Design, modeling and fabrication of a constant flow pneumatic micropump

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2007 J. Micromech. Microeng. 17 891

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IOP PUBLISHING JOURNAL OF MICROMECHANICS AND MICROENGINEERING

J. Micromech. Microeng. 17 (2007) 891–899 doi:10.1088/0960-1317/17/5/007

Design, modeling and fabrication of aconstant flow pneumatic micropumpWalker Inman1,2, Karel Domansky2, James Serdy1,Bryan Owens1, David Trumper1 and Linda G Griffith1,2

1 Mechanical Engineering Department, Massachusetts Institute of Technology,77 Massachusetts Ave, Cambridge, MA 02139, USA2 Biological Engineering Division, Massachusetts Institute of Technology, 77 MassachusettsAve, Cambridge, MA 02139, USA

Received 22 January 2007, in final form 8 March 2007Published 3 April 2007Online at stacks.iop.org/JMM/17/891

AbstractThis paper characterizes a bi-directional pneumatic diaphragm micropumpand presents a model for performance of an integrated fluidic capacitor. Thefluidic capacitor is used to convert pulsatile flow into a nearly continuousflow stream. The pump was fabricated in acrylic using a CNC mill. Thestroke volume of the pump is ∼1 µL. The pump is self-priming, bubbletolerant and insensitive to changes in head pressure and pneumatic pressurewithin its operating range. The pump achieves a maximum flow rate of5 mL min−1 against zero head pressure. With pneumatic pressure set to40 kPa, the pump can provide flow at 2.6 mL min−1 against a head pressureof 25 kPa. A nonlinear model for the capacitor was developed and comparedwith experimental results. The ratio of the time constant of the capacitor tothe cycle time of the pump is shown to be an accurate indicator of capacitorperformance and a useful design tool.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Numerous liquid handling applications in life sciences andmedical diagnostics require continuous flow that can begenerated with non-mechanical micropumps based on, forexample, an electrohydrodynamic [1], magnetohydrodynamic[2] or electro-osmotic [3] principle. However, thesemicropumps are not always fully compatible with biologicalsystems. Non-mechanical micropumps also suffer frompractical problems such as electrolytic bubble formation [2, 4]and a strong dependence of flow on fluid composition [5, 6].Mechanical aperiodic displacement micropumps (e.g. syringepumps) do not have these problems but tend to be suitableonly for pumping finite volumes of fluid [7]. Reciprocatingdisplacement micropumps (e.g. diaphragm pumps) are notrestricted by fluid volume, but their flow is pulsatile. Totake advantage of the attractive features of reciprocatingdisplacement micropumps, such as ease of implementationinto larger networks and integration into microfluidic systems[8–11], but to control flow pulsatility, this paper reports on thedesign, fabrication, modeling and performance of a diaphragmmicropump with active valves and a built-in capacitor.

Life science research laboratories in academia andindustry typically have distributed outlets for vacuum andcompressed air. With the necessary infrastructure already inplace, it is very effective to actuate diaphragm micropumpspneumatically. Pneumatic actuation allows for the offloadingof the necessary timing and driving mechanisms to anelectro-pneumatic controller connected to the microfluidicdevice by pneumatic lines. This arrangement can makethe microfluidic device very simple, inexpensive and evendisposable. Additionally, multiple devices can be driven bya single controller. Since the microfluidic valves and pumpsdo not contain electronic components, they can be used forextended periods of time in a harsh environment (i.e. inincubators with relative humidity approaching 100%). Finally,in contrast to other valve and pump actuating principles(e.g. thermomechanical, thermopneumatic or piezoelectric),pneumatic actuation is much less sensitive to changes inambient temperature.

The proposed bi-directional micropump features aclamshell-like pump chamber, two active valves and a fluidiccapacitor. The contoured shape of the pump chamber used incombination with a thin, flexible membrane reduces actuation

0960-1317/07/050891+09$30.00 © 2007 IOP Publishing Ltd Printed in the UK 891

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pump chamber

capacitor

fluidic resistor

pneumatic connections

inlet valve

membrane

outlet valve

Figure 1. Schematic cross-section of the pumping system.

pressure requirements and leads to a constant stroke volume. Arelatively large stroke volume allows for a high compressionratio and results in a pump that is self-priming and bubbletolerant. The capacitor converts pulsatile flow from thepump into continuous flow. Models for assessing capacitordesigns were developed and a parameter indicating capacitorperformance was established.

The pump was fabricated by standard CNC machiningbut is readily amenable to other fabrication and replicationtechniques such as laser machining [12] or micromolding[13, 14]. With CNC machining, a clean room microfabricationfacility is not needed, and a variety of machinable materialscan be chosen based on the target application.

2. Design

A schematic cross-section of the pumping system is illustratedin figure 1. The system consists of a pump chamber, two activevalves and a fluidic capacitor.

Fluid is pumped by opening the inlet valve, filling thepump chamber, reversing the state of the valves and drainingthe pump chamber. Movement of the membrane between therigid surfaces of the pump chamber sets the stroke volume. Atleast one valve is closed at all times to prevent backflow whenpumping against the head pressure. The pumping sequence,shown in figure 2, can be run in the forward or reverse direction.

A representative volume output from one pump cycle isschematically illustrated in figure 3. It can be seen that flowoccurs in bursts during certain phases and is zero or negativeduring other phases. To filter out the pulses and achieve anapproximately constant flow, the pump is equipped with afluidic capacitor.

2.1. Pump

The pump was made by sandwiching a thin, flexible membranebetween two plates. The top plate contains the top half of thepump chamber, valve seats and fluidic channels. The bottomplate contains the bottom half of the pump chamber, the valvesand connections to the pneumatic lines.

A valve is opened when negative air pressure pulls themembrane toward the bottom plate. Positive air pressurecloses the valve by pressing the membrane against the valveseat. The pump chamber fills when negative pressure isapplied to the membrane, and drains in response to positive airpressure.

A model of the pump is shown in figure 4. It highlightsfeatures made in the top and bottom plates. The pump chamberhas a 1.5 × 3 mm footprint and a 1.58 mm radius of curvature.The combined volume of the top and bottom halves of the

phase 1: open inlet valve

phase 2: fill pump chamber

phase 3: close inlet valve

phase 4: open outlet valve

phase 5: drain pump chamber

phase 6: close outlet valve

Figure 2. Schematic cross-sections and top view photographs of thevalves and pump chamber illustrating the pump cycle.

0 20 40 600.0

0.4

0.8

1.2

Time (ms)

phase: 5 6 1 2 3 4

Figure 3. Volume output from the pump through one pumping cycleis plotted versus time. Numbers indicate phases of the pump cycle.

pumpchamber

valves

valveseat

membrane

fluidicchannel

pneumaticconnections

(a) (b)

Figure 4. A 3D model of the pump elements. Only the volumesfilled with fluid (blue) or air (gray) are shown. Both the top (a) andbottom half (b) of the pump features are presented.

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Design, modeling and fabrication of a constant flow pneumatic micropump

(a)

(b)

(c)

Figure 5. The clearance of air bubbles through one complete cycleof the pump. In the first image, the pump is filled with air bubbles(a). The pump chamber is drained and the bubbles are ejected(b) and the chamber is refilled with fluid (c).

pump chamber is 0.92 µL. The circular valves have the samewidth and radius of curvature as the pump chamber. The fluidicchannels have a 0.4 mm × 0.4 mm D-shaped cross-section.Small inserts between the top plate and the membrane preventpneumatic pressure from deflecting the membrane into thefluidic channels. This eliminates pneumatic bleed off.

In order to maintain a set flow rate, it is essential thata constant volume of fluid is pumped during each cycle.This is facilitated by the contoured surfaces of the pumpchamber that limit the maximum deflection of the membrane.Additionally, the fluidic channel was cut across the length ofthe pump chamber. This prevents the flexible membrane fromthrottling or closing the outlet of the pump chamber beforeall fluid is ejected, alleviating problems of valve leakage.Similarly, a small channel in the bottom plate ensures thatthe membrane does not prematurely seal off the pneumaticinput when vacuum is applied. These channels significantlyimprove pump consistency and performance. Unfortunately,the channels also increase the area of unsupported surfacesin the chambers. This makes the stroke volume slightlydependent on pneumatic pressure.

For liquid micropumps to be self-priming and bubbletolerant, Richter et al [15] established that the compressionratio of a pump (stroke volume/dead volume) should bemaximized. The compression ratio of the pump describedin this paper is approximately 1.3. Additionally, the taperedends of the fluidic channels reduce the possibility of bubbleentrapment. The bubble clearing capability of the pump isdemonstrated by a sequence of images in figure 5.

2.2. Capacitor

The main components of the fluidic capacitor shown infigure 1 are a flexible membrane and a fluidic resistancesupplied by a filter. Based on information provided bythe manufacturer, the hydraulic resistance of the filter(SVLP09050, Millipore Corp., Bedford, MA) was 10 kPa/(mL/s).

When flow is in the direction shown in figure 1,flow from the pump into the capacitor chamber maintainsan approximately constant fluid pressure by deflecting themembrane downward. This pressure drives continuous flowthrough the filter at the capacitor outlet.

When flow is in the opposite direction, fluid first passesthrough the capacitor before entering the pump. In this

P < Patm P > Patmpump

PatmPatm

PatmPatm (a) (b)

Figure 6. A two-capacitor system filters flow pulses both entering(a) and leaving (b) the pump. In (a), lower than atmosphericpressure draws fluid through the fluidic resistor, and in (b) elevatedpressures drive flow through the resistor.

connections toregulated air andvacuum

display forflow rate

LEDs indicateflow direction

solenoid

valves

buttons forsetting directionand flow rate connections

to the pump

Figure 7. The controller.

orientation, pressure lower than atmospheric pressure in thecapacitor chamber draws fluid through the resistor at the inlet.Flow as it enters the pump system is continuous, but is pulsatileat the pump outlet. Some applications may require continuousflow on both sides of the pump; the two-capacitor systemshown in figure 6 can be used in these situations.

2.3. Controller

The electro-pneumatic controller shown in figure 7 was usedto actuate the valves and pump chamber. Compressedair and vacuum were connected to three-way solenoidvalves (LHDA0521111H, The Lee Company, Westbrook,CT) through regulators (P15 Wilkerson, Richland, MI andIRV3000, SMC, Indianapolis, IN, not shown). Actuation ofthe solenoids was done using a microcontroller (ATTINY26L,Atmel, San Jose, CA).

2.4. Fabrication

The acrylic micropump was fabricated using a three-axiscomputer numerical controlled (CNC) mill. The pumpchamber and the valves were cut using a 3.15 mm diameterball end mill. The fluidic channels were created with a 0.4 mmdiameter ball mill.

The top half of the pump was attached with screws tothe bottom half to sandwich a polyurethane membrane (ST-625FS, Stevens Urethane, Easthampton, MA). Because thepump features are only 190 µm deep, it was important to use arelatively thin (∼25 µm) membrane. Selection of a membranewith a thickness comparable to the depth of the pump features

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W Inman et al

n

w

P

r

σ

θσ

Figure 8. A balance of forces between pressure acting on thecircular area of the membrane and tension in the membrane actingaround the circumference of the membrane.

can negatively affect pump performance due to penetration ofthe clamped membrane into the pump features. Dowell pinswere used to ensure proper alignment of the pump features.

3. Models

3.1. Pump chamber

The volume V of a pump chamber with a round footprint isgiven by the equation for a spherical cap:

V = π

24

[16r3

p − (8r2

p + w2)√

4r2p − w2

], (1)

where rp is the radius of curvature and w is the diameter ofthe cap. Since the pump chamber has an obround footprint, itsvolume increases by

(l − w)

[r2

p sin−1

(w

2rp

)− w

4

√4r2

p − w2

], (2)

where w is now the width of the cap and l is the length of thechamber. The additional length term accounts for the middlesection between the semi-circular ends.

For a circular chamber, the balance of forces shown infigure 8 between pressure P, which acts on the projected areaof the chamber, and membrane tension, acting around thecircumference of the chamber is

P [π(w/2)2] = σn(πwt), (3)

where w is the width of the chamber, t is the membranethickness and σ n is the component of membrane tensile stressacting normal to a flat membrane. This component of tensilestress can be found using

σn = σ sin θ = σw

2r, (4)

where r is the radius of curvature of the membrane and σ isthe tensile stress in the membrane. This leads to

P = 2σ t

r, (5)

which is analogous to the Young–Laplace equation for pressureinside a spherical droplet where the tensile stress in themembrane, the product σ t, represents surface tension.

Sigma is the product of strain ε and Young’s modulus E(σ = ε E). Strain is calculated using

ε = lf − li

li= 2r

wsin−1

( w

2r

)− 1, (6)

where li is the width of the chamber (w) and lf is the length ofthe chamber surface (the arc length of the membrane). Using(5) and (6), a relationship between pressure and membranedeflection is found:

P = 4Et

w

[sin−1

( w

2r

)− w

2r

]. (7)

A Young’s modulus of 15 MPa was measured for themembrane in the described system. Because a thin, flexiblemembrane is used, only tension is considered, and moment,shear and compression are all neglected.

According to (7), in order to deflect a 1.5 mm diameterround membrane to a radius of curvature of 1.58 mm,the pressure differential across the membrane must beapproximately 20 kPa.

For an obround chamber, strain across the long axis is lessthan across the short axis. The strain along this axis is givenby

εl = 2r

lsin−1

( w

2r

)− w

l= ε

w

l, (8)

where l is the length of the chamber. Estimates for the obround,3 × 1.5 mm, chamber suggest the minimum actuation pressuredrops to approximately 12 kPa.

3.2. Capacitor

Fluidic capacitance describes how volume in the capacitorchanges in response to fluid pressure:

C = dV

dP. (9)

Fluidic capacitance can be provided with a number of physicaldevices that can be linear or nonlinear. Examples of linearelements include an open-top reservoir or a closed reservoirwith a spring-loaded piston. For membrane capacitors witha high Young’s modulus, capacitance can be modeled as aconstant acknowledging the fact that deflection is typicallyless than the membrane thickness [16]. Examples of nonlinearcapacitors include an air bubble inside a closed chamber orflow channels with elastic walls [17]. Linear fluidic capacitorsare easier to characterize but can be difficult to integrate intoa microfluidic system. In contrast, nonlinear capacitors canbe easy to implement and are effective over a larger range ofoperating conditions. Models for membrane capacitors havebeen developed; however, they do not account for the actualgeometry of the deflected membrane [17–19]. The followingmodel accounts for the nonlinear relationship between fluidpressure and the geometry of the deflected membrane and forthis reason is a more accurate predictor of performance.

The described pump and valves use a thin, flexiblemembrane. For this reason, it was advantageous to employthe same membrane in the capacitor design. For the describedcircular capacitor, V and P are defined by (1) and (7),respectively. Both of these equations are based on theassumption that the deflected membrane forms a sphericallycurved surface.

By taking the derivative of (1) and (7), capacitance isfound in terms of the radius of curvature of the membrane:

C = πr3

4E

(8r2 − w2 − 4r

√4r2 − w2

2r − √4r2 − w2

). (10)

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Design, modeling and fabrication of a constant flow pneumatic micropump

0 1 2 30

100

200

300

Pressure (kPa)

20 mm

15 mm

10 mm

5 mm

Figure 9. Capacitance versus pressure for capacitors of differentdiameters.

Ideally, an equation describing capacitance in terms of pressureshould be found; however, since r is not readily described asa function of P, this direct equation was not found. Instead,capacitance and pressure values across a range of radii werecalculated and plotted for several capacitor diameters. As canbe seen in figure 9, this capacitor is nonlinear. It is importantto mention that pressure shown in this figure is the pressuredifference across the capacitor membrane.

Pressure was calculated by multiplying the average flowrate by the fluid resistance of the filter. A value for capacitancewas found by using this pressure. If there is another significantcontributor to fluid pressure, such as hydrostatic pressure,this will cause capacitance values to drop and the followingcalculations will need to be adjusted. More importantly, if airpressure below the membrane is tuned to match fluid pressure,the pressure difference across the membrane will decrease andcapacitance will increase.

The closer the membrane is maintained near the neutral(flat) position, by tuning air pressure under the membrane tomatch fluid pressure, the higher the values for capacitance willbe. The willingness of a flat membrane to deflect under asmall pressure (i.e. the large capacitance) is the result of thegeometries involved. When the membrane is initially flat, asmall amount of deflection will result in a sizeable change incapacitor volume. As the capacitor is loaded, increasinglylarger amounts of membrane strain are required to increasevolume in the capacitor region. For example, a very smallamount of deflection in terms of membrane strain, 0.04% strainalong the centerline of a 10 mm capacitor, will hold a relativelylarge volume, 5 µL. This small amount of strain requires asmall pressure differential, 0.0033 kPa, and thus capacitanceis large. When the capacitor is initially loaded with 20 µL, anincrease in membrane strain from 0.7% to 1.1% is required todeflect the membrane enough to accommodate an additional5 µL. This requires an increase in pressure from 0.21 kPa to0.4 kPa, and thus capacitance is much lower. Ten timesmore strain and over 50 times more pressure are required todeflect the pre-loaded capacitor membrane. Since capacitanceis change in volume per change in pressure, this increaserepresents an order of magnitude decrease in capacitance.If it is feasible to maintain an air pressure below thecapacitor membrane that keeps the membrane relatively flat,performance of the capacitor will be significantly increased.

The time constant τ is capacitance times the fluidicresistance of the filter R, 10 kPa/(mL/s):

τ = RC. (11)

0.01 0.1 1 100.1

1

10

100

Flow Rate (mL/min)

cycl

e

20 mm15 mm

10 mm5 mm

Figure 10. Ratio of time constant to cycle time of the pump plottedin log scale across a range of flow rates for several capacitordiameters.

The time constant indicates how long it takes a system torespond to an input. If the input is a volume of fluid ejectedfrom the pump into the capacitor, the time constant indicateshow long before 63% of this fluid is sent from the capacitorthrough the fluidic resistor at the system exit. When a capacitoris used to filter out fluctuations in a signal, the time constantshould be longer than the period of the longest signal thecapacitor is expected to filter. For the described system, thetime constant should be longer than the time to pump onecycle.

As flow rate increases, fluid pressure rises. Consequently,the time constant and performance of the capacitor decrease.With higher flows, the cycle time of the pump tc also decreases.A flow pattern with a shorter cycle time is easier to stabilizebecause there is less time with no flow between pump strokes.Taking the ratio τ/tc allows a comparison between the abilityof the system to filter flow pulses and the signal that the systemis expected to filter. Figure 10 shows calculated values forτ/tc for several capacitor diameters across a range of flowrates.

The time constant ratio is dependent on a large numberof parameters. A relationship between these parameters wasfound from the model. Each parameter was varied acrossa large range and power law regression was used to makecorrelations between different variables and τ/tc. An equationwas found to estimate this ratio describing flow stability:

τ

tcycle≈ 0.037

1

Vstrokew3.33

(QR

Et

)0.33

, (12)

where Q is the flow rate, R is the fluidic resistance at thecapacitor outlet, Vstroke is the stroke volume, E is Young’smodulus of the membrane, t is the membrane thickness andw is the capacitor diameter. For time constant ratios that arerelatively close to 1, equation (12) closely estimates the directcalculations from the model. More importantly, equation (12)shows the relative influence of each parameter on τ/tc, and isa useful tool when designing a pump system for continuousflow applications.

From this equation, it can be seen that the diameter of thecapacitor has the strongest effect on flow stabilization. Thevolume of the pump chamber also plays an important role.Flow stability is inversely proportional to the stroke volume.The remaining parameters (Q, R, Et) impact performance to alesser extent. This is because when varied they both positively

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and negatively impact flow stability. For example, when ahigher resistance is used to increase the time constant (11)and thus increase flow stability, pressure inside the capacitorincreases and capacitance is reduced, lowering flow stability.The combined result is only a slight increase in flow stability.

Similarly, when overall flow rate is decreased, the effectson flow stability are both positive and negative. In thedescribed system, the cycle time of the pump must increase inorder to reduce overall flow rates. This results in a flow patternthat is more difficult to filter. Coupled with this increase incycle time is a decrease of pressure in the capacitor region.This reduced pressure positively impacts the performance ofthe capacitor and partially offsets the negative influence of theincreased cycle time. In a study by Yang et al [18, 19], theeffects of average flow and signal frequency were characterizedusing a system where these two parameters were separable.The results showed that increasing average flow negativelyimpacts capacitor performance while increasing frequencypositively impacts performance. Since flow rate and frequencyare coupled when using a reciprocating pump, increased flowwill result in only a small net improvement in flow stability.

3.3. Flow from the capacitor

Flow from the capacitor was modeled using MATLAB. Aflow pattern from the pump to the capacitor was constructedusing the phases of the pump and the volume of the pumpchamber and valves. Flow output at incremental time pointswas computed based on the input flow pattern.

After starting the pump, it takes a number of cycles tocharge the capacitor. These cycles were not the subject ofthe simulation. Instead, it focused on operation of the fullycharged capacitor.

The simulation begins by estimating the volume of thefully charged capacitor. Using (1), the radius of curvature ofthe membrane is found from this volume. From this radius,the pressure in the capacitor is determined using (7). Thispressure drives flow through a fluidic resistor at the capacitorexit. Once flows exiting and entering the capacitor are known,a capacitor volume is found for the next time point and theprocess repeats. The volume of fluid exiting the capacitor isfound by integrating flow over time. Comparisons betweenthe model and measured data are shown in the next section.

4. Pump characterization and model validation

Flow from the pump is independent of pneumatic pressure andhead pressure within certain limits. Outside these limits, thestroke volume is not set by the size of the pump chamber. Theoperating range of the pump is the subject of this section, whichalso characterizes the capacitor and compares the models toexperimental results.

4.1. Pneumatic pressure

The minimum pneumatic pressure required to fully actuatethe membrane was determined at a cycle frequency of 5 Hz.This frequency allowed sufficient time for the membrane toactuate. Equal positive and negative pressures were used. Asmall glass capillary was connected to the exit of the pump,

0 10 20 30 40 500.0

0.5

1.0

Pressure (kPa)

Figure 11. Stroke volume in relation to actuation pressure. Thepump was driven at 5 Hz.

0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0

Time (ms)

50 kPa40 kPa

30 kPa20 kPa10 kPa

Figure 12. Volume of fluid ejected from the pump chamber duringphase five of the pumping cycle for various pneumatic pressures.

bypassing the capacitor. The capillary was mounted on aruler and the position of fluid in the capillary before and after50 pump cycles was measured. The difference in positionswas used to determine a fluid volume. Volume measurements,normalized to the number of cycles, are plotted in figure 11.

When sufficient pressure was applied, the measured strokevolume was 0.95 µL. This value is very close to the calculatedvolume of the pump chamber (0.92 µL). Differences in pumpchamber volume could be explained by accuracy limitations inthe fabrication process or deflection of the membrane into thepneumatic and fluidic channels that span the pump chamber.As predicted by the model, the pneumatic pressure required tofully actuate the membrane was between 12 and 20 kPa.

4.2. Phase timing

There are six phases in a cycle of the pump. Execution ofeach phase requires a certain amount of time and that time wasmeasured. The controller was set to allow ample time for fiveof the six phases, and the time for the remaining phase wasvaried. Flow was measured using the methods described insection 4.1. The results for draining the pump chamber areshown in figure 12.

It can be seen that the volume of fluid ejected from thepump chamber increases with time. Once the pump strokecompleted, no additional fluid was pumped. The slopes ofthese curves represent flow rates from the pump. The highestactuation pressures drove fluid at the fastest rates.

Figure 13 shows the time required to fill the pumpchamber. As seen in both figures 12 and 13, the pumpresponse changed only minimally when pneumatic pressure

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Design, modeling and fabrication of a constant flow pneumatic micropump

0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0

Time (ms)

50 kPa

40 kPa

30 kPa

20 kPa

10 kPa

Figure 13. Volume of fluid filling the pump chamber during phase 2of the pump cycle.

0 20 40 60 80 1000

1

2

3

4

5

Frequency

Flow

(m

L/m

in)

0 kPa5 kPa10 kPa15 kPa20 kPa25 kPa

Figure 14. Flow rate as a function of frequency and head pressurefor a pneumatic pressure of 40 kPa.

Table 1. Times required to complete each phase of the pump cycle.

Minimumtime (ms)

Step 1: open inlet valve 0.4Step 2: fill pump chamber 3.7Step 3: close inlet valve 1.4Step 4: open outlet valve 0.4Step 5: drain pump chamber 4.5Step 6: close outlet valve 1.4

was increased from 30 to 50 kPa. As a result, positive andnegative 40 kPa were selected as optimal pneumatic actuationpressures.

The time required to actuate the valves was found in asimilar manner. The minimum time required for each phaseof the pump cycle is shown in table 1.

These times result in a maximum frequency of 85 Hz.When times were set for lower frequencies, phases 1 and 4were allotted 33% of the total cycle time, phases 2 and 5used 11% and 3 and 6 used 6%. These percentages correlateroughly with the times shown in table 1.

4.3. Head pressure

The relationship between flow and head pressure wasinvestigated. The height of a horizontally mounted capillarywas adjusted relative to the pump in order to achieve thedesired head pressures. Flow was measured across a rangeof frequencies for head pressures ranging from 0 to 25 kPa.The results are shown in figure 14.

0 3 65

0

5

0

25

50

75

Pressure (kPa)

10 mm measured5 mm measured

10 mm model5 mm model

Figure 15. Volume displacement of the capacitor versus fluidpressure is compared against the model. Capacitors of twodiameters (5 and 10 mm) were measured and modeled.

0 2 4 60

20

40

60

Pressure (kPa)

10 mm measured

5 mm measured10 mm model

5 mm model

Figure 16. Capacitance measurements compared with the model.

The initial linear slope of this figure signifies a constantstroke volume. Declining flow rates signify that the membraneis no longer conforming to the rigid walls of the chamberand the pump is sensitive to changes in pneumatic and headpressure. Therefore, it is desirable to operate the pumps in thelinear region.

At 85 Hz the pump achieves 5 mL min−1 against zerohead. Against a head pressure of 25 kPa, the pump can achieve2.6 mL min−1 at 50 Hz. At the lower frequencies, variationsin head pressure do not affect the performance of the pump.

4.4. Capacitor

Volume of fluid in the capacitor was measured in responseto fluid pressures ranging from negative to positive 6 kPa.In these measurements, a capillary was attached to the exitof the capacitor and the valves in the pump were closed. Thecapillary was raised or lowered to generate hydrostatic pressurein the capacitor and the corresponding volume was recorded.The results are plotted in figure 15 and compared with thecapacitor model.

Fluidic capacitance was calculated from the measureddata using central differences. Figure 16 compares measuredcapacitance with the model and shows good agreementespecially at higher pressures. At lower pressures, the modelunderestimates capacitance. These discrepancies can beattributed to stretching the membrane across the capacitorchamber during assembly.

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W Inman et al

0 0.5 1.0 1.5 2.0 2.50

0.5

1.0

1.5

2.0

2.5

Time (ms)

no capacitor

5 mm capacitor

10 mm capacitor

modelmeasured

= 0.25cycle

= 2.5cycle

Figure 17. Comparison of measured capacitor performance to thecapacitor model for a flow rate of 0.05 mL min−1. The time constantratio, estimated using (12), is shown for the two capacitors.

0 0.1 0.2 0.3 0.40

1

2

3

4

Time (ms)

5 mm capacitor10 mm capacitor

2 mL/min

= 0.85

1 mL/min

0.68

0.5 mL/min

0.548.5

6.85.4

cycle

Figure 18. Flow from two different capacitors for several flow rates.The time constant ratio from (12) is shown for each curve.

4.5. Flow from the capacitor

In order to measure performance of the capacitor, fluid waspumped through a capillary and a high-speed video camerawas used to track the end position of the fluid. A comparisonwas made between two different capacitor diameters (5 and10 mm) and no capacitor. The high-speed video camera(Phantom V7.1, Vision Research, Wayne, NJ) wasprogrammed to image at millisecond time increments. UsingMATLAB, the end position was tracked and converted into avolume. Since the two capacitors were attached to pumps withslightly different pump chamber volumes (1.17 and 1.08 µL),volume measured from the larger pump chamber was scaledby 0.9 in order to facilitate the comparison of capacitors. Thecapillary was also attached directly to the pump exit in orderto measure a system with no capacitor. Figure 17 comparesthe model with experimental results.

As is predicted by the model, the 10 mm capacitoreffectively filters fluid pulses and a nearly constant flow streamis generated. The 5 mm capacitor does not completely removepulses and the model slightly overestimates performance. Thiscould be the result of several factors including differencesbetween the actual fluidic resistance and resistance used in themodel.

Figure 18 shows measurements for several other flowrates. As τ/tc increases, flow variations decrease. Using the10 mm diameter capacitor, fluid pulses have been eliminatedfrom the system for all flow rates. When the 5 mm diametercapacitor is used, flow variations become less pronounced at

higher flows. At 2 mL min−1, the time constant ratio reaches0.9 and flow variations are still present. However, when thetime constant ratio is increased to 2.5 (figure 17), there is apronounced decrease in flow variations.

5. Discussion of pump and capacitor design

The system described in this paper integrates a fluidic capacitorand a pneumatic pump in order to achieve pulseless flow. Forapplications that do not require pulseless flow, the pump can beused without a capacitor. In this case, the pump still providesnumerous benefits such as a large range of flow rates and lowsensitivity to changes in head pressure and pneumatic pressure.Similarly, the capacitor can be used to filter out flow pulsesgenerated by other types of reciprocating membrane pumps.

If it is necessary to reduce flow pulses generatedby pneumatically driven, reciprocating displacementmicropumps, there are several approaches that can be chosen.One approach is to reduce the stroke volume of the pumpand rely on natural capacitance in the system to filter out smallpulses. For example, if soft lithography is used for fabrication,the flexible walls of PDMS microchannels provide naturalcapacitance.

Reducing the stroke volume can, however, negativelyimpact performance of the pump. To provide the desiredflow, the pump must be operated at higher frequencies. Thisincreases the requirements on the pneumatic system andnecessitates a smaller volume in the pneumatic control lines(e.g. shorter distance between the pump and the controller).Reducing the stroke volume can also impact the pump’s abilityto clear air bubbles. Additionally, as the size and depth of pumpfeatures are reduced, the thickness of the membrane must alsobe reduced. Finally, small pump features require more precisefabrication techniques.

Another approach for reducing flow pulsatility indisplacement micropumps is to quickly fill the pump chamberand drain it at the desired flow rate. This approach requiresprecise control of fluidic resistances and a balance of headpressures and pneumatic pressures. Because all of theseparameters are coupled, it is difficult to change flow ratesarbitrarily.

The approach used in this paper addresses the requirementof constant flow that is insensitive to head pressure by firstdesigning a robust pump, then separately addressing flowpulsatility. Robustness of the pump was achieved by usingpneumatic pressures that reliably deflected the membrane tothe contoured surfaces of the pump chamber. Flow rate canbe varied across a large range by simply changing the pumpfrequency. The capacitor diameter is then chosen to filterfluctuations across the desired flow range.

Ideal applications for the pump and capacitor systeminclude miniaturized perifused or perfused cell culture systemssuch as bioreactors [20–25] and bioprocessors where this pumpcan provide substantial advantages over routinely used rotaryperistaltic pumps. Other appropriate applications includesituations where it is necessary to image, probe or manipulatecells, microorganisms, beads or any other small objectsunder highly constant flow conditions. Flow and pressurevariations on various timescales can be detrimental in livecell investigations because they can lead to variations in shear

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Design, modeling and fabrication of a constant flow pneumatic micropump

stress, cell movement or even cell dislodgment. Typically, asyringe pump is used in these studies; however, its utility islimited in long-term experiments because it can only pump afinite volume. In contrast, the reported pump is not limited involume and when coupled with the capacitor, can provide atight control of flow rate over extended periods of time.

For applications such as precise dosing or metering, thecombination of a pump and capacitor may not be appropriate.Since volume of fluid stored in the capacitor is a function offluid pressure, immediately after starting the pump, flow fromthe capacitor increases until it is fully charged. Transienteffects due to charging and discharging the capacitor canconstitute a problem for these types of applications.

6. Conclusions

A bi-directional pneumatic diaphragm micropump has beenfabricated and characterized. It features a pump chamber withcontoured surfaces that limit the maximum deflection of ahighly flexible membrane. The pump was shown to be self-priming, bubble tolerant and insensitive to changes in headand pneumatic pressures. Flow bi-directionality was achievedby using active valves. An integrated capacitor was used toconvert pulsatile flow generated by the pump into a nearlyconstant flow stream. A nonlinear model for the capacitor wasdeveloped and compared with experimental results. The ratioof the time constant of the capacitor to the cycle time of thepump was shown to be an accurate indicator of the capacitorperformance and a useful design tool. Typical applications ofthe pump and capacitor system include situations where it isnecessary to culture, image, probe or manipulate cells underhighly constant flow conditions.

Acknowledgments

We would like to thank Dr James W Bales of the EdgertonCenter at MIT for helping with high-speed video cameraimaging, Gerald Wentworth and Pat McAtamney of theLaboratory for Manufacturing and Productivity at MIT forallowing access to the machine shop, Mark Tobenkin of theMIT Electronics Research Society for his help designingthe controller, Will Grover for helpful discussions on microdiaphragm pumps, Stevens Urethane for generously givingsamples of urethane membranes and SMC Corporation ofAmerica for providing a vacuum regulator. Research wassupported by the DuPont MIT Alliance, Pfizer and NSFBiotechnology Process Engineering Center.

References

[1] Bart S F, Tavrow L S, Mehregany M and Lang J H 1990Microfabricated electrohydrodynamic pumps SensorsActuators A 21 193–7

[2] Jang J and Lee S S 2000 Theoretical and experimental study ofmhd (magnetohydrodynamic) micropump SensorsActuators A 80 84–9

[3] Manz A, Effenhauser C S, Burggraf N, Harrison D J, Seiler Kand Fluri K 1994 Electroosmotic pumping andelectrophoretic separations for miniaturized chemicalanalysis systems J. Micromech. Microeng. 4 257–65

[4] Guzman K A D, Karnik R N, Newman J S and Majumdar A2006 Spatially controlled microfluidics using low-voltageelectrokinetics J. Microelectromech. Sys. 15 237–45

[5] Brechtel R, Hohmann W, Rudiger H and Watzig H 1995Control of the electroosmotic flow by metal-salt-containingbuffers J. Chromatogr. A 716 97–105

[6] Lucy C A and Underhill R S 1996 Characterization of thecationic surfactant induced reversal of electroosmotic flowin capillary electrophoresis Anal.Chem. 68 300–5

[7] Laser D J and Santiago J G 2004 A review of micropumpsJ. Micromech. Microeng. 14 R35–R64

[8] Grover W H, Skelley A M, Liu C N, Lagally E T andMathies R A 2003 Monolithic membrane valves anddiaphragm pumps for practical large-scale integration intoglass microfluidic devices Sensors Actuators B 89 315–23

[9] Unger M A, Chou H-P, Thorsen T, Scherer A and Quake S R2000 Monolithic microfabricated valves and pumps bymultilayer soft lithography Science 288 113–6

[10] Thorsen T, Maerkl S J and Quake S R 2002 Microfluidiclarge-scale integration Science 298 580–4

[11] Huang C-W, Huang S-B and Lee G-B 2006 Pneumaticmicropumps with serially connected actuation chambersJ. Micromech. Microeng. 16 2265–72

[12] Young A M, Bloomstein T M and Palmacci S T 1999Contoured elastic-membrane microvalves for microfluidicnetwork integration J. Biomech. Eng. 121 2–6

[13] Xia Y and Whitesides G M 1998 Soft lithography Ann. Rev.Mater. Sci. 28 153

[14] Heckele M and Schomburg W K 2004 Review on micromolding of thermoplastic polymers J. Micromech.Microeng. 14 R1-R14

[15] Richter M, Linnemann R and Woias P 1998 Robust design ofgas and liquid micropumps Sensors Actuators A 68 480–6

[16] Goldschmidtboing F, Doll A, Heinrichs M, Woias P,Schrag H J and Hopt U T 2005 A generic analytical modelfor micro-diaphragm pumps with active valves J.Micromech. Microeng. 15 673–83

[17] Zengerle R and Richter M 1994 Simulation of microfluidsystems J. Micromech. Microeng. 4 192–204

[18] Yang B, Metter J L and Lin Q 2005 Using compliantmembranes for dynamic flow stabilization in microfluidicsystems 18th IEEE Int. Conf. Micro Electro MechanicalSystems (MEMS 2005) (Miami, FL, 2005) pp 706–9

[19] Yang B and Lin Q 2005 Modeling of a micro flow stabilizationdevice for lab-on-chip applications Proc. 9th Int. Conf. onMiniturized Systems for Chemistry and Life Sciences(µTAS) (Boston, 9–13 October 2005) pp 1118–20

[20] Domansky K, Inman W, Serdy J and Griffith L G 2006Multiwell cell culture plate format with integratedmicrofluidic perfusion system Proc. of SPIE: Microfluidics,BioMEMS, and Medical Microsystems IV (San Jose, 23–28January) vol 6112 61120F-1–7

[21] Domansky K, Inman W, Serdy J and Griffith L G 2005 3dperfused liver microreactor array in the multiwell cellculture plate format Proc. 9th Int. Conf. on MiniturizedSystems for Chemistry and Life Sciences (µTAS) (Boston,9–13 October 2005) pp 853–5

[22] Lee P J, Hung P J, Rao V M and Lee L P 2006 Nanoliter scalemicrobioreactor array for quantitative cell biologyBiotechnol. Bioeng. 94 5–14

[23] Hung P J, Lee P J, Sabounchi P, Lin R and Lee L P 2005Continuous perfusion microfluidic cell culture array forhigh-throughput cell-based assays Biotechnol.Bioeng. 89 1–8

[24] Leclerc E, Sakai Y and Fujii T 2004 Microfluidic pdms(polydimethylsiloxane) bioreactor for large-scale culture ofhepatocytes Biotechnol. Prog. 20 750–5

[25] Prokop A, Prokop Z, Schaffer D, Kozlov E, Wikswo J,Cliffel D and Baudenbacher F 2004 Nanoliterbioreactor:long-term mammalian cell culture at nanofabricated scaleBiomed. Microdevices 6 325–39

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