Nam-Trung Nguyen
Assistant Professor,
Mem.ASME Xiaoyang Huang
Associate Professor
Toh Kok Chuan
Associate Professor,
Mem.ASME School of Mechanical and Production
Engineering, Nanyang Technological University,
Singapore639798MEMS-Micropumps:A Review
Microfluidics has emerged from the MEMS-technology as an important rearchfield and a promising market.This paper gives an overview on one of the most important microf-luidic components:the micropump.In the last decade,various micropumps have been developed.There are
only a few review papers on microfluidic devices and none of them were dedicated only to micropumps.This review paper outlines systematically the pump principles and their realization with MEMS-technology.Comparisons regarding pump size,flow rate,and backpressure will help readers to decide their proper design before starting a microfluidics project.Different pump principles are compared graphically and discusd in terms of their advantages and disadvantages for particular applications.͓DOI:10.1115/1.1459075
͔
1Introduction
Microelectromechanical systems͑MEMS͒have enabled a wide range of nsors and actuators to be realized by allowing nonelec-trical devices onto microchips.In the early years of MEMS-development,fluidic components were among thefirst devices which were realized in microscale using silicon technology.The most common components were:flow nsors,microvalves and micropumps.With the growing importance of genomics,proteom-ics,and the discovery of new drugs,microfludic systems became hot rearch objects.Thefield of microfluidics expanded to the development of numerous micro devices:filters,mixers,reactors, parators.New effects such as electrokinetic effects,acoustic streaming,magnetohydrodynamic effect,electrochemical,and more,which previously were neglected in macroscopic applica-tions,now gained their importance in microscale.
A recent report of System Planning Corporation͓1͔estimated a microfluidics market of3to 4.5billions US$and an annual growth rate for scales of25percent–35percent.The report con-sidered four types of microfluidic devices:fluid control devices, gas and liquid measurement devices,medical testing devices,and other devices.The reportfigured out that the most promising mi-crofluidics products are devices for DNA,protein analysis,and drug discovery.
Since the establishment of the term‘‘microfludics,’’veral ex-cellent review papers on microfluidic de
vices have been pub-lished.Graven et al.gave a general overview onfluidic prob-lems in micro scale͓2͔.Shoji and Esashi discusd microfluidics from the device point of view and considered micropumps,micro-valves andflow nsors͓3͔.Ho and Tai discusd the MEMS-applications forflow control in the macroscopic domain͓4͔.El-wenspoek et al.summarized their works on microfludics in͓5͔. Stemme discusd microfluidic devices under such categories: passive devices͑channel,valves,filters͒,flow nsors,and dia-phragm pumps͓6͔.Zengerle and Sandmaier concentrated on mi-crovalves,micropumps and their commercialization strategy͓7͔. Since thefield has been growing rapidly,it’s very difficult to cover all kinds of microfluidic devices in a single review.In con-trast to the previous reviews,this paper only deals with micro-pumps and discuss their design methodology as well as the de-velopment of pump designs in the published examples.The design methodology will cover two main aspects:the pump principles and their comparison.With this concept,the paper tries to give a general view on micropumps,and to help microfluidics designers making their development decision easily.
Using the micromachining technology,a wide range of mi-
感人事迹crodevices has been realized.The most important micromachining
techniques are bulk micromachining,surface micromachining,
and LIGA technology.Bulk micromachining us the starting sub-
strate͑a silicon wafer͒as device material.Surface micromachin-
ing is performed on the surface of a substrate,the substrate itlf
usually doesn’t have a function in devices.LIGA-technology ͑German acronym for Lithographie Galvanoformung Abformung͒creates high aspect ratio structures using X-ray lithography and
electroplating.A short description of the technologies was given
in͓4͔.Many MEMS-devices combine two or more of the above
techniques.A new trend,especially for microfluidic devices,us
plastic as device material.The common machining technologies
for the devices are micro plastic molding or hot embossing.
Combining with on-going investigation of polymer microelectron-
ics,plastic microdevices promi a low-cost alternative to their
silicon counterparts.
2Pump Principles
In contrast to another MEMS-devices,micropumps are one of
the components with a largest variety of operating principles.Like
other MEMS-applications,thefirst approach made by rearchers
was the micromachining realization of well-known principles
from the macroscale.Micropumps can be divided in two mean
categories:mechanical pumps and nonmechanical pumps.
Thefirst category usually utilizes moving parts such as check
valves,oscillating membranes,or turbines for delivering a con-
stantfluid volume in each pump cycle͓8͔.The cond category
adds momentum to thefluid for pumping effect by converting
another energy form into the kinetic energy.While thefirst cat-
手工作品图片大全egory was mostly ud in macroscale pumps and micropumps
with relatively large size and largeflow rates,the cond category
共线向量
discovers its advantages in the microscale.Since the viscous force
in microchannels increas in the cond order with the miniatur-
ization,thefirst pump category cannot deliver enough power in
order to overcome its highfluidic impedance.
Forflow rates larger than10ml/min,miniature pumps or mac-
roscale pumps are the most common solution.The typical opera-
tion range of positive displacement micropumps lies between10l/min to veral ml/min.Forflow rate
s less than10l/min, alternative dynamic pumps are needed for accurate control of the smallfluid amounts.With theflow rates,most of the pumps are working in the range of Reynolds number from1–100, and therefore in a laminar regime.
All the pump principles,which were realized recently in mi-
croscale,are discusd in details in the following subctions. 2.1Mechanical Pumps.All mechanical pumps require a mechanical actuator,which generally converts electric energy into mechanical work.The comparison of mechanical works generated
新年手抄报的内容
Contributed by the Fluids Engineering Division for publication in the J OURNAL
OF F LUIDS E NGINEERING.Manuscript received by the Fluids Engineering Division
August7,2000;revid manuscript received November7,2001.Associate Editor:
Y.Matsumoto.
384ÕVol.124,JUNE2002Copyright©2002by ASME Transactions of the ASME
by different pumps is discusd later in this paper.Shoji ͓3͔di-vided actuators into two mean categories:external actuators and integrated actuators.
External actuators include:electromagnetic actuators with sole-noid plunger and external magnetic field,disk type or cantilever type piezoelectric actuators,stack type piezoelectric actuators,pneumatic actuators,and shape memory actuators.The biggest drawback of external actuators is their large size,which restricts the size of the whole micro-pumps.The advantage is the relatively large force and displacement generated by external actuators.Integrated actuators are micromachined with the pumps.Most common integrated actuators are electrostatic actuators,thermop-neumatic actuators,electromagnetic actuators,and thermome-chanic ͑bimetallic ͒actuators.Despite their fast respon time and good reliability,electrostatic actuators cau small force and very small stroke.With special curved electrodes,electrostatic actua-tors are suitable for designing micropumps with very low power consumption.Thermopneumatic actuators generate large pressure and relatively large stroke.This actuator type was therefore often ud for mechanical pumps.Thermopneumatic actuators and bi-metallic actuators require a large amount of thermal energy for their operation,and conquently,consume a lot of electric power.High temperature and complicated thermal management are fur-ther drawbacks of the actuator types.Electromagnetic actuators require an ex
ternal magnetic field,which also restricts the pump size.Their large electric current caus thermal problems and high electric energy consumption.
Check-Valve Pumps.Check-valve pump is the most common pump type in the macroscale.The first attempts in designing a micro pump were the realization of check-valve pumps.Figure 1illustrates the general principle of a check-valve pump.The pump consists of:
•An actuator unit;a pump membrane that creates the stroke volume ⌬V ,
•A pump chamber with the dead volume V 0,
•Two check-valves,which start to be opened by the critical pressure difference ⌬p crit .
Richter et al.͓16͔determined the operation conditions of a check-valve pump as:
•Small compression ratio which is the ratio between the stroke volume and the dead volume ϭ⌬V /V 0,
•High pump pressure p (͉p Ϫp out ͉Ͼp crit ,͉p Ϫp in ͉Ͼp crit ).
Following design rules can be ud in order to fulfill the above conditions:
•Minimize the critical pressure ⌬p crit by using more flexural valve design or valve material with small Young’s modulus,•Maximize the stroke volume ⌬V by using actuators with large stroke or more flexible pump membrane,
•Minimize the dead volume V 0by using thinner spacer or wafer,
•Maximize the pump pressure p by using actuators with large forces.The terms for passive microvalves ud in this paper were de-fined by Shoji in ͓3͔.One of the first micropumps made in silicon was prented by van Lintel ͓9͔.The pump had check-valves in form of a ring diaphragm,which was relatively stiff and need a large lateral area.That makes one valve consume a large silicon area,which has almost the same size of a pump chamber,Fig.2͑a ͒.The same valves were also ud in the pumps reported in ͓10͔and ͓11͔,which had thermopneumatic actuators instead of piezodisks.The next improvement was the pump prented by Shoji ͓12͔,which had check-valves made of polysilicon by using surface micromachining.The valve is a disk supported by four thin polysilicon beams.This design allows small valves to be integrated under the pump chamber.Zengerle ͓13,14͔prented another small and more flexible design.The valve has a form of a cantilever,Fig.2͑f ͒.Koch et al.͓15͔and Wang et al.͓16͔pro-pod the same valve type in their micropumps.
Another way to make check-valve flexible is using material with smaller Yong’s modulus.Table 1compares the common ma-terials ud for check-valves in micro pumps.Polyimide,polyes-ter,and parilene is one order more flexible than silicon.Pumps prented by Shomburg et al.͓17,18͔ud polyimide as material for the disk valve ͑Fig.2͑b ͒͒.The pump reported in ͓19͔and that prented by Kaemper et al.͓20͔had polyimide ring diaphragm valves ͑Fig.2͑c ͒͒.A similar design using polyester valve was reported by Boehm et al.͓21͔.In the pump prented by Meng et al.͓22͔,the disk valve was realized in parylene ͑Fig.2͑d ͒͒.The next optimization is to fabricate the pump membrane with flexural material like polyimide ͓19͔͑Fig.2͑c ͒͒or silicone ruber ͓22͔͑Fig.2͑d ͒͒.The membranes require small actuating
pres-Fig.1General structure of a micro check-valve
pump
Fig.2Check-valve micropumps:…a …piezoelectric actuator with ring mesa valves;…b …pneumatic actuator with polyimide disk valves;…c …pneumatic actuator with membrane valves;…d …pneumatic actuator with rubber membrane and parylene disk valves;…e …piezoelectric actuator with polysilicon disk valves;…f …electrostatic actuator with silicon cantilever valves;…g …pi-ezoelectric actuator silicon cantilever valves;…h ,i ,j …piezoelec-tric actuator with ring mesa valves.
Journal of Fluids Engineering
JUNE 2002,Vol.124Õ385
sure and have large deflection as well as large stroke volume.This type of membrane is suitable for pneumatic or thermopneumatic actuators.
Using thinner spacer or thinner wafer for the pump chamber can minimize the dead volume.The pump prented by Zengerle ͓13͔͑Fig.2͑f ͒͒was in this way improved in the version prented by Linnemann et al.͓23͔.The middle wafer was polished and thined to 70micron.As a result,the compression ratio incread from 0.002to 0.085͓24͔.The improved pump design was able to pump ga
s and was lf-priming.The design of van Lintel ͓9͔͑Fig.2͑a ͒͒was improved from the later version ͓25͔͑Fig.2͑b ͒͒and had a compression ratio of 1.15.This pump was lf-priming and in-nsitive to ambient pressure becau of the implementation of a special pump membrane limiter.Another good design,which minimizes the dead volume in the Linnemann’s pump,was com-bining the check-valve with the pump chamber realized by Gass et al.͓26,27͔͑Fig.2͑i ͒͒.
Table 2lists the most important parameters of the above check-vale pumps and tho reported in ͓28–33͔.The pump designs depicted in Fig.2also illustrate the ‘‘evolution’’in designing check-valve micropumps.The development shows clearly how the pump chamber becomes smaller,and how the check-valves and the pump membrane become more flexible.Most of the de-veloped micropumps tend to have a piezoelectric disk as actuator,which is reasonable for the performance and size needed for this pump type.
Peristaltic Pumps.As oppod to check-valve pumps,peri-staltic pumps don’t require passive valves for the flow rectifica-tion.The pump principle is bad on the peristaltic motion of the pump chambers,which squeezes the fluid into the desired direc-tion.Theoretically,peristaltic pumps need 3or more pump cham-bers with reciprocating membrane.Most of the realized pumps have 3chambers.Some pumps were designed with active valves,which in fact reprent pump chambers,a
lso belong to the cat-egory of peristaltic pumps.The optimization strategies are maxi-mizing the compression ratio and increasing the number of pump chambers ͑Table 3͒.小学生爱国演讲稿
Since a peristaltic pump doesn’t require high chamber pressure,the most important optimization factors are the large stroke vol-ume and the large compression ratio.The first peristaltic micro pump prented by Smits ͓34͔͑Fig.2͑a ͒͒had piezoelectric actua-tors and pump chambers etched in silicon.Shinohara et al.͓35͔prented a similar design with the same performance.
Judy ͓36͔propod a pump,which utilized surface microma-chining and electrostatic actuators ͑Fig.2͑b ͒͒.The pump chamber,and conquently the dead volume,can be kept very small.No results for maximum flow rate and backpressure were reported for this pump.
The pump reported by Folta et al.͓37͔͑Fig.2͑c ͒͒ud ther-mopneumatic actuators,the pump chamber height was 10micron.However,the heat loss caud by the good thermal conductivity of silicon minimized the thermopneumatic effect and incread the power consumption.
Mizoguchi et al.͓38͔͑Fig.2͑d ͒͒also ud thermopneumatic actuators for driving 4pump chambers,the pump had external lar light as heat source.Similar to the methods discusd in the previous ction,Grosjean et al.ud silicone rubber in order to form the pump membrane ͓39͔͑Fig.2͑e ͒͒.With exte
rnal pneu-matic sources,the pump could generate a flow rate up to 120l/min.In thermopneumatic operation,the pump only delivered few l/min like the similar designs in ͓37͔and ͓38͔.
The pump prented by Cabuz et al.͓40͔incread the com-pression ratio to 10by using curved pump chambers and flexible plastic pump membrane for electrostatic actuation.The numerous pump chambers were designed by using a three-dimensional array structure ͑Fig.2͑f ͒͒.With the optimization measures,the pump was able to deliver 8ml/min with only 75V drive voltage and 4mW electrical power ͑Fig.3͒.
RFPA
Valveless Rectification Pumps.The structure of valveless rec-tification pumps is similar to tho of check-valve pumps.The only difference is that instead of using check-valves the pumps u diffur/nozzle or valvular conduit structures for flow rectifi-cation.Maximizing the stroke volume and minimizing the dead volume can optimize this pump type.
Stemme ͓41͔prented the first pump with diffur/nozzle structures.The pump was fabricated in brass using precision ma-chining ͑Fig.4͑a ͒͒.Further development of this pump leads to the flat design in silicon ͓42–44͔͑Fig.4͑b ͒͒.Using small opening angles ͑7–15deg ͒,the flow is pumped out of the diffur structure ͑Fig.2͑a ͒͒.With deep reactive ion etching ͑DRIE ͒,small chamber height,and conquently small dead volume and large compres-sion ratio were achieved.
The pump effect appears in the opposite direction if the opening angle is large.The pump prented by Gerlach had an opening of 70.5deg,which is determined by the ͗111͘surface freed with anisotropic wet etching ͓45–47͔͑Fig.4͑c ͒͒.This pump design was optimized in the work of Jeong and Yang ͓48͔.The stroke volume was incread by using the thermopneumatic actuator and corrugated pump membrane.Ullman gave in ͓49͔a theoretical analysis of diffur/nozzle pumps.
Forster et al.͓50,51͔applied the valvular conduits structure which was first invented by Tesla ͓52͔in micro scale.The inlet/outlet structures shown in Fig.5cau the rectification effect without check-valves.This pump type can be realized easily in silicon with DRIE-technology.
Table 1Young’s modulus of different
materials
Table 2Typical parameters of check-valve micropumps …val-ues for water,except †18‡for air
…
Table 3Typical parameters of peristaltic micropumps …values for water
…
386ÕVol.124,JUNE 2002
Transactions of the ASME
Another approach of valve-less pumping was propod by Stehr et al.͓53,54͔.The pump principles were called the elastic buffer mechanism ͑Fig.6͑a ͒͒and the variable gap mechanism ͑Fig.6͑b ͒͒.This pump type is able to pump liquids in two directions depending on its drive frequency.Nguyen et al.also dem
onstrated the pump effects in a similar structure ͓55͔͑Fig.6͑c ͒͒.
Maysumoto et al.͓56͔prented another valveless concept by using the temperature dependency of water viscosity.The fluidic impedance at the outlet and the inlet are modulated by means of heat.The heating cycles were synchronized with the pump fre-quency.Table 4lists the most important parameters of the dis-cusd valveless rectification micro pumps.普通话英语
Rotary Pumps.Another mechanical pump type,which can be realized with micro machining technique,is the rotary pump.The rotary pump has a big advantage of pumping highly viscous fluids ͑Table 5͒.
Ahn et al.͓57͔͑Fig.7͑a ͒͒prented a micropump with a mi-croturbine as rotor in an integrated electromagnetic motor.The pump simply adds momentum to the fluid by means of fast mov-ing blades.The rotor,stator,and coils are fabricated by electro-plating of iron-nickel alloy.The high aspect ratio structures were fabricated at a low cost by using conventional photolithography of
polyimide.
Fig.3Realization examples of peristaltic micropumps …not to scale …:…a …piezoelectric actuators with glass membrane;…b …electrostatic actuators with polysilicon membrane;…c …ther-mopneumatic actuators with silicon membrane;…d …thermop-neumatic actuators with silicon membrane and fiber guided la-r as heat source;…e …thermopneumatic actuators with rubber membrane;…f …electrostatic actuators with curved
electrodes.
Fig.4Realization examples of valveless rectification micro pumps …not to scale …:…a …piezoelectric actuator with external diffur Õnozzle elements;…b …piezoelectric actuator with planar integrated diffur Õnozzle elements;…c …piezoelectric actuator with vertical diffur Õnozzle elements;…d …thermoelectric actua-tors with corrugated membrane and vertical diffur Õnozzle el-
ements.
Fig.5Valvular conduit
pump
Fig.6Other valveless pumps
Table 4Typical parameters of valveless rectification micro-
pumps
Table 5Typical parameters of rotary pumps …typical size is the size of the turbine or the gear wheel
…
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JUNE 2002,Vol.124Õ387
The micropump prented by Doepper et al.͓58͔͑Fig.7͑b ͒͒had two gear wheels made of iron-nickel alloy with LIGA-technique.An external motor drove the gear.The gears forced the fluid along by squeezing it to an outlet.Actuating by means of an external magnetic field is possible,but it is so far not reported.Mass production of this pump can be realized with plastic molding.
Ultrasonic Pump.Ultrasonic principle is a gentle pump prin-ciple with no moving parts,heat and strong electric field involved.The pump effect is caud by the acoustic streaming,which is induced by a mechanical traveling wave ͑Fig.8͑a ͒͒.The mechani-cal wave can be a flexural plate wave ͑FPW ͓͒59,60͔or a surface acoustic wave ͓61,62͔.The mechanical waves are excited by in-terdigitated transducers ͑IDT,Fig.8͑b ͒͒placed on a thin mem-brane coated with piezoelectric film ͓59,60͔or on a piezoelectric bulk material ͓61,62͔.The pumps have a thin flow layer of about 20micron ͑for water ͒͑Fig.8͑a ͒͒,and are therefore also suitable for particle paration applications.Using curved IDT,locally sample concentration can be achieved with this kind of pump.2.2Nonmechanical Pumps
Electrohydrodynamic Pumps.Electrohydrodynamic ͑EHD ͒pumps are bad on electrostatic forces acting on dielectric fluids.The force density F acting a dielectric fluid with free space-charge density q f in an inhomogeneous electric field E is given as ͓63͔
:
(1)
where is the fluid permittivity,P is the polarization vector,and is the mass density.EHD pumps can be categorized into two main types:the EHD induction pump and the EHD injection pump.The EHD induction pump is bad on the induced charge at the material interface.A traveling wave of electric field drags and pulls the induced charges along the wave direction ͑Fig.9͑a ͒͒.The first micromachined EHD induction pump was prented by Bart et al.͓63͔,similar designs were reported by Fuhr et al.͓64–67͔and Ahn et al.͓68͔.A fluid velocity of veral hundred micron per cond can be achieved with this pump type.For better pump-ing effect,a temperature gradient and conquently a conductivity gradient across the channel height was generated by an external heat source and heatsink ͑Peltier element ͓͒67͔.
In the EHD injection pump,the Colomb force is responsible for moving ions injected from one or both electrodes by means of electrochemical reaction ͑Fig.9͑b ͒͒.Richter et al.demonstrated this pump principle with micromachined silicon electrodes ͓69,70͔.The pressure gradient bults up in the electric field caus the pump effect.Furuya et al.ud electrode grids,standing per-pendicular to device surface,in order to increa the pressure gradient ͓71͔.The pump can deliver 0.12ml/min with a drive voltage of 200V .Table 6lists the most important parameters of the EHD-pumps discusd above.
Electrokinetic Pumps.In contrast to the EHD-pumps,electro-kinetic pumps utilize the electrical field for pumping conductive fluid.The electrokinetic phenomenon can be divided into electro-phoresis and electroosmosis.
Electrophoresis is the effect,by which charged species in a fluid are moved by an electrical field relative to the fluid molecules.The velocity of the charged species is proportional to the field strength E :
伤感美文V ϭep E
(2)
where ep is the electrophoretic mobility of the species.Electro-phoresis is ud for paration of molecules like DNA molecules.In contrast to electrophoresis,electroosmosis is the pumping effect of a fluid in a channel under the application of an electrical field.A surface charge exists on the channel wall.The surface charge comes either from the wall property or the adsorption of charges species in the fluid.In the prence of an electrolyte so-lution,the surface charge induces the formation of a double layer on the wall by attracting oppositely charged ions from the solu-tion.An external electrical field forces the double layer to
move.
Fig.7Rotary
pumps
Fig.8Ultrasonic
pumps
Fig.9Principles of electrohydrodynamic pumps
Table 6Typical parameters of electrohydrodynamic
micropumps
388ÕVol.124,JUNE 2002Transactions of the ASME
Due to the viscous force of the fluid,the whole fluid in the chan-nel moves with a flat velocity profile ͑plug flow ͒:
V ϭeo E
(3)
where eo is the electroosmotic mobility of the fluid.Due to its nature,the electroosmosis effect was ud for pumping fluid in small channels without applying a high external pressure.In micro analysis systems electroosmosis effect is ud for delivering buffer solution,and in combination with the electrophoretic effect,for parating molecules.The most common application of elec-trokinetic pumps is the paration of large molecules like DNA or proteins.The device propod by Harison et al.͓72,73͔could gen-erate a fluid velocity of 100m/s with a field strength of 150V/cm.Webster et al.͓74,75͔us the gel electrophoresis for pa-rating DNA-molecules in microchannel with relatively low field strength ͑5to 10V/cm ͒.
Pha Transfer Pump.Beside the ultrasonic principle,electro-hydrodynamic principle and electrokinetic principle,pha trans-fer is another principle for pumping fluid in small channels,in order to overcome the high fluidic impedance caud by viscous forces.This principle us the pressure gradient between the gas pha and liquid pha of the same fluid for pumping it.The realization in microscale is simpler than in other pump types.Takagi et al.͓76͔prented the first pha transfer pump ͑Fig.10͑a ͒͒.The alternate pha change is generated by an array of 10integrated heaters.The same pump principle was realized with stainless steel and 3heaters in ͓77͔.Jun and Kim ͓78,79͔fabri-cated a much smaller pump bad on surface micromachining.The pump had 6integrated polysilicon heaters in a channel with 2micron height and 30micron width ͑Fig.10͑b ͒͒.The pump is capable to deliver a flow velocity of 160l/s or flow rates less than 1nanoliter per minute.
Electro Wetting Pump.The electro-wetting pump was pro-pod by Matsumoto et al.͓80͔.The pump principle us the de-pendence of the tension between solid/liquid interface on the charge of the surface.The principle can be ud for direct pump-ing,but no example was reported.Lee and Kim ͓81͔reported a micro actuator bad on electro-wetting of mercury drop,which can be ud for driving a mechanical pump with check valves as propod in ͓80͔.
Electrochemical Pump.Electrochemical pumps u the pres-sure of gas bubbles generated by electr
olysis water.Bi-directional pumping can be achieved by rerving the actuating current,which makes the hydrogen and oxygen bubbles reacting back to
water ͓82͔.The pumped fluid volume can be measured by esti-mating the gas volume with the measurement of the conductivity between electrodes 2and 3͑Fig.11͒.
Magnetohydrodynamic Pump.The pumping effect of a Mag-netohydrodynamic ͑MHD ͒pump is bad on the Lorentz force acted on a conducting solution:
F ϭI ϫBw ,
(4)
where I is the electric current across the pump channel,B the magnetic field strength and w the distance between the electrode ͑Fig.12͑a ͒͒.Lemoff et al.͓83,84͔realized this principle in silicon ͑Fig.12͑b ͒͒.The pump was able to generate a not-pulsatile flow like that of EHD-pumps and electrokinetic pumps.A maximum flow velocity of 1.5mm/s can be achieved ͑1M NaCl solution,6,6V ͒.MHD-pumps generate a parabolic velocity profile,similar to a pressure driven flow in channels.
3Scaling Law for Micropumps
The first question,which aris in dealing with micropumps,is what kind of pump can be actually called a micropump?Is that the size of the pump itlf or is that the fluid amount the pump can handle?Since the above question is still unanswered,Fig.13il-lustrates the typical sizes versus the maximum flow rates of the published micropumps listed as references.The pump
chamber
Fig.10Pha transfer
pumps
Fig.11Electrochemical
pump
Fig.12Magnetohydrodynamic pump:…a …schematic of con-cept,…b …design example,fluid flows out of page
plane
Fig.13Flow rate versus typical size for mechanical pumps …the numbers indicate the corresponding references …Table 7Typical parameters of pha transfer
micropumps
Journal of Fluids Engineering JUNE 2002,Vol.124Õ389
