow and Aubry, 2003.

periodical, switches of the flows from a high to a low flowrate (Glasgow and Aubry, 2003). In this way, a pulsation ofthe whole stream is achieved promoting mixing; such axialmixing is not given otherwise for laminar flows.

CFD simulations concerning a pressure-driven variant offlow switching are described inGlasgow and Aubry (2003).The design proposed uses a tri-layered injection. Within therange of inlet flow rates from 1.0 to 8.5 mm/s (fromRe=0.3to 2.55) for temporal invariant (non-pulsed) operation, thedegree of mixing is rather low; according to the relation

Lm = Pe · w a decrease of the flow rate induces a smallerresidence time and thus a higher mixing length. Time puls-ing of one inlet flow rate distorts the interface to an asym-metrically curved shape which changes with time. Thereby,material transport is promoted and mixing is enhanced. Thedegree of mixing is now 22%, being 79% larger than forconstant flows. The periodicity and the number of pulsingstreams have a notable influence of the mixing efficiency.The best results are obtained for two pulsed inlet flows hav-ing a phase difference of 180◦ (amplitude and frequency


Figure 22. Pointcaré sections of the chaotic micromixer for different values of the amplitude�p and angle frequency� of the perturbation. The Pointcarésection(a′) shows the data in a geometric different way, via polar coordinates. This allows a presentation with continuous angle�. Source: Niu and Lee,2003.

being the same). CFD simulations show the bending of thefluid interface along the channel cross-section and the re-spective stretching and folding in the direction of the flow(seeFig. 21). The corresponding degree of mixing is notablyincreased to 59%.

This concept can be extended to the multiple, pulsing in-jection of flows into one microchannel; such devices are sofar hypothetical and certainly would require a complex con-trol system (Niu and Lee, 2003). By these means, chaoticadvection can be generated. A detailed simulation study de-scribes the effect of the variation of the amplitude and anglefrequency of the perturbation for a multi-injection design.For a given parameter set, the coexistence of chaotic andquasi-periodic areas is found (seeFig. 22). An increase ofthe amplitude from there at fixed frequency results in the

formation of chaotic areas that are not homogeneously dis-tributed within the bulk fluid. At still higher amplitude, theso-called Kolmogorov–Arnold–Moser (KAM) curves, posi-tioned at the interfaces between chaotic and quasi-periodicareas, break up to islands (seeFig. 22). As a special feature,outer and inner chaotic areas are found. By plotting the Lya-punov exponent versus the amplitude and angle frequency,optimal operating parameters were concluded.

For electroosmotic-driven flow, periodic flow switchingcan be achieved in a similar way, now by using non-uniform� potentials along the conduits’ walls to induce chaotic ad-vection (Qian and Bau, 2002). Both spatial and tempo-ral control of the� potential can be achieved by imposingan electric field perpendicular to the solid–liquid interface.Practically speaking, the generation of such normal electric


Figure 23. Streamline pattern for the superimposed flow structure, byswitching between two flow patterns, forh = 2, h being the periodicityof the electrode arrangement (top). Pointcaré sections for various periodsT = 2, 4, and 6 andh = 2. A passive tracer particle was initially insertedat (x0, y0) = (0, 0.01), and its motions were followed by 3000 periods(bottom). x and y are coordinates referring to the mixer dimensions.Source: Qian and Bau, 2002.

fields can be accomplished by placing multiple electrodesbeneath the solid–liquid interface.

The effect of switching between several flow fields at var-ious periods was analysed for a simple two-electrode con-figuration by particle tracking simulation (Pointcaré maps)(Qian and Bau, 2002). At high periodicity, a simple super-position of the flow fields is achieved (seeFig. 23). Elliptic

fixed points surrounded by closed orbits (tori) of various pe-riods are found. For larger periods, chaotic behaviour arises,the hyperbolic fixed point is disrupted and the tori are per-turbed (seeFig. 23). A chaotic region appears with homo-clinic tangle and the formation of new hyperbolic and ellipticpoints. When further increasing the period, the complexityof the flow becomes more pronounced. First, the particleswander around the superimposed pattern. Then, particles arestrayed further away from the “regular path” and samplemost of the cell’s area. Chaotic advection is now present.When using four embedded electrodes, even more complexflow fields are achieved, as to be expected, which are in partssimilar to those generated by switching with two electrodes.

3.2. Acoustic fluid shaking

An air bubble in a liquid medium can act as actua-tor, when it is energised by an acoustic field, i.e., thebubble surface behaves like a vibrating membrane (Liuet al., 2003, 2002). This bubble actuation is largely deter-mined by the bubble resonance characteristics (for moredetails hereunto see,Liu et al., 2003, 2002). Bubble vi-bration due to a sound field induces friction forces at theair/liquid interface which cause a bulk fluid flow around theair bubble, termed cavitation microstreaming or acousticmicrostreaming. Circulatory flows lead to global convec-tion flows with “tornado”-type pattern which fasten mix-ing. For pulsation the insonation frequency has to meetthe resonance frequency which is, of course, strongly de-pendent on the bubble radius. The bubble then has to befixed at a solid boundary. Sonic irradiation without use ofair bubbles causes only little fluid motion. In turn, sonicirradiation with the use of air bubbles caused consider-able gross fluid motion for a dyed solution (Liu et al.,2003, 2002). Due to the uniform distribution of the air pock-ets, mixing is induced in the complete microchamber andnot localised to one part only. A dilution-type experimentwas made for one-bubble microstreaming mixing using adyed solution. The dye completely fills the drum-shaped mi-crochamber (300�m depth; 15 mm diameter) within about110 s (Liu et al.,2002). Using four bubbles, only 45 s areneeded for the same task, an improvement in mixing timeof about 40%. Mixing in a further improved microdevicewith nine bubbles was performed (seeFig. 24) (Liu et al.,2002). The influence of the amplitude and of the wave type(sinusoidal or square) has been reported as well.

Immunomagnetic cell capture experiments need mixingof the bacterial cell (e.g.Esherichia coliK12) matrix sus-pended in blood with magnetic capture beads, which resultsin a highly effective immunomagnetic cell capture. Bacterialviability assay experiments demonstrated that acoustic mi-crostreaming mixing has a relatively low-shear strain field(Liu et al., 2002). The capture efficiencies of acoustic mix-ing (90%, at best) were as high as for conventional vor-tex mixing (91%, at best). They were much larger than for


Figure 24. Photographs showing acoustic microstreaming in a microcham-ber (with 125�m depth and 12×15 mm area) which has nine top bubbles(300�m depth and 2 mm diameter) at the times (a) 0 s; (b) 28 s; (c) 1 min7 s; and (d) 1 min 46 s.Source: Liu et al., 2002.

non-mixed samples (4%, at best). Double staining tests withSYTO 9 green fluorescence and propidium iodide red fluo-rescence showed that the blood cells and bacteria remainedintact after mixing.

3.3. Elektrokinetic instability

Mixing can be accomplished by the action of fluctuatingelectric fields (Oddy et al., 2001). In this way, rapid stretch-ing and folding of material lines are induced, similar tothe effect of stirring. As electrokinetic instability (EKI) theinitiation of a flow instability by oscillating electroosmoticflows is defined (Oddy et al., 2001). Most common, sinu-soidal oscillation of electric fields is applied. EKI is adequatefor mixing flows at very low Reynolds number (∼ 1). Inone realised example, comparatively low frequencies, below∼ 100 Hz, and electric field strengths in excess of 100V/mmwere applied for channels with dimensions of about 50�m.A small square mixing chamber is connected to two oppo-site electrodes; the two liquids are fed in 90◦-orientation tothe electrodes into the chamber and one outlet is placed onthe side of the chamber (seeFig. 25) (Oddy et al., 2001).

By a fluorescent experiment, full-field images of the entiremixing chamber of the EKI mixer device with parts of theinlet-, outlet- and side excitation channels were taken. In themixing chamber rapid stretching and folding of the fluores-cence tracer is observed (Oddy et al., 2001). Consequently,a homogeneous fluorescence texture in the outlet channel isfound. A mixing time of 2.5 s for a mixing volume of 0.1�lwas determined, which is superior to the performance of aformer prototype device (13 s).

Ensemble-averaged probability density functions andpower spectra of the instantaneous spatial intensity profileswere used to quantify the mixing process, completing the

Figure 25. Design of an electrokinetic instability micromixer, sec-ond-generation device, based on the results obtained with the first design.The electrokinetic instability is confined to the square mixing chambershown in the centre of the schematic and, to a small part, to fluid channelregions attached to it.Source: Oddy et al., 2001.

information given by direct imaging (Oddy et al., 2001).The integration of the fluorescence intensity over measure-ment volumes (voxels) by a high-resolution CCD cameraprovides a measure of the mixing degree to which twostreams are mixed within each voxel volume. In the initialunmixed state with no AC field, the image power spectrumis characterised by a frequency band slightly elongated inthe vertical direction. In the state of mixing development,advective flux arises which creates high-spatial frequencygradients in the power spectra. New interfacial area is per-petually generated within the flow. In the final, mixed state,these high-frequency bands are damped. The correspondingwell-stirred power spectra are hence isotropic.

3.4. Electrowetting-induced droplet shaking

It is described above that by electrowetting droplets canbe merged and passive mixing takes place (Palk et al., 2003).However, the layered, segregated structure within the mergeddroplet does not lead to fast mixing. For this reason, activemixing by electrowetting was developed, basically leadingto a shaking of the merged droplet. This turned out to beparticularly effective when using multi-electrode arrays. Fora four-electrode array (600�m electrode gap; 8 Hz, 1.32�ldroplet volume; 50V) complex patterns of fluid motion werefound, giving much reduced mixing times as compared topassive mixing. In contrast, the shaking of the droplets bytwo- or three-electrode arrays leads to flow reversibility withthe result that newly generated interfaces vanish and theoriginal pattern is restored, as fluorescence imaging demon-strates (seeFig. 26).

3.5. Ultrasound/piezoelectric membrane action

Mixing can be achieved by ultrasound using lead–zirconate–titanate (PZT) membranes, a piezoelectric ce-ramic, operated in the kHz range (Yang et al., 2001). In this


Figure 26. (a) Possible droplet positions and directions in three-electrode mixing. (b) Time lapse images of three-electrode mixing at 8 Hz.Source: Palket al., 2003.

way, liquid streams can be moved and even turbulent-likeeddies are induced. Favourably ultrasonic action is coupledinto a closed volume, a microchamber.

An ultrasonic micromixer was realised and tested bya dilution experiment, employing the dye uranine (Yanget al., 2001). In the absence of ultrasonic mixing, two stablefluid regions with the separated water liquid and the uraninesolution were found in the mixing chamber, mixing beinglimited to the interface by slow molecular diffusion.

Upon ultrasonic action, turbulence occurred, moving ma-terial throughout the whole mixing chamber (Yang et al.,2001). After termination of ultrasonic mixing, the initialpattern was rapidly restored, the two zones separated by astraight interface. From video observation, a mixing time ofabout 2 s was estimated. Spatially resolved fluorescence in-tensity measurements gave the same information as by lightmicroscopy, in a quantitative manner. Initially, a concentra-tion profile with step function at the fluid interface is dis-played, while after ultrasonic mixing a uniform concentra-tion on a medium level is obtained throughout the mixingchamber (seeFig. 27).

Another micromixer based on a thin piezoelectrically ac-tuated membrane is described inWoias et al. (2000). Bycolorimetric measurement the impact of the frequency andamplitude of actuation on the mixing efficiency was char-acterised. An optimum signal amplitude between 30 and40V was found corresponding to a total membrane stroke of6.7�m. For lower voltages, mixing is incomplete. At higheramplitude, no further improvement was noted. Owing to thevery small mixing chamber fast changes of mixing can beinduced. In particular, the feasibility of the concept for per-forming of a large number of colorimetric cuvette assayswas demonstrated.

A micromixer incorporated with a piezoelectrically drivenvalveless micropump uses turbulence for mixing (Yang

Figure 27. Qualitative mixing performance by plotting the non-calibratedfluorescence intensity measured near the outlet of the mixing chamberalong a cross-sectional line as a function of the position on this line.The mixing performances are shown before (grey curve) and after (blackcurve) the ultrasonic action.Source: Yang et al., 2001.

et al., 1998). The mixer has two pairs of diffusers at theinlet and outlet of the chamber. Mixing was followed bydilution-type experiments with dyed solutions.

3.6. Microimpellers

Conventionally, stirring with impellers is the most com-mon way to accomplish mixing of larger volumes, typicallyheld in tanks. Since in many�TAS applications liquids inmixing chambers of comparatively extended volume have tobe mixed, it is not too far-fetched to develop miniaturisedstirrers (Lu et al., 2001). Claimed advantages of microim-pellers are the possibility to match the impeller diameterto the mixing volume, to perform large-area mixing, to un-dergo mixing on-demand (switch on/off), and the flexibility


of the mixing approach e.g. concerning the choice of liquids.Microimpellers of several tens microns diameter consistingof a cap, hub and two rotary blades were made by electro-plating from the ferromagnetic material Permalloy (Lu et al.,2001). Within about 1 min complete mixing was achievedat a stirrer rotational speed of 600 rpm (mixing volume of0.17�l/ min in a mixing chamber 2.5 mm long and 40�mdeep).

3.7. Specialty active mixing

A magneto-hydrodynamic mixer (West et al., 2002)utilises arrays of electrodes deposited on the walls of a mi-crochannel. Through alternate potential differences acrosspairs of electrodes currents in various directions of the mix-ing volume are generated. By coupling of an electric andmagnetic field, forces are exerted on the fluid. Via variableelectrode patterning, complex flow fields can be induced.Thereby, a so-called cellular motion was initiated to enlargethe fluid interfaces for mixing.

An integrated mixer/valve with a cantilever-plate flap-per valve allows for non-continuous mixing by diffusion(Voldman et al., 1998). Mixing is performed within less than5 s at mixing lengths ranging from 9 to 55 mm for flow ratesof 0.3–1.8 ml/h.

4. Conclusions and outlook

Meanwhile, the choice of micro and microstructured mix-ers is sufficiently broad; commercial catalogue products areeven available for production purposes. Devices are acces-sible for a large flow range from ml/h to m3/h and differentmeans of mixing can be utilised, e.g. differing in energy in-put and fouling sensitivity. Certainly there is still room fornew designs and principles, but these are not the tasks ofutmost importance for future developments.

The next developments should establish the microstruc-tured mixers as ordinary pilot-scale and production appara-tus in chemical industry. The existing mixing devices haveto be equipped with additional functions such as heatingand sensing. Still, more robust and professional designs areneeded and field trials have to be conducted to evaluate thepotential in an industrial environment. Besides such tech-nical improvement, the emergence of a market has to beactively initiated and supported. The emerging new compa-nies selling such devices in the field need assistance duringstart-up to bring their products on the market.

The large choice of micromixers, particularly activelymixing ones, demands for a benchmarking and splitting intomore scientifically and more field-experienced approaches.So far mainly test solutions were applied for mixing charac-terisation; in future the developments should go into appli-cation, mixing real-case solutions. Since these are usuallyelements within an integrated�TAS device their commer-cial implementation is closely linked to the introduction ofthese miniaturised analytical tools in the market.

Generally, it is the mission of this paper to add a furtherpiece to render microstructured mixers as normal, accessoryapparatus which the biologist, chemist or chemical engineercan use, extending the performance of existing apparatus ina kind of multi-scale approach.

Acknowledgements

F. Schönfeld acknowledges support by the DFG-Forschergruppe FOR 516/1 (Mikro- und Nanochemie),German Ministry of Research and Education, grant number16SV1355.

References

Aref, H., 1984. Stirring by chaotic advection. Journal of Fluid Mechanics143, 1–21.

Aubin, J., et al., 2003. Characterization of the mixing quality inmicromixers. Chemical Engineering and Technology 26 (12), 1262–1270.

Auroux, P.A., et al., 2002. Micro total analysis systems, 2: analyticalstandard operations and applications. Analytical Chemistry 74 (12),2637–2652.

Bayer, T., Himmler, K., Hessel, V., 2003. Don’t be baffled by static mixers.Chemical Engineering (5), 2–9.

Bertsch, A., et al., 2001. Static micromixers based on large-scale industrialmixer geometry. Lab on a Chip 1, 56–60.

Bessoth, F.G., de Mello, A.J., Manz, A., 1999. Microstructure for efficientcontinuous flow mixing. Analytical Communications 36, 213–215.

Böhm, S., et al. (Eds.), 2001. A rapid vortex micromixer for studyinghigh-speed chemical reactions. In: Ramsey, J.M., van den Bag, A.(Eds.) Micro Total Analysis Systems. Kluwer Academic Publishers,Dordrecht, pp. 25–27.

Bökenkamp, D., et al., 1998. Microfabricated silicon mixers forsubmillisecond quench flow analysis. Analytical Chemistry 70,232–236.

Branebjerg, J., Larsen, U.D., Blankenstein, G. (Eds.), 1996. Fastmixing by parallel multilayer lamination. Proceedings of the SecondInternational Symposium on Miniaturized Total Analysis Systems;Analytical Methods & Instrumentation, Special Issue�TAS’96, Basel,pp. 228–230.

de Mello, A., Wootton, R., 2002. But what is it good for? Applicationsof microreactor technology for the fine chemical industry. Lab on aChip 2, 7N–13N.

Drese, K., 2003. Optimization of interdigital micromixers via analyticalmodeling—exemplified with the SuperFocus mixer. ChemicalEngineering Journal 101 (1–3), 403–407.

Ehlers, S., et al., 2000. Mixing in the offstream of a microchannel system.Chemical Engineering and Processing 39, 291–298.

Ehrfeld, W., et al., 1999. Characterization of mixing in micromixers bya test reaction: single mixing units and mixer arrays. Industrial &Engineering Chemistry Research 38 (3), 1075–1082.

Ehrfeld, W., Hessel, V., Löwe, H., 2000. Microreactors. Wiley-VCH,Weinheim.

Ehrnström, R., 2002. Miniaturization and integration: challenges andbreakthroughs in microfluidics. Lab on a Chip 2, 26N–30N.

Fletcher, P.D.I., et al., 2002. Micro reactors: principle and applications inorganic synthesis. Tetrahedron 58 (24), 4735–4757.

Floyd, T.M., et al. (Eds.), 2000. Novel liquid phase microreactorsfor safe production of hazardous speciality chemicals. MicroreactionTechnology: Third International Conference on MicroreactionTechnology. Proceedings of IMRET 3, Springer, Berlin, pp. 171–180.


Freitas, S., et al., 2003. Solvent extraction employing a static micromixer:a simple, robust and versatile technology for the microencapsulationof proteins. Journal of Microencapsulation 20 (1), 67–85.

Gavriilidis, A., et al., 2002. Technology and application ofmicroengineered reactors. Transactions IChemE 80/A (1), 3–30.

Glasgow, I., Aubry, N., 2003. Enhancement of microfluidic mixing usingtime pulsing. Lab on a Chip 3, 114–120.

Gobby, D., Angeli, P., Gavriilidis, A., 2001. Mixing characteristicsof T-type microfluidic mixers. Journal of Micromechanics andMicroengineering 11, 126–132.

Graveson, P., Branjeberg, J., Jensen, O.S., 1993. Microfluidics—a review.Journal of Micromechanics and Microengineering 3 (4), 168–182.

Haas-Santo, K., et al. (Eds.), 2001. A Microstructure Reactor Systemfor the Controlled Oxidation of Hydrogen for Possible Application inSpace. Springer, Berlin.

Hardt, S., Schönfeld, F., 2003. Laminar mixing in different interdigitalmicromixers—part 2: numerical simulations. A.I.Ch.E. Journal 49 (3),578–584.

Hardt, S., et al., 2001a. Simulation of droplet formation in micromixers.In: Fourth International Conference on Modeling and Simulations ofMicrosystems, Hilton Head Island, SC, pp. 223–226.

Hardt, S., et al., 2001b. Mixing and emulsification processes inmicromixers. In: Computational Methods for Multiphase Flow,Orlando, USA, pp. 217–228.

Hardt, S., et al., 2002. Radial and tangential injection of liquid/liquid andgas/liquid streams and focusing thereof in a special cyclone mixer.In: Rinard, I., Hoch, B. (Eds.) Sixth International Conference onMicroreaction Technology, IMRET 6, New Orleans, USA. A.I.Ch.E.Publications No. 164, pp. 329–344.

Haswell, S.T., Watts, P., 2003. Green chemistry: synthesis in microreactors. Green Chemistry 5, 240–249.

He, B., et al., 2001. A picoliter-volume mixer for microfluidic analyticalsystems. Analytical Chemistry 73 (9), 1942–1947.

Hessel, V., Löwe, H., 2003. Micro chemical engineering:components—plant concepts—user acceptance. Chemical Engineeringand Technology 26(1)(Part I), 13–24.

Hessel, V., et al., 2003. Laminar mixing in different interdigitalmicromixers—part I: experimental characterization. A.I.Ch.E. Journal49 (3), 566–577.

Hessel, V., Hardt, S., Löwe, H., 2004. Chemical Micro ProcessEngineering—Fundamentals, Modelling and Reactions. Wiley-VCH,Weinheim.

Hong, C.-C., Choi, J.-W., Ahn, C.H. (Eds.), 2001. A novel in-plane passivemicromixer using coanda effect. In: Ramsey, J.M., van den Berg, A.(Eds.) Micro Total Analysis Systems. Kluwer Academic Publishers,Dordrecht, pp. 31–33.

Jähnisch, K., et al., 2004. Chemistry in microstructured reactors.Angewandte Chemie—International Edition 43 (4), 406–446.

Jen, C.-P., et al., 2003. Design and simulation of the micromixer withchaotic advection in twisted microchannels. Lab on a Chip 3, 77–81.

Jensen, K.F., 1998. Smaller, faster chemistry. Nature 393 (6), 735–736.Jensen, K.F., 2001. Microreaction engineering—is small better? Chemical

Engineering Science 56, 293–303.Jiang, F., et al., 2004. Helical flows and chaotic mixing in curved micro

channels. A.I.Ch.E. Journal 50 (9), 2297–2305.Kakuta, M., et al., 2003a. Time-resolved Fourier transform infrared

spectrometry using a microfabricated continuous flow mixer:application to protein conformation study using the example ofubiquitin. Lab on a Chip 3, 82–85.

Kakuta, M., et al., 2003b. Micromixer-based time-resolved NMR:applications to ubiquitin protein conformation. Analytical Chemistry75 (4), 956–960.

Kang, T.G., Kwon, T.H., 2004. Colored particle tracking method formixing analysis of chaotic micromixers. Journal of Micromechanicsand Microengineering 14, 891–899.

Kestenbaum, H., et al., 2000a. Silver-catalyzed oxidation of ethylene toethylene oxide in a microreaction system. Industrial & EngineeringChemistry Research 41 (4), 710–719.

Kestenbaum, H., et al., 2000b. Synthesis of ethylene oxide in a catalyticmicroreactor system. Studies in Surface Science and Catalysis 130,2741–2746.

Knapp, M.R., et al., 2001. Commercialized and emerging Lab-on-a-Chipapplications. In: Ramsey, J.M., van den Berg, A. (Eds.) Micro TotalAnalysis Systems. Kluwer Academic Publishers, Dordrecht, pp. 7–9.

Knight, J.B., et al., 1998. Hydrodynamic focussing on a silicon chip:mixing nanoliters in microseconds. Physical Review Letters 80 (17),3863.

Lee, Y.-K., et al., 2001. Chaotic mixing in electrokinetically andpressure driven micro flows. In: Microreaction Technology—IMRET5: Proceedings of the Fifth International Conference on MicroreactionTechnology.Springer, Berlin, pp. 185–191.

Liu, R.H., et al., 2001. Plastic on-line chaotic micromixer for biologicalapplications. In: Ramsey, J.M., van den Berg, A. (Eds.) MicroTotal Analysis Systems. Kluwer Academic Publishers, Dordrecht,pp. 163–164.

Liu, R.H., et al., 2002. Bubble-induced acoustic micromixing. Lab on aChip 2, 151–157.

Liu, R.H., et al., 2003. Hybridization enhancement using cavitationmicrostreaming. Analytical Chemistry 75 (8), 1911–1917.

Löb, P., et al., 2004. Steering of liquid mixing speed in interdigitalmicromixers—from very fast to deliberately slow mixing. ChemicalEngineering and Technology 27 (3), 340–345.

Loebbecke, S., et al., 2000. Applications of FTIR microscopy for processmonitoring in silicon microreactors. In: VDE World MicrotechnologiesCongress, MICRO.tec 2000, EXPO Hannover.VDE Verlag, Berlin,pp. 789–791.

Loebbecke, S., et al., 2002. Black box microreactor? Possibilities for abetter control and understanding of microreaction processes by applyingsuitable analytics. In: Sixth International Conference on MicroreactionTechnology, IMRET 6, New Orleans, USA. A.I.Ch.E. Publications No.164, pp. 37–38.

Loebbecke, S., et al., 2004. Experimental approaches to betterunderstanding of mixing efficiency of microfluidic devices. ChemicalEngineering Journal 101 (1–3), 409–419.

Löwe, H., et al., 2000. Micromixing technology. In: Fourth InternationalConference on Microreaction Technology, IMRET 4, Atlanta, USA.A.I.Ch.E. Topical Conference Proceedings, pp. 31–47.

Lu, L.-H., Ryu, K.S., Liu, C. (Eds.), 2001. A novel microstirrer andarrays for microfluidic mixing. In: Ramsey, J.M., van den Berg, A.(Eds.) Micro Total Analysis Systems. Kluwer Academic Publishers,Dordrecht, pp. 28–30.

Manz, A., Becker, H. (Eds.), 1998. Microsystem Technology in Chemistryand Life Science, vol. 194. Springer, Heidelberg.

Mengeaud, V., Josserand, J., Girault, H.H., 2002. Mixing processes ina zigzag microchannel: finite element simulations and optical study.Analytical Chemistry 74, 4279–4286.

Miyake, R., et al., 1993. Micromixer with fast diffusion. In: IEEE-MEMS’93. Fort Lauderdale, USA, pp. 248–253.

Niu, X., Lee, Y.-K., 2003. Efficient spatial-temporal chaotic mixing inmicro-channels. Journal of Micromechanics and Microengineering 13,454–462.

Oddy, M.H., Santiago, J.G., Mikkelsen, J.C., 2001. Electrokineticinstability micromixing. Analytical Chemistry 73 (24), 5822–5832.

Oroskar, A.R., Vanden Bussche, K., Towler, G., 2000. Scale up vsnumbering up—can miniaturization change the rules in chemicalprocessing. In: VDE World Microtechnologies Congress, MICRO.tec2000, EXPO Hannover.VDE Verlag, Berlin, pp. 385–392.

Ottino, J.M., 1989. The Kinematics of Mixing Stretching, Chaos, andTransport. Cambridge University Press, Cambridge.

Palk, P., Pamula, V.K., Fair, R.B., 2003. Rapid droplet mixers for digitalmicrofluidic systems. Lab on a Chip 3, 253–259.

Pennemann, H., et al., 2004a. Investigations on pulse broadening fortransient catalyst screening in gas/liquid systems. A.I.Ch.E. Journal 50(8), 1814–1823.


Pennemann, H., et al., 2004b. Application of micro reactors: benchmarkingfor analytical applications and lab-scale synthesis. Organic ProcessResearch & Development 8 (3), 422–435.

Pennemann, H., Hessel, V., Löwe, H., 2004c. Chemical microprocess technology—from laboratory-scale to production. ChemicalEngineering Science 59 (22–23), 4789–4794.

Penth, B., 1999. Method and device for carrying out chemical and physicalprocesses, WO 00/61275. Germany.

Penth, B., 2000. New non-clogging microreactor for chemical processingand nano materials. In: Micro.tec 2000, VDE World MicrotechnologiesCongress Expo 2000, Hannover, Germany.VDE Verlag, Berlin,pp. 401–405.

Qian, S., Bau, H.H., 2002. A chaotic electroosmotic stirrer. AnalyticalChemistry 74 (15), 3616–3625.

Ramsey, J.M. (Ed.), 1996. Miniature chemical measurement systems.Proceedings of the Second International Symposium on MiniaturizedTotal Analysis Systems; Analytical Methods & Instrumentation, SpecialIssue�TAS’96, Basel, pp. 24–27.

Reyes, D.R., et al., 2002. Micro total analysis systems, 1: introduction,theory, and technology. Analytical Chemistry 74 (12), 2623–2636.

Roessler, A., Rys, P., 2001. Selektivität mischungsmaskierter reaktionen:Wenn die Rührgeschwindigkeit die Produktverteilung bestimmt.Chemie in unserer Zeit 35 (5), 314–322.

Schenk, R., et al., 2002. Micromixers as a tool for powder production.Chemical Engineering Transactions (1), 909–914.

Schenk, R., et al., 2004. Nanopowders produced using microreactors.Encyclopedia of Nanoscience and Nanotechnology 7, 287–296.

Schierholz, W., Lauschke, G., Ott, S., 1997. Kontinuierlicher chaotischerKonvektionsmischer, -wärmetauscher und -reaktor, DE 19731891: 7.Hoechst AG, Germany.

Schönfeld, F., Hardt, S., 2003. Simulation of helical flows inmicrochannels. A.I.Ch.E. Journal 50 (4), 2297–2305.

Schönfeld, F., Hessel, V., Hofmann, C., 2004. An optimised split-and-recombine micro mixer with uniform ‘chaotic’ mixing. Lab on a Chip4, 65–69.

Schubert, K., et al., 1994. Method and device for performing chemicalreactions with the aid of microstructure mixing, WO 95/30476:35. Bayer Aktiengesellschaft, Forschungszentrum Karlsruhe GmbH,Germany.

Schubert, K., et al., 2001. Microstructure devices for applications inthermal and chemical process engineering. Microscale ThermophysicalEngineering 5, 17–39.

Schwesinger, N., Frank, T., 1995. Device for mixing small quantities ofliquids, WO 96/30113. Merck Patent GmbH; Darmstadt, Germany.

Schwesinger, N., Frank, T., Wurmus, H., 1996. A modular microfluidicsystem with an integrated micromixer. Journal of Micromechanics andMicroengineering 6, 99–102.

Seidel, R.U., et al. (Eds.), 2000. A capillary force filled auto-mixingdevice. Microreaction Technology: Third International Conference onMicroreaction Technology. Proceedings of IMRET 3. Springer, Berlin,pp. 189–197.

Skelton, V., et al., 2000. Micro reaction technology: synthetic chemicaloptimisation methodology of Wittig synthesis enabling a semi-automated micro reactor for combinatorial screening. In: Fourth

International Conference on Microreaction Technology, IMRET4, Atlanta, USA. A.I.Ch.E. Topical Conference Proceedings,pp. 78–88.

Solomon, T.N., Mezic, I., 2003. Uniform resonant chaotic mixing in fluidflows. Nature 425 (9), 376–380.

Stroock, A.D., et al., 2002a. Chaotic mixing in microchannels. Science295 (1), 647–651.

Stroock, A.D., et al., 2002b. Patterning flows using grooved surfaces.Analytical Chemistry 74 (20), 5306–5312.

Tatterson, G.B., 1994. Scaleup and Design of Industrial Mixing Processes.McGraw-Hill, New York.

van den Berg, A., Bergveld, P., 1995.�-TAS: miniaturized total chemicalanalysis systems. In: van den Berg, A., Bergveld, P. (Eds.) Micro TotalAnalysis Systems. Kluwer Academic Press, Dordrecht, Amsterdam,pp. 1–4.

van den Berg, A., Lammerink, T.S.J., 1998. Micro Total Analysis Systems:Microfluidic Aspects, Integration Concept and Applications. Topics inCurrent Chemistry, vol. 194. Springer, Heidelberg, pp. 21–49.

Veenstra, T.T., et al., 1998. Characterization method for a new diffusionmixer applicable in micro flow injection analysis systems. Journal ofMicromechanics and Microengineering 9, 199–202.

Veser, G., 2001. Experimental and theoretical investigation of H2 oxidationin a high-temperature catalytic microreactor. Chemical EngineeringScience 56, 1265–1273.

Villermaux, J., et al., 1991. Use of parallel competing reactions tocharacterize micromixing efficiency. A.I.Ch.E. Symposium Series 88(286), 6.

Voldman, J., Gray, M.L., Schmidt, M.A., 1998. Liquid mixing studieswith an integrated mixer/valve. In: Harrison, J., van den Berg, A.(Eds.) Micro Total Analysis Systems. Kluwer Academic Publishers,Dordrecht, pp. 181–184.

Werner, B., et al., 2002. Specially suited micromixers for process involvingstrong fouling. In: Sixth International Conference on MicroreactionTechnology, IMRET 6, New Orleans, USA. A.I.Ch.E. Publications No.164, pp. 168–183.

Werner, B., Hessel, V., Löb, P., 2005. Mixers with microstructural foils forchemical production purposes. Chemical Engineering and Technology,in press.

West, J., et al., 2002. Application of magnetohydrodynamic actuation tocontinuous flow chemistry. Lab on a Chip 2, 224–230.

Woias, P., Hauser, K., Yacoub-George, E. (Eds.), 2000. An active siliconmicromixer for�TAS applications. In: van den Berg, A., Olthuis, W.,Bergveld, P. (Eds.) Micro Total Analysis Systems. Kluwer AcademicPublishers, Dordrecht, pp. 277–282.

Yang, Z., et al., 1998. Micro mixer incorporated with piezoelectricallydriven valveless micropump. In: Harrison, J., van den Berg, A.(Eds.) Micro Total Analysis Systems. Kluwer Academic Publishers,Dordrecht, pp. 177–180.

Yang, Z., et al., 2001. Ultrasonic micromixer for microfluidic systems.Sensors and Actuators A 93, 266–272.

Zech, T., et al., 2000. Superior performance of static micromixers.In: Fourth International Conference on Microreaction Technology,IMRET 4, Atlanta, USA. A.I.Ch.E. Topical Conference Proceedings,pp. 390–399.

Documents

Micromixers—a review on passive and active mixing principles