Proceedings of the 1st IEEE InternationalConference on Nano/Micro Engineered and Molecular Systems

January 18 - 21, 2006, Zhuhai, China

Electrorheologic Liquid Crystals in Microsystems:Model and Measurements

Michae De Volderl *, Kazuhiro Yoshida2, Shinichi Yokota2, Dominiek Reynaerts''Division PMA, Department ofMechanical Engineering, KULeuven, Belgium2Precision and Intelligence Laboratory, Tokyo Institute ofTechnology, Japan

Abstract-Fluids with a controllable viscosity gained a lot ofinterest throughout the last years. One of the advantages of thesefluids is that they allow to fabricate hydraulic components suchas valves with a very simple structure. Although the properties ofthese fluids are very interesting for microsystems, theirapplicability is limited at microscale since the particles suspendedin these fluids tend to obstruct microchannels. This paperinvestigates the applicability of electrorheologic Liquid Crystals(LC's) in microsystems. Since LC's do not contain suspendedparticles, they show intrinsic advantages over classic rheologicactive fluids in microapplications. As a matter of fact, LCmolecules are usually only a few nanometers long, and therefore,they can probably be used in systems with sub-micrometerchannels or other nanoscale applications. This paper presents anovel model describing the electrorheologic behavior of thesenanoscale molecules. This model is used to simulate a microvalvecontrolled by LC's. By comparing measurements and simulationsperformed on this microvalve it is possible to prove that themodel developed in this paper is very accurate. In addition, thesesimulations and measurements revealed other remarkableproperties of LC's, such as high bandwidths and high changes inflow resistance.

Keywords-liquid crystals, electrorheology, microvalves

I. INTRODUCTION

Fluids with a controllable viscosity gained a lot of interestthroughout the last years. Some of these fluids such asmagnetorheological fluids (MRF) and electrorheological fluids(ERF) are now widely applied in active dampers and valves.Despite the remarkable properties of these fluids, theirapplicability is limited at microscale since the particlessuspended in these fluids tend to obstruct microchannels [1, 2].This paper investigates the use of electrorheologic LiquidCrystals (LC's) in microsystems [1, 3]. Since LC's do notcontain suspended particles, they show intrinsic advantagesover classic rheologic active fluids in microapplications. As amatter of fact, LC molecules are usually only a few nanometerslong, and therefore, they can probably be used in systems withsub-micrometer channels or other nanoscale applications.

Figure 1 depicts the size of a 4-n-pentyl-4'-cyanobiphenyl(5CB) LC molecule, approximately 2 nm long, on the samescale as particles suspended in GER of 20 nm [4] and incommercial MRF of 20 ptm [2]. This picture shows that LCmolecules are an order of magnitude smaller than the particlessuspended in classic rheologic fluids.

LC GER

- 10nm

Figure 1. Comparison of the size of different rheologic fluids on the samescale.

Despite the promising characteristics of LC's aselectrorheological fluids, the physics needed to understandtheir behaviour have not yet been described in detail [3]. Negita[5], Rodriguez [6] and van Saarloos [7] described theelectrorheology of LC's. However they only reported staticflow characteristics whereas this paper describes the influenceof both static and dynamic altering electric fields. In addition,most of these publications investigate flows with a constantshear rate over the height of the channel, which is not valid inmany practical applications as for instance in the case of themicrovalves described in [3].

II. PHYSICAL MODEL

A. IntroductionFigure 2 shows the different phases of LC molecules of the

type 5CB. The term liquid crystal refers to a phase thatcombines properties of the isotropic liquid phase and theanisotropic solid phase. This means that the LC phase has onthe one hand flow characteristics such as a flow viscosity andon the other hand solid properties such as elasticity constants.

'''-e t.~~~~~~~~~

Liqui

Liquid Crystal Solid

Figure 2. Illustration of the phases ofthe liquid crystal 5CB.

In this paper, the orientation of the molecules in the LCphases is controlled in order to change the flow rate through achannel. This principle is illustrated in figure 3 that shows the

This project wasfunded by the Institutefor the promotion ofinnovationand Technology in Flanders, by the Fundfor Scientific research - Flanders,by the Interuniversity Attraction Pole AMS and by the Grant-in-Aidforscientific research in priority areas, No. 16078205 ofthe ministry ofEducation, culture, sports, science and technology ofJapan.

*Contact author: e-mail michael.devolder(mech.kuleuven.be

1-4244-0140-2/06/$20.00 C)2006 IEEE 236

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flow of LC molecules through a channel. In the absence of anelectric field (figure 3, left), the axis of the LC molecules isparallel to the flow direction (Q). In this case, the flowresistance of the molecules is low, resulting in a low pressuredrop over the channel. On the other hand, it is possible to alignthe molecules with an electric field (E) (figure 3, right) due toan induced electric dipole in the molecules. In that case, theflow resistance of the molecules is much higher and therefore,the pressure drop over the channel increases.

Flow Only Flow & Elec. fieldChannelwall $===

Electrode

LC .

molecule r Q

D. Elastic TorqueUnlike ideal liquids, LC's show elastic properties similar to

solid materials. These elastic properties can be taken intoaccount by the Frank elastic constants Kii [8]. In the situation offigure 3, it is possible to describe the elastic torque by equation(3) [1].

T = (K11 sin2 (0) + K33 cos2 (0))( d20)

-d+ (K11 - K33) sin(0) cos(0).-

(3)

E. Dynamic torquesIn case of dynamic flow simulations, a torque due to the

rotational inertia and to the viscous damping must be taken intoaccount. This results in equation (4) [1].

d 20 dOTdynl dt2 dt (4)

Figure 3. Behaviour of LC's when subject to a viscous shear flow (left) andto a viscous shear flow and electric field (right).

By identifying the different torques acting on each LCmolecule, a model is developed that describes the orientation ofthe LC molecules (0) as a function of their position (z) in thechannel.

B. Shear Flow TorqueA common approach to describe the flow of LC's is

established by Ericksen, Leslie and Parodi (ELP-theory) [8].From this theory, it can be derived that the torque T, workingon a sheared molecule is determined by equation (1) in the caseof the two dimensional situation depicted in figure 3 [1].

T = [a3 sin2 (0)-2 cos2(0)]a dv2 dz

with a2,3 the Leslie viscosity coefficients [8] and v the flowvelocity.

C. Electric TorqueA second force working on the molecules is due to an

induced dipole, generated by the electric field, as illustrated infigure 1, bottom right. The torque caused by the electric fieldTel can be described by equation (2) [8].

l=_ a °' * F2* sin(20)T/ 2

with I the rotational inertia, y the rotational viscousdamping and t the time.

F Torque EquilibriumThe equilibrium of the torques described above, results in

equation (5).

d 20 dO 2 2 (1))( d2 )I ~+y =(K1 sin2 (0)+K33Cos2().dj

dt2 dt33d

+(K1 -K33). sin(O) cos(O). (d) (5)

+[a sin2(0) -a 2()] dv£a 2 sin(20)

A last important torque is caused by the interaction betweenthe LC molecules and the channel wall. In this paper, weassume a strong anchoring of the molecules parallel to thechannel wall [8]. This anchoring is illustrated in figures 3 and 4in which the molecules are parallel to the channel wall in itsvicinity. This anchoring phenomenon is taken into account bythe boundary conditions of the numerical method that will bedescribed hereafter.

If the flow velocity profile is assumed to be parabolic, as inthe case of ideal laminar flows [7], and if we assume thatK1 zK33 [5, 8], the differential equation (5) can easily be solvednumerically. An example of a numerical simulation performedwith a Runge Kutta algorithm of 4th order is given in figure 4for arbitrary model parameters. In this simulation, each of thearrows represents a LC molecule.

(2)with &, the permittivity of vacuum and ca the dielectric

anisotropy of the liquid crystal.

237

(1)

Outlet Electrode Channel\XAI-A

0 0.1 0.2 0.3 0.4 0.5Normalized distance from channel wall

Figure 4. Simulation ofLC molecule orientation in a channel (top: schematicoverview, bottom: simulation results)

The orientation 0 of the molecules discussed above isemployed to calculate the pressure drop AP over the channel asa function of the flow rate Q and the electric field E. Moreprecisely, the pressure drop is calculated by assuming that thepressure drop is depending on an average orientation angle0 as described in equation (6).

AP = k. [a3 sin2(6)- 2 cos2(6)]. Q (6)

Figure 5. Outline of the microvalve.

B. Static CharacteristicsIn a first phase, the flow rate and the pressure drop over the

valve are measured as a function of the applied electric field.Measurements and simulations of a valve with a height of 0.15mm are shown in figure 6. This figure clearly shows that thephysics of the developed model are in agreement with the realbehaviour of the LC's. It is also interesting to note that changesin apparent flow viscosity with a factor 5 can be achieved.

The constant k depends on the channel geometry. In whatfollows, three simplifications will be made in order todetermine 0 easily and to limit the calculation time. First, theinfluence of the stiffness is neglected, similar to [5]. Second,the flow velocity profile is assumed to be triangular rather thanparabolic as assumed in the calculation of figure 4. Third, therotational inertia can be neglected at moderate frequenciesbecause of the small size of the molecules [1]. These threeapproximations are particularly useful in the case of dynamicsimulations, and still result in a remarkable agreement betweensimulations and measurements as shown in the next section.

III. VALIDATION OF THE MODEL: SIMULATION ANDMEASUREMENTS ON A MICROVALVE

A. Test Set-upIn this section, the above model will be applied to simulate

the flow of LC's through a microvalve controlled by LC's.This way, we hope to prove both, the accuracy of our modeland the potential of LC's as ERF's in microsystems.

The microvalve investigated in this paper is depicted infigure 5. The dimensions of the channel are 5 mm in length, 1.2mm in width and 0.08 mm or 0.15 mm in height. The channeland the supply ports have been fabricated by a double sideTMAH-etch. The electrode is sputtered on a glass plate andattached to the channel by anodic bonding. The fluid usedduring the measurements is the MLC-6457-000 (Merck Japan,Ltd.). The base viscosity is 24 mPa.s at 23°C and the density isabout 990 kg/m3.

80

(0L-

o

a)4o

0)a)

-.3- MeasurementsSimulations

60

40

6kVWmm 5kV/mm

4kV/mm

3kV/mm

2kV/mm

20F

I.0 20 40 60 80

Flow [mm/s]100 120

Figure 6. Measurement of the pressure drop as a function of the flow rateand the electric field at 20°C.

C. Dynamic CharacteristicsIn addition, the developed model can predict the dynamic

behaviour of LC's when they are employed as an ERF. Forinstance, if a sinusoidal electric field of 1 Hz between 0 and 5kV/mm is applied to the valve, the measured variation inpressure drop is shown in figure 7 (a). This experiment isperformed using a channel with a height of 0.15 mm at flowrates of 11 mm3/s and 42 mm3/s. Figure 7 (b) is a simulation ofthe measurements shown in figure 7 (a). Note that the shapes ofthe measured and calculated pressure drops correspond well.

238

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innuunl

80PA

2 60

- 40

,22060En

-H; o2

0 1 2 3 4 5Tme [s]

(a) Measurem ents

60L:40

O2 I

0 0 1 2Time [s]

The measurements of Pa and APd are repeated for differentfrequencies of the electric field and are plotted in figure 8 (a).These measurements are performed using a sinusoidal electricfield between 0 kV/mm and 5 kV/mm and a channel height of0.15 mm. Figure 8 (b) shows the same characteristics as figure8 (a) but based on simulations. Simulations and measurementsare in good agreement, nevertheless, our model is unable todescribe Pa above 100 Hz. This can be due to due tophenomena like dielectric relaxation, which are not taken intoaccount since they normally take place at much higherfrequencies [1].

2.5 kV/mm - 3000 /s - 22°C16

, 14L 12O 10

8

2-- -Amplitude

Average_ l~~~~~~~~~~~~~ I10 100

Frequency [Hz]1000 10000

2.5 kV/mm - 13000 /s - 22°C4 530 -

W 25 A0Lm 20 -

10.a 15-0)u 10-

X 5 -

Figure 7. Measurements (a) and simulations (b) of the pressure dropvariation of a LC valve subject to a sinusoidal electric field of 1Hz for flow

rates of42 mm3/s (top line) and 11 mm3/s (bottom line).

By repeating these measurements and simulations atdifferent frequencies, it is possible to gain insight in thefrequency response of LC's. We will describe the dynamicbehaviour by the average pressure drop over the channel Pa andthe dynamic variation in pressure drop APd [1]. The definitionofPa and APd is illustrated in figure 7.

70

60

aL 50

o 40ci0X 30

X 20tL

10

0

(a) Measurements

10 100 1000Frequency [Hz]

5 kV/mm - 3000 /s - 22°C30 -

, 25 -

a.

m 20 -

0a 15-n 10-

X 5 -

0 -

10000

- Average-Amplitude -

10

10 100 1000 10000

Frequency [Hz]

70 -

60 -

0.w. 50

2 40-a2 30-0 20-k 10

(b) Simulations

W...A........Pa..

Pa-.-APd <

1 10 100

Frequency [Hz]

100 1000Frequency [Hz]

5 kV/mm - 13000 /s - 22°C

10000

50 -

40-

o 300%- 20 -U,U,L 10 -H Amplitude

O- _vrg10

1000 10000100

Frequency [Hz]1000 10000

Figure 8. Measured (a) and simulated (b) frequency characteristics ofthe LCinside a microchannel at a flow rate of42 mm3/s (temperature 20°C).

Figure 9. Frequency characteristics ofLC's in a microchannel with a heightof 150 gim.

239

.n)

1

1

During our measurements we noticed that the dynamicbehaviour of the system is not only depending on the type ofLC [9], but also on the flow rate, the amplitude of the electricfield and the dimensions of the channel. Since microsystemsoften operate at high frequencies, additional measurementshave been performed in order to gain insight in the parametersthat influence the bandwidth. Figure 9 shows the frequencyresponse of a channel with a height of 0.15 mm, a length of 5mm and a width of 1.2 mm at different flow rates andamplitudes of the electric field. Figure 10 shows similarmeasurements for a channel height of 0.08 mm. In order tocompare measurements at different channel heights on asimilar basis, the comparisons will be based on shear rate (Q)rather than on flow rate (Q), using equation (7).

6B.H 2 (7)

with B the channel width and H the channel height. Basedon the measured values ofAPdit is possible to define a kind ofbandwidth of the change in pressure drop. Although the term'bandwidth' is normally only used for linear systems we willdefine it here as the frequency at which APd is reduced with 3dB from the static characteristics. This bandwidth is a criterionfor the frequency up to which a change in viscosity can beinduced in the LC's. As shown by figures 9 and 10, thebandwidth of the electrorheologic LC's increases with the flowrate. The bandwidths of the channels of 0.08 mm depicted infigure 10 are considerably lower than those of the channels of0.15 mm depicted in figure 9. In many applications, the voltageused to control electrorheological fluids must be minimized.This can be achieved by decreasing the channel height.Although lower channel heights do not have a lot of influenceon the change in apparent viscosity, they result in lowerbandwidths as shown in figures 9 and 10.

35 -

Qa.

0

L.a)U,U,G)a.

10 100Frequency [Hz]

50

L¶ 40

0ae

a)L 100 0

50 -

X 40-

30,

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9'10-

0-

1000 10000

= Average1 10 Amplitude

110 100 1000 100(Frequency [Hz]

\ Average\ + Amplitude

1 $

10 100Frequency [Hz]

1000 10000

)O0

TABLE I. MEASURED BANDWIDTHS OF THE PRESSURE DROP VARIATIONOVER A CHANNEL FILLED WITH ELECTRORHEOLOGICAL LC's.

2.5 kV/mm 5 kV/mm

80 pm 3000 s-1 2.5 Hz 2 Hz

10ooo s-1 7 Hz 3.5 Hz

150 pm 3000 s-1 (10 Hz) 20 Hz13000 s-1 55 Hz 45 Hz

80,pm 5kV/mm 10000/s 21°C100

0f 80-

o 60

- 40 -

20-0~

10 100Frequency [Hz]

1000 10000

Table 1 summarizes the measurements of the bandwidthsdiscussed above. This kind of information is important for theapplication of electrorheologic LC's in practical systems as forinstance the microvalves described in [3]. The bandwidthsreported above for channels of 150 ptm are relatively highcompared to that of other rheologic fluids. For instance, if weassume a It order lag response, the homogeneous ERFpresented in [10], have a bandwidth of 3 Hz. Similarly, thegiant ERF presented in [4] show a bandwidth of 16 Hz, and theMRF presented in [20] a bandwidth of 14 Hz.

Figure 10. Frequency characteristics ofLC's in a microchannel with a heightof 80 gim.

Future research will investigate the dynamic behaviour ofLC's in more detail. Furthermore, the fluids and the modeldescribed in this paper will be used in more complex systemsas for instance a 3-port LC valve [3] and an integratedhydraulic microsystem similar to [3, 12].

240

80 pm 2.5 kV/mm 3000 /s 21°C

80 pm 2.5 kV/mm 10000 /s 21°C

80 pm 5kV/mm 3000 /s 21°C

1

IV. CONCLUSIONSThis paper discusses the applicability of electrorheologic

LC's in microsystems. Since these fluids do not containsuspended particles, they are particulary interesting formicrosystems. Therefore, a physical model that describes thebehaviour of electrorheologic LC's has been developed. Themodel can be used for the interpretation and prediction of bothstatic and dynamic characteristics of electrorheologic LC's.The model is validated by comparing measurements andsimulation performed on a microvalve. Comparison ofmeasurements and simulation results shows that the modeldeveloped in this paper is able to simulate both static anddynamic properties accurately. Measurements presented in thispaper reveal that bandwidths of more than 50 Hz and changesin apparent flow viscosity with a factor 5 can been achieved.Finally, measurements showed that the bandwidth isdepending on the shear rate, electric field and the channelgeometry.

REFERENCES

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[3] K. Yoshida, M. Kikuchi, J. -H. Park and S. Yokota, "Fabrication ofmicro electro-rheological valves (ER valves) by micromachining andexperiments", Sensors and Actuators A, Vol. 95, pp 227-233, 2002.

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[6] J. A. Reyes, 0. Manero, R. F. Rodriguez, "Electrorheology of nematicliquid crystals in uniform shear flow", Rheol. Acta 40, pp 426-433,2001.

[7] J. T. Gleeson, W. van Saarloos, "Propagation of excitations induced byshear flow in nematic liquid crystals", Physical Review A, vol 44/4, pp2588-95, 1991.

[8] D. Demus, J. Goodby, G. W. Gray, H. -W. Spiess, V. Vill, Handbook ofLiquid Crystals Vol.1: Fundamentals, Wiley-VCH, germany, pp 231-548, 1998.

[9] K. Yoshida, J.-H. Park, H. Yano, S. Yokota, S. Yun, "Study of valve-integrated microactuator using homogeneous electro-rheological fluid",Sensors and Materials, Vol.17, No.3, pp. 97-112, 2005.

[10] M. Kohl, Fluidic actuation by electrorheological microdevices,Mechatronics, vol. 10, pp. 583-594, 2000.

[11] K. Yoshida, H. Takahashi, S. Yokota, M. Kawachi, K. Edamura, Abellows-driven motion control system using a magneto-rheological fluid,Proc. 5th JFPS International symposium on Fluid Power, pp. 403-408,2002

[12] M. De Volder, J. Peirs, D. Reynaerts, J. Coosemans, B. Puers, 0. Smal,B. Raucent, "Production and characterization of a hydraulicmicroactuator", J. of micromech. and microeng., Vol 15/7, pp S15-21,2005.

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