Effect of a non‑newtonian load on signature S2 for quartz

This document is downloaded from DR‑NTU (httpsdrntuedusg)Nanyang Technological University Singapore

Effect of a non‑newtonian load on signature S2 forquartz crystal microbalance measurements

Choi Jae‑Hyeok Kanazawa Kay K Cho Nam‑Joon

2014

Choi J H Kanazawa K K amp Cho N J (2014) Effect of a non‑newtonian load on signatureS2 for quartz crystal microbalance measurements Journal of sensors 2014 1‑8

httpshdlhandlenet10356103237

httpsdoiorg1011552014373528

copy 2014 Jae‑Hyeok Choi et al This is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution andreproduction in any medium provided the original work is properly cited

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Research ArticleEffect of a Non-Newtonian Load on Signature 119878

2for Quartz

Crystal Microbalance Measurements

Jae-Hyeok Choi12 Kay K Kanazawa3 and Nam-Joon Cho124

1 School of Materials Science and Engineering Nanyang Technological University 50 Nanyang Avenue Singapore 6397982 Centre for Biomimetic Sensor Science Nanyang Technological University 50 Nanyang Drive Singapore 6375533Department of Chemical Engineering Stanford University Stanford CA 94305 USA4 School of Chemical and Biomedical Engineering Nanyang Technological University 62 Nanyang Drive Singapore 637459

Correspondence should be addressed to Nam-Joon Cho njchontuedusg

Received 12 July 2014 Accepted 27 October 2014 Published 13 November 2014

Academic Editor Ignacio R Matias

Copyright copy 2014 Jae-Hyeok Choi et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The quartz crystal microbalance (QCM) is increasingly used for monitoring the interfacial interaction between surfaces andmacromolecules such as biomaterials polymers and metals Recent QCM applications deal with several types of liquidswith various viscous macromolecule compounds which behave differently from Newtonian liquids To properly monitor suchinteractions it is crucial to understand the influence of the non-Newtonian fluid on the QCM measurement response As aquantitative indicator of non-Newtonian behavior we used the quartz resonator signature 119878

2 of the QCMmeasurement response

which has a consistent value for Newtonian fluidsWe thenmodified De Keersquos non-Newtonian three-parameter model to apply it toour prediction of 119878

2values for non-Newtonian liquids As a model we chose polyethylene glycol (PEG400) with the titration of its

volume concentration in deionized water As the volume concentration of PEG400 increased the 1198782value decreased confirming

that the modified De Keersquos three-parameter model can predict the change in 1198782value Collectively the findings presented herein

enable the application of the quartz resonator signature 1198782 to verify QCM measurement analysis in relation to a wide range of

experimental subjects that may exhibit non-Newtonian behavior including polymers and biomaterials

1 Introduction

The quartz crystal microbalance (QCM) has been widelyemployed as a label-free acoustic sensor to monitor masschanges due to adsorption on a surface [1ndash4] QCM appli-cations have been extended to measure viscoelastic macro-molecular interactions with the surfaces of fluids includingnatural and synthetic macromolecules such as DNA [56] proteins [7 8] microorganisms [9] endothelial cells[10] polymers [11ndash13] and polyelectrolyte multilayers [14]Through these studies QCM measurements have shownthat viscoelastic fluids containing macromolecules exhibitdifferent behavior from that of Newtonian fluids

An early description of the viscoelastically coupled QCMresonator gave an example of measured changes in thefrequency and resistance of the liquid-loaded QCM [2 15]The Sandia group provided a complete description of theQCMrsquos theoretical and experimental responses [16 17] with

results for water-glycerol mixtures [16] and water and water-glycerol mixtures [17] The Kasemo group presented theeffects resulting from the electrical conductivity of the liquid[18]They demonstrated block diagrams of the instrument forstudying both the parallel and the series resonance Increas-ingly complex mechanical properties of both glassy andrubbery materials have also been studied using impedanceanalysis [19]

In addition other groups have reported numerous QCMstudies that aim to understand the viscoelastic behaviorof macromolecules as a thin film physically adsorbed orchemically conjugated on the QCM substrate [5ndash8 11ndash13 19ndash29] or as a viscous liquid remaining on the substrate [30ndash34] Recent studies have shown the potential to decouple themass adsorption-forming thin layer from the fluid viscosityand density [23 35]

To verify the QCM measurement response for increas-ingly diverse applications there has been interest in

Hindawi Publishing CorporationJournal of SensorsVolume 2014 Article ID 373528 8 pageshttpdxdoiorg1011552014373528

2 Journal of Sensors

the development of methods for initial checks of the instru-ment Recently we developed simple calculations involvingthe changes in the resonator properties when loaded bya liquid which yield fixed values when the resonator isloaded with a Newtonian liquid We refer to these simplecalculations as signatures 119878

1and 119878

2 For a given resonator

these signatures were found to have fixed values independentof the fluid density and viscosity [36] 119878

1was calculated from

the changes in resonant frequency and resistance at theresonance of the quartz microbalance as follows

1198781=

1003816100381610038161003816Δ1198911003816100381610038161003816

Δ119877 (1)

where the magnitudes of Δ119891 and Δ119877 are the changes in theresonant frequency and resistance respectively when loadedwith the fluid 119878

1can be expressed simply in terms of some

fixed properties of the quartz resonator such as the shearmodulus the electrical capacitance and the fixed geometricalvalues of the thickness and electrode area [36] As an examplethe value for one type of simple 5MHz resonator yieldeda value of 119878

1= 203 under a Newtonian liquid load This

required measurement methods to obtain the values of theresonant frequency and resistance of the resonator such asimpedance analysis [37 38] or amplitude sensitive oscillators1198782was a signature calculated from the changes in the resonant

frequency and energy dissipation (or change in 119876) of theresonator when loaded with a Newtonian fluid

1198782=

1003816100381610038161003816Δ1198911003816100381610038161003816

119873Δ119863=1198911119880

2 (2)

where the magnitudes of Δ119891 and Δ119863 are the changes in theresonant frequency and energy dissipation respectively and119873 is the harmonic number In the case of 119878

2 the value for

such a loading turns out to be simply one-half of the unloadedfundamental resonator frequency For the quartz resonator119873 can take on odd values The use of measurement devicessuch as the commercial Q-Sense device made these deter-minations very convenient and it was possible to identifythe change at several harmonic frequencies Hence due tothe convenience of measuring 119878

2 we concentrate on studies

related to 1198782in this study Using the same simple 5MHz type

resonators used for the 1198781tests the value of 119878

2was then

25MHz [36]1198781and 1198782 calculated from the measured values served as

effective indicators of the proper instrument behavior whenthe resonator was loaded with a Newtonian fluid The valuesof 1198781and 119878

2were found to be very close to the measured

values when using a Newtonian fluid such as ethanol orwater However when a liquid-polymer mixture fluid wasused deviations from those values appeared The deviationsfrom the constant value became larger as the mass fraction ofthe polymer mixture increased These deviations might arisefrom the non-Newtonian character of the mixtures at largevolume concentrations of polymer

To evaluate and analyze the value of 1198782in QCM mea-

surements involving macromolecules we used polyethyleneglycol (PEG) as a model system because the molecular

weight can be varied and it has high solubility [37ndash39]For PEG monomers in the molecular weight range between200 and 20000Da PEG monomers with an average molec-ular weight of 400Da (PEG400) were selected for ourexperiments because it shows both Newtonian behavior atlower concentrations and non-Newtonian behavior at higherconcentrations [13 24 28] Once the experimental 119878

2values

were collected we investigated whether the 1198782values from

the theoretical viscoelastic non-Newtonian model modifiedfromDe Keersquos three-parameter model [40] could be fit to theexperimental values of 119878

2to verify whether the application of

1198782can be extended to the initial system check-up indicator

for non-Newtonian fluids

2 Materials and Methods

21 Materials Polyethylene glycol (PEG) was purchasedfrom Sigma-Aldrich Co LLC (product number 202398) Asthe average molecular weight (119872

119899) of the PEG is 400Da it is

referred to as PEG400 in this study The density of PEG400is 1128 gmL and its melting point is 4ndash8∘C PEG400 wasdiluted with 10mM Tris buffer with 100mM NaCl pH 74in MilliQ-deionized water with high resistivity (MilliPoreOregon USA) The PEG400 was diluted according to thevolume concentration () from 1 to 100 To homogenizePEG400 with buffer the mixture was vortexed for severalminutes Immediately before experiment the solution wasvortexed again to ensure the PEG400 solution was fullyhomogenized All bubbles were excluded before solutioninjection for measurements

22 QCM Substrate Silicon oxide-coated quartz crystal sub-strates (QSX303) for QCM measurements were obtainedfrom Q-Sense (Gothenburg Sweden) The cleaning proce-dure for the silicon oxide substrates was as follows First thesilicon oxide substrates were cleaned with 1 SDS and rinsedwith ethanol Second they were rinsed with deionized waterand then with ethanol Next they were dried with nitrogenair Finally the substrates were exposed to oxygen plasmatreatment at maximum power (Harrick Plasma Ithaca NYUSA) for 1 minute immediately before experiment

23 Quartz Crystal Microbalance (QCM) The Q-Sense E4instrument from Q-Sense (Gothenburg Sweden) was usedfor measurements This instrument measures the change inthe resonance frequency Δ119891 and the energy dissipation Δ119863when the volume concentration () of PEG400 in 10mMTrisbuffer with 100mM NaCl pH 74 in MilliQ water increasedfrom 1 to 70 From 1 to 10 the volume concentration() of PEG400 increased by 1 every 15 minutes From 10to 70 it increased by 10 in every 20sim25 minutes [41] Atthe fundamental frequency 5MHz an AT-cut piezoelectriccrystal was excited at the 3rd 5th 7th 9th and 11th overtones(15 25 35 45 and 55MHz in order) and Δ119891 and Δ119863were measured After the initial measurement in air 10mMTris buffer with 100mM NaCL and pH 74 was injected forthe initial stabilization of the QCM signals As the volumeconcentration () of PEG400 increased the 119891 and 119863 in

Journal of Sensors 3

the higher overtones became unstable Therefore only thestable data are shown in the QCM results However 119891 and119863 at the 3rd 5th and 7th overtones were stable until the endof the experiment with 70 PEG400

24 Rheometry APhysicaMCR501 stress-controlled rheom-eter (Anton Paar GmbH Graz Austria) was used at a fixedtemperature of 24∘C in order to measure the viscosity ofPEG400 solutions in the volume concentration range of 1 to100 as a unit of cP At the same volume concentration () ofPEG400 solutions the viscosities were measured at the shearrate 1 Sminus1 The viscosities were measured at least three timesfor each volume concentration of PEG400

3 Results and Discussion

31 Modification of Viscoelastic Non-Newtonian Model Auseful description for a Maxwellian fluid was provided in[42] Here we modify the corresponding analytical descrip-tion by taking into account the De Kee expression AMaxwellian fluid exhibits Newtonian behavior at very lowfrequencies but exhibits energy storage or elastic behavior athigh frequencies and can therefore be represented as follows

120578119871=120578DC

(1 + 119895120596120591)120573 (3)

120578119871is a complex quantity that represents the complex viscosity

of the Maxwellian fluid and 120591 is the relaxation time for theliquid-elastic mixture At frequencies where 120596120591 is negligiblysmall the complex viscosity reduces to the constant valueof 120578DC which is the DC value of the fluid viscosity In thislow frequency regime the behavior reduces to that for aNewtonian liquid The quantity 120573 is a parameter that allowsfor a distribution of relaxation times When 120573 = 1 theexpression for 120578

119871reduces to that of a simple Maxwellian liq-

uid with a single relaxation time This analytical descriptionof a Maxwellian fluid suggested that we could analyze thebehavior of a Maxwellian fluid in the quartz resonator Basedon theDeKee expression (3) includes the parameter120573 whichis more complex than the expression for a Maxwellian liquidgiven for example by equation (14) in [40]We now considerthe effects of these parameters on the rheological propertiesof the liquid

119866119891=

119894120596120578119891

1 + 119894120596120591 (4)

Here 119866119891is the complex shear modulus 120596 is the angular

frequency 120578119891is the low frequency constant viscosity and 119905

is the relaxation time Comparing it to (3) it can be seen that(4) is represented in terms of the shear modulus rather thanthe viscosity but otherwise shows the same dependence onthe low frequency viscosity and the relaxation time There isalso the absence of a 120573 term which indicates that a simpleMaxwellian fluid is characterized by a single relaxation time120591 This is shown here only to demonstrate that the De Keeexpression reduces to that for the simple Maxwellian liquidwhen 120573 = 1

Quartz parameters

Fluid

Admittance (Y)

Freq resis

Equiv circuit

Zero matrix (Matz)

Signature S2

parameters

Figure 1 Block representation of the various subroutines used inthe detailed calculations

It is not our intention to show thatwhenfluidmixtures areused the deviations from 119878

2result from the fact that the fluid

is Maxwellian It is very unlikely that a given non-Newtonianfluid is purely Maxwellian Nor do we intend to providea detailed description of the non-Newtonian nature of thefluid mixture The purpose of this study is to demonstratethat the experimental variations in 119878

2exhibit the types of

behavior that would be consistent with the fluid exhibitingboth liquid and elastic properties similar to that which asimple Maxwellian fluid might exhibit and that 119878

2can more

broadly serve as an effective measure of the proper operationof the experimental instrument

32 Block Diagram of Calculations Rather than attemptingto find an analytical solution for the 119878

2signature with the use

of a Maxwellian liquid we decided to use a computationalapproach For all viscoelastic materials there exists a decaylength for the shear wave A fundamental assumption in thecomputational approach is that the thickness of the liquidapplied to the QCM is much greater than this frequency-dependent decay length of the shear wave in the liquid Weassume that the decay length in the fluid is small enough thatthe approximation of infinite thickness can be taken for theliquid A diagram of the basis of the theoretical calculationsis shown in Figure 1

The various parameters describing the quartz and theliquid are first input into the program The first subroutineis for calculating the electrical admittance of the QCMresonator at any arbitrary frequency Amodified Butterworthvan Dyke equivalent circuit is used to model the crystal[43] A simplified representation of this circuit is shownin Figure 2 The equivalent circuit consists of the elementsrepresenting the unloaded quartz resonator and the elementsrepresenting the viscoelastic fluid The unloaded resonatorconsists of three elements 119871 119862

119904 and 119877 119871 and 119862

119904yield

the resonant frequency of the unloaded QCM through therelation 120596

119880119871119862119878= 1 119877 represents the losses inherent in


Quartz

Liquid

L

R

Cp Cs

L liq

Rliq

Figure 2 Simplified Butterworth van Dyke equivalent circuit usedto represent the QCM circuit loaded with a viscoelastic liquid

the resonator even when unloaded The energy dissipationof the unloaded resonator can be expressed in terms of 119877through the relation119863 = 119877(120596

119880119871)

The first calculation is to determine the values of theresonant frequency the resistance and the dissipation forthe unloaded resonator This step is necessary because thecalculations involve the changes in the measured values ofthe resonant frequency and dissipation with the changesdefined as the difference between the measured values whenunder load and unloaded respectively The unloaded valuesare obtained by setting the appropriate value of the quartzthickness 119889119876 and the effective electrical contact area in thevalues for the quartz parameters and to set as a value ofzero density for the liquid film parameters The admittanceis calculated and the resonant frequencies and resistanceat the various harmonics are calculated in the ldquoFreq Resisrdquoblock The equivalent circuit parameters are then calculatedto yield the values of the resonant frequency resistance anddissipation of the zero matrix Matz Zero matrix is shownin dash-dot outline in Figure 1 to indicate that it is the initialcalculation As stated earlier the value of 119878

2for loading under

a Newtonian fluid was found to be half of the unloadedresonant frequency As the values of the physical parametersof the quartz resonator are fixed only the thickness can bevaried to change the resonant frequency of the QCM Thethickness of the quartz resonator was chosen so that at thelow frequency limit of 119878

2(the Newtonian limit) the value of

1198782was in basic agreement with the measured valueTo calculate the resonant frequencies resistance and dis-

sipation when theQCM is loaded with a fluid the parametersof the fluid are entered in the block ldquoFluid Paramsrdquo Theseparameters include the density and complex viscosity of thefluid mixture Once the relevant resonant frequencies andresistance andor dissipation are obtained the calculations

Table 1 1198782values calculated from the experiment for polyethylene

glycol (PEG400) with the titration from 0 to 70 volume concen-tration

Volume (PEG400)

3rdovertone

5thovertone

7thovertone

9thovertone

0 2397 2351 2394 24155 2420 2415 2380 245010 2445 2389 2436 245320 2443 2390 2396 242130 2419 2378 2365 238340 2402 2320 2327 230350 2382 2291 2267 223660 2352 2195 2200 213870 2296 2184 2137 2011

for the signature can proceed Instead of characterizing therelaxation time by the variable 120591 a characteristic transitionangular frequency 120596

119879is defined by 120596

119879120591 = 1 By changing

the frequency from the angular frequency 120596 to the truefrequency 119891 (3) can be written as

120578119871=120578DC

(1 + 119895(119891119891119905))120573 (5)

The variable 119891119879in (5) is a transitional frequency characteriz-

ing the non-Newtonian nature of the fluid It is convenient touse this variable as a parameter because it relates directly tothe test frequency 119891

33 QCMMeasurements TheQCMmeasurements were firstrecorded in air and then in Tris buffer solution only asshown in Figures 3(a) and 3(b) The QCM measurementscontinuouslymonitored the changes in frequency and energydissipation Figure 3 shows the rapidly increasing changesin frequency and energy dissipation when higher volumeconcentrations () of PEG400 were injected After rapidlyincreasing both the frequency and dissipation signals sta-bilize and become constant The volume concentration ofPEG400 increased by 1 every 15 minutes from 0 upto 10 From 10 to 70 the concentration increasedby 10 every 20ndash25 minutes Once the concentration ofPEG400 reached 10 more time was allowed to stabilizethe changes in frequency and dissipation The change infrequency negatively increased but that of energy dissipationpositively increased The trends were similar but in theopposite direction Based on the shifts in frequency andenergy dissipation corresponding volume concentration ofPEG400 in the solution the 119878

2value at each overtone number

was determined in accordance with (2)It was clearly observed that the values of 119878

2changed

according to the changes in the volume concentration andresonant frequency as follows The first observation is thatthe value of 119878

2decreased at the same resonant frequency as

the volume concentration of PEG400 increased as shown inTable 1 The second observation is that as the volume con-centration of PEG400 increased the value of 119878

2decreased as

the resonant frequency (or the order of overtones) increased


0 50 100 150 200 250 300

7060504030201032

Time (min)

0 1 4 5 6 7 98

N = 3

N = 5

N = 7

N = 9

N = 11

N = overtone

minus2000

minus1800

minus1600

minus1400

minus1200

minus1000

minus800

minus600

minus400

minus200

0

Δfnn

(Hz)

n=

over

tone

s

(a)

0

100

200

300

400

500

600

700

800

900

706010 50403020320 1 4 5 6 7 98

0 50 100 150 200 250 300Time (min)

N = 3

N = 5

N = 7

N = 9

N = 11

N = overtone

Δen

ergy

diss

ipat

ion

(10minus6)

(b)

Figure 3 Changes in (a) frequency and (b) energy dissipation over time obtained from the QCM-D experiment PEG400 was injected inincrements from 1 to 70 volume concentrationThe injected volume concentration of PEG400 in each time period is marked on the graph

at the same volume concentration of PEG400 as shown inTable 1 The trend of the first observation for 119878

2is similar to

that reported byWang et al [28] using solutions of PEG withthe same molecular weight but they did not specify whichresonant frequency or overtone their observation applied toand only one value per concentration of PEG400 was shownTherefore our second observation is a unique result Thevalues of 119878

2at overtone 119899 = 3 (15MHz) for 50sim70PEG400

are offset from the main trend in the values of 1198782at the same

concentration for the full range of concentrations The sametrends are also observed at other overtones

34 Application of the Modified Non-Newtonian Model Wenext compared the experimentally obtained 119878

2values with

theoretically calculated 1198782values that were computed based

on the block diagram in Figure 1 (see [43] for specifics ofthe algorithm) De Keersquos model has three parameters 119891

119879

120573 and 120578DC and was taken into account in the calculationsSpecifically the simplest De Keersquos model was used where120573 = 1 (the Maxwellian fluid model) It describes a fluidwith a single transition frequency as described above inthe theoretical results The fluid data used for the modelingis shown in Table 2 The first and second columns presentthe volume concentration and density of PEG400-watermixtures respectively The density values (in kgsdotmminus3) wereinterpolated from data taken from general references Thethird column is the viscosity of the fluid mixture in Pasdotsmeasured by rheometry The final column presents the onlyvariable 119891

119879 that was chosen freely as an input in order to

obtain a good fit with the experimental dataIn this last column the 0 value had a very high value

of 119891119879in order to emulate a Newtonian fluid over the range

of frequencies The values for 5 and 10 were also veryhigh and resulted in the fluids still having a frequency

Table 2 Variables used for the theoretical calculations

Volume (PEG400)

Density(kgsdotmminus3)

DC viscosity120578DC (Pasdots)

Transition frequency119891119879(MHz)

0 99970 0000640 1E125 108653 0000727 5E1010 110887 0000995 5E1020 111751 0001315 600030 112029 0002032 300040 112109 0003137 80050 112145 0004813 50060 112160 0007697 33070 112170 0011300 250

independent of 1198782 similar to that of a Newtonian liquid The

remaining values of 119891119879were taken to yield theoretical values

that approximate the measured values of 1198782 The variations

of density and DC viscosity are shown in Figure 4 Whilethe change in the density is only small to moderate the DCviscosity is seen to change strongly with the fluid volumeconcentration In any case these variations were taken intoaccount in the theoretical modeling for 119878

2 The experimental

results are compared to the theoretical calculations for 1198782in

Figure 5The experimental values for 119878

2are not constant but

change with the resonant frequency as described abovefor mixed fluids The theoretical plots show the variationof 1198782with resonant frequency for a fluid that has the

characteristics described by the simple De Kee relationWhile the symbols do not lie directly on the theoreticalcurves it is clear that if a simple model with a singletransition frequency is used for each fluid mixture the major


0 10 20 30 40 50 60 70 80980

1000

1020

1040

1060

1080

1100

1120

1140

Volume fraction of PEG ()

Flui

d de

nsity

(kgmiddot

mminus3)

(a)

0 10 20 30 40 50 60 70 800000

0001

0002

0003

0004

0005

0006

0007

0008


DC

visc

osity

(Pamiddot

s)

(b)

Figure 4 Variations in (a) fluid density and (b) DC viscosity as a function of the PEG400 volume concentration

15 20 25 30 35 40 45

20

21

22

23

24

25

Sign

atur

e 2 (M

Hz)

Resonant frequency (Hz)

Exp 0Exp 5Exp 10Exp 20Exp 30Exp 40Exp 50Exp 60Exp 70

0510203040506070

Figure 5 Comparison between theoretical calculations and experi-mental values of 119878

2The lines show the theoretical calculations of 119878

2

while the symbols represent the experimental values of 1198782

behavior of the experimental points is reproduced includingthe decrease in the values of 119878

2with increasing frequency

and the values at the lowest resonant frequency studied(the third harmonic) These decreases take place both as afunction of the resonant frequency and as a function of theincreasing volume concentration of PEG400 We believe thatsuch behavior indicates the correctness of the assumptionnot only that the non-Newtonian nature of the fluid is the

0 10 20 30 40 50 60 70 80100

1000

10000

100000


log f

T(M

Hz)

Figure 6 Values of 119891119879used in the theoretical calculations for each

PEG400 volume concentration The values taken for 119891119879vary rather

smoothly over the range of concentrations

origin of the variation in 1198782 but also that the instrument

used for the QCM measurements was operating properlyAt the higher concentrations of PEG400 the fluid had adecreasing transition frequency as presented in Figure 6Modeled as a Maxwellian (single transition frequency) fluidthe mixture becomes more viscous as the concentration ofPEG400 increases as anticipated

4 Conclusions

The calculations obtained from a model that included themixture of a complex Maxwellian fluid with the solventagreed reasonably well with several types of behavior of theobserved variations in 119878

2 Specifically the low frequency

and mass density mixture showed a limiting value towardthe constant representing a Newtonian fluid at the lowestfrequencies With increasing frequency the decrease in thevalue of 119878

2was reasonably represented by the calculations


although it should be emphasized that it is the generalbehavior that is reproduced not the detailed behavior Thecalculated values of 119878

2decreased both with increases in

the resonant frequency and with increases in the contentof the Maxwellian fluid or viscosity The amount of theexperimental changes was in reasonable agreement with thecalculated values We believe that this study provides fairlystrong evidence that one major source of the deviations of 119878

2

from the constant value expected for Newtonian fluids is theaddition of an elastic component to the fluid viscoelasticity Inaddition if PEG400 is used as a measurement standard themeasured values of 119878

2can be used as a check on the proper

operation of the instrument over the frequency range used

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge support from the NationalResearch Foundation (NRF-NRFF2011-01) the NationalMedical Research Council (NMRCCBRG00052012) andNanyang Technological University to Nam-Joon Cho

References

[1] M Cassiede J-L Daridon J H Paillol and J Pauly ldquoChar-acterization of the behaviour of a quartz crystal resonatorfully immersed in a Newtonian liquid by impedance analysisrdquoSensors and Actuators A Physical vol 167 no 2 pp 317ndash3262011

[2] K Keiji Kanazawa and J G Gordon II ldquoThe oscillation fre-quency of a quartz resonator in contact with liquidrdquo AnalyticaChimica Acta vol 175 no C pp 99ndash105 1985

[3] T Nomura and M Okuhara ldquoFrequency shifts of piezoelectricquartz crystals immersed in organic liquidsrdquoAnalytica ChimicaActa vol 142 pp 281ndash284 1982

[4] M Yang MThompson andW C Duncan-Hewitt ldquoInterfacialproperties and the response of the thickness-shear-mode acous-tic wave sensor in liquidsrdquo Langmuir vol 9 no 3 pp 802ndash8111993

[5] A Tsortos G Papadakis and E Gizeli ldquoShear acoustic wavebiosensor for detecting DNA intrinsic viscosity and conforma-tion a study with QCM-Drdquo Biosensors and Bioelectronics vol24 no 4 pp 836ndash841 2008

[6] K M M Aung X Ho and X Su ldquoDNA assembly onstreptavidin modified surface a study using quartz crystalmicrobalance with dissipation or resistance measurementsrdquoSensors and Actuators B Chemical vol 131 no 2 pp 371ndash3782008

[7] A Doliska V Ribitsch K S Kleinschek and S Strnad ldquoVis-coelastic properties of fibrinogen adsorbed onto poly(ethyleneterephthalate) surfaces by QCM-Drdquo Carbohydrate Polymersvol 93 no 1 pp 246ndash255 2013

[8] FHook B Kasemo TNylander C Fant K Sott andH ElwingldquoVariations in coupled water viscoelastic properties and film

thickness of aMefp-1 protein film during adsorption and cross-linking a quartz crystal microbalance with dissipation mon-itoring ellipsometry and surface plasmon resonance studyrdquoAnalytical Chemistry vol 73 no 24 pp 5796ndash5804 2001

[9] X-L Su and Y Li ldquoA QCM immunosensor for Salmonelladetection with simultaneous measurements of resonant fre-quency and motional resistancerdquo Biosensors and Bioelectronicsvol 21 no 6 pp 840ndash848 2005

[10] K A Marx T Zhou A Montrone D McIntosh and S JBraunhut ldquoQuartz crystal microbalance biosensor study ofendothelial cells and their extracellular matrix following cellremoval evidence for transient cellular stress and viscoelasticchanges during detachment and the elastic behavior of the purematrixrdquoAnalytical Biochemistry vol 343 no 1 pp 23ndash34 2005

[11] M I Ivanchenko H Kobayashi E A Kulik andN B DobrovaldquoStudies on polymer solutions gels and grafted layers usingthe quartz crystal microbalance techniquerdquo Analytica ChimicaActa vol 314 no 1-2 pp 23ndash31 1995

[12] J C Munro and CW Frank ldquoPolyacrylamide adsorption fromaqueous solutions on gold and silver surfaces monitored by thequartz crystal microbalancerdquoMacromolecules vol 37 no 3 pp925ndash938 2004

[13] M Yoshimoto Y Yuda H Aizawa H Sato and S KurosawaldquoDynamic properties of the polyethylene glycol molecules onthe oscillating solid-liquid interfacerdquo Analytica Chimica Actavol 731 pp 82ndash87 2012

[14] S M Notley M Eriksson and L Wagberg ldquoVisco-elasticand adhesive properties of adsorbed polyelectrolyte multilayersdetermined in situ with QCM-D and AFM measurementsrdquoJournal of Colloid and Interface Science vol 292 no 1 pp 29ndash372005

[15] C E Reed K K Kanazawa and J H Kaufman ldquoPhysicaldescription of a viscoelastically loaded AT-cut quartz res-onatorrdquo Journal of Applied Physics vol 68 no 5 pp 1993ndash20011990

[16] S J Martin V E Granstaff and G C Frye ldquoCharacterizationof a quartz crystal microbalance with simultaneous mass andliquid loadingrdquo Analytical Chemistry vol 63 no 20 pp 2272ndash2281 1991

[17] H L Bandey ldquoModeling the responses of thickness-shearmode resonators under various loading conditionsrdquo AnalyticalChemistry vol 71 no 11 pp 2205ndash2214 1999

[18] MRodahl FHook andBKasemo ldquoQCMoperation in liquidsAn explanation of measured variations in frequency and Qfactor with liquid conductivityrdquo Analytical Chemistry vol 68no 13 pp 2219ndash2227 1996

[19] R Lucklum G Behling R W Cernosek and S J MartinldquoDetermination of complex shearmodulus with thickness shearmode resonatorsrdquo Journal of Physics D Applied Physics vol 30no 3 pp 346ndash356 1997

[20] D Johannsmann K Mathauer G Wegner and W KnollldquoViscoelastic properties of thin films probed with a quartz-crystal resonatorrdquo Physical Review B vol 46 no 12 pp 7808ndash7815 1992

[21] D Johannsmann J Gruner J Wesser K Mathauer G WegnerandWKnoll ldquoVisco-elastic properties of thin films probedwitha quartz crystal resonatorrdquoThin Solid Films vol 210-211 part 2pp 662ndash665 1992

[22] MAndersson J AnderssonA SellbornM Berglin BNilssonand H Elwing ldquoQuartz crystal microbalance-with dissipationmonitoring (QCM-D) for real time measurements of blood


coagulation density and immune complement activation onartificial surfacesrdquo Biosensors amp Bioelectronics vol 21 no 1 pp79ndash86 2005

[23] Z Parlak C Biet and S Zauscher ldquoDecoupling mass adsorp-tion from fluid viscosity and density in quartz crystal microbal-ance measurements using normalized conductance modelingrdquoMeasurement Science and Technology vol 24 no 8 Article ID085301 2013

[24] S Qin X Tang L Zhu Y Wei X Du and D-M ZhuldquoViscoelastic signature of physisorbed macromolecules at thesolid-liquid interfacerdquo Journal of Colloid and Interface Sciencevol 383 no 1 pp 208ndash214 2012

[25] ADomackO Prucker J Ruhe andD Johannsmann ldquoSwellingof a polymer brush probed with a quartz crystal resonatorrdquoPhysical Review EmdashStatistical Physics Plasmas Fluids andRelated Interdisciplinary Topics vol 56 no 1 pp 680ndash689 1997

[26] B Wu K Wu P Wang and D-M Zhu ldquoAdsorption kineticsand adsorption isotherm of poly(N-isopropylacrylamide) ongold surfaces studied using QCM-Drdquo Journal of Physical Chem-istry C vol 111 no 3 pp 1131ndash1135 2007

[27] D-M Zhu J Fang B Wu and X Du ldquoViscoelastic responseand profile of adsorbed molecules probed by quartz crystalmicrobalancerdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 77 no 3 Article ID 031605 2008

[28] P Wang J Fang S Qin Y Kang and D M Zhu ldquoMolecularweight dependence of viscosity and shear modulus of polyethy-lene glycol (PEG) solution boundary layersrdquo Journal of PhysicalChemistry C vol 113 no 31 pp 13793ndash13800 2009

[29] S J Geelhood C W Frank and K Kanazawa ldquoTransientquartz crystal microbalance behaviors comparedrdquo Journal of theElectrochemical Society vol 149 no 1 pp H33ndashH38 2002

[30] H Muramatsu E Tamiya and I Karube ldquoComputation ofequivalent circuit parameters of quartz crystals in contact withliquids and study of liquid propertiesrdquo Analytical Chemistryvol 60 no 19 pp 2142ndash2146 1988

[31] A Saluja and D S Kalonia ldquoMeasurement of fluid viscosityat microliter volumes using quartz impedance analysisrdquo AAPSPharmSciTech vol 5 no 3 article e47 2004

[32] A L Kipling and M Thompson ldquoNetwork analysis methodapplied to liquid-phase acoustic wave sensorsrdquo AnalyticalChemistry vol 62 no 14 pp 1514ndash1519 1990

[33] DWang PMousavi P J HauserWOxenham andC S GrantldquoQuartz crystal microbalance in elevated temperature viscousliquids temperature effect compensation and lubricant degra-dation monitoringrdquo Colloids and Surfaces A Physicochemicaland Engineering Aspects vol 268 no 1ndash3 pp 30ndash39 2005

[34] S J Martin G C Frye and K O Wessendorf ldquoSensing liquidproperties with thickness-shear mode resonatorsrdquo Sensors andActuators A Physical vol 44 no 3 pp 209ndash218 1994

[35] A Itoh and M Ichihashi ldquoA frequency of the quartz crystalmicrobalance (QCM) that is not affected by the viscosity ofa liquidrdquo Measurement Science and Technology vol 19 no 7Article ID 075205 2008

[36] N-J Cho J NDrsquoAmour J StalgrenWKnoll K Kanazawa andC W Frank ldquoQuartz resonator signatures under Newtonianliquid loading for initial instrument checkrdquo Journal of Colloidand Interface Science vol 315 no 1 pp 248ndash254 2007

[37] I Teraoka Polymer Solutions John Wiley amp Sons New YorkNY USA 2002

[38] P A Albertson Partition of Cell Particles and MacromoleculesJohn Wiley amp Sons New York NY USA 1986

[39] R Webster V Elliott B K Park D Walker M Hankinand P Taupin ldquoPEG and PEG conjugates toxicity towardsan understanding of the toxicity of PEG and its relevanceto PEGylated biologicalsrdquo in PEGylated Protein Drugs BasicScience and Clinical Application F M Veronese Ed pp 127ndash146 Birkhauser Basel Switzerland 2009

[40] D De Kee J Stastna and M B Powley ldquoInvestigation of anew complex viscosity modelrdquo Journal of Non-Newtonian FluidMechanics vol 26 no 2 pp 149ndash160 1987

[41] F Hook M Rodahl P Brzezinski and B Kasemo ldquoEnergydissipation kinetics for protein and antibody-antigen adsorp-tion under shear oscillation on a quartz crystal microbalancerdquoLangmuir vol 14 no 4 pp 729ndash734 1998

[42] G McHale R Lucklum M I Newton and J A CowenldquoInfluence of viscoelasticity and interfacial slip on acoustic wavesensorsrdquo Journal of Applied Physics vol 88 no 12 pp 7304ndash7312 2000

[43] K K Kanazawa ldquoSteady state and transient QCM solutionsat the metalmdashsolution interfacerdquo Journal of ElectroanalyticalChemistry vol 524 pp 103ndash109 2002

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014


Shock and Vibration


Mechanical Engineering

Advances in


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of


Distributed Sensor Networks


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Active and Passive Electronic Components


Chemical EngineeringInternational Journal of

Control Scienceand Engineering

Journal of


Antennas andPropagation




Navigation and Observation


Advances inOptoElectronics


Volume 2014

RoboticsJournal of


Research ArticleEffect of a Non-Newtonian Load on Signature 119878

2for Quartz

Crystal Microbalance Measurements

Jae-Hyeok Choi12 Kay K Kanazawa3 and Nam-Joon Cho124

1 School of Materials Science and Engineering Nanyang Technological University 50 Nanyang Avenue Singapore 6397982 Centre for Biomimetic Sensor Science Nanyang Technological University 50 Nanyang Drive Singapore 6375533Department of Chemical Engineering Stanford University Stanford CA 94305 USA4 School of Chemical and Biomedical Engineering Nanyang Technological University 62 Nanyang Drive Singapore 637459

Correspondence should be addressed to Nam-Joon Cho njchontuedusg

Received 12 July 2014 Accepted 27 October 2014 Published 13 November 2014

Academic Editor Ignacio R Matias

Copyright copy 2014 Jae-Hyeok Choi et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The quartz crystal microbalance (QCM) is increasingly used for monitoring the interfacial interaction between surfaces andmacromolecules such as biomaterials polymers and metals Recent QCM applications deal with several types of liquidswith various viscous macromolecule compounds which behave differently from Newtonian liquids To properly monitor suchinteractions it is crucial to understand the influence of the non-Newtonian fluid on the QCM measurement response As aquantitative indicator of non-Newtonian behavior we used the quartz resonator signature 119878

2 of the QCMmeasurement response

which has a consistent value for Newtonian fluidsWe thenmodified De Keersquos non-Newtonian three-parameter model to apply it toour prediction of 119878

2values for non-Newtonian liquids As a model we chose polyethylene glycol (PEG400) with the titration of its

volume concentration in deionized water As the volume concentration of PEG400 increased the 1198782value decreased confirming

that the modified De Keersquos three-parameter model can predict the change in 1198782value Collectively the findings presented herein

enable the application of the quartz resonator signature 1198782 to verify QCM measurement analysis in relation to a wide range of

experimental subjects that may exhibit non-Newtonian behavior including polymers and biomaterials

1 Introduction

The quartz crystal microbalance (QCM) has been widelyemployed as a label-free acoustic sensor to monitor masschanges due to adsorption on a surface [1ndash4] QCM appli-cations have been extended to measure viscoelastic macro-molecular interactions with the surfaces of fluids includingnatural and synthetic macromolecules such as DNA [56] proteins [7 8] microorganisms [9] endothelial cells[10] polymers [11ndash13] and polyelectrolyte multilayers [14]Through these studies QCM measurements have shownthat viscoelastic fluids containing macromolecules exhibitdifferent behavior from that of Newtonian fluids

An early description of the viscoelastically coupled QCMresonator gave an example of measured changes in thefrequency and resistance of the liquid-loaded QCM [2 15]The Sandia group provided a complete description of theQCMrsquos theoretical and experimental responses [16 17] with

results for water-glycerol mixtures [16] and water and water-glycerol mixtures [17] The Kasemo group presented theeffects resulting from the electrical conductivity of the liquid[18]They demonstrated block diagrams of the instrument forstudying both the parallel and the series resonance Increas-ingly complex mechanical properties of both glassy andrubbery materials have also been studied using impedanceanalysis [19]

In addition other groups have reported numerous QCMstudies that aim to understand the viscoelastic behaviorof macromolecules as a thin film physically adsorbed orchemically conjugated on the QCM substrate [5ndash8 11ndash13 19ndash29] or as a viscous liquid remaining on the substrate [30ndash34] Recent studies have shown the potential to decouple themass adsorption-forming thin layer from the fluid viscosityand density [23 35]

To verify the QCM measurement response for increas-ingly diverse applications there has been interest in

Hindawi Publishing CorporationJournal of SensorsVolume 2014 Article ID 373528 8 pageshttpdxdoiorg1011552014373528



1and 119878





1198781=

1003816100381610038161003816Δ1198911003816100381610038161003816

Δ119877 (1)







1198782=

1003816100381610038161003816Δ1198911003816100381610038161003816

119873Δ119863=1198911119880

2 (2)


2 the value for





2was then








2values

















120578119871=120578DC

(1 + 119895120596120591)120573 (3)





119866119891=

119894120596120578119891

1 + 119894120596120591 (4)




Quartz parameters

Fluid

Admittance (Y)

Freq resis

Equiv circuit

Zero matrix (Matz)

Signature S2

parameters







2can more






119904 and 119877 119871 and 119862

119904yield




Quartz

Liquid

L

R

Cp Cs

L liq

Rliq



119880119871)


2for loading under







Volume (PEG400)

3rdovertone

5thovertone

7thovertone

9thovertone

0 2397 2351 2394 24155 2420 2415 2380 245010 2445 2389 2436 245320 2443 2390 2396 242130 2419 2378 2365 238340 2402 2320 2327 230350 2382 2291 2267 223660 2352 2195 2200 213870 2296 2184 2137 2011



119879120591 = 1 By changing


120578119871=120578DC

(1 + 119895(119891119891119905))120573 (5)






2changed




2decreased as



0 50 100 150 200 250 300

7060504030201032

Time (min)

0 1 4 5 6 7 98

N = 3

N = 5

N = 7

N = 9

N = 11

N = overtone

minus2000

minus1800

minus1600

minus1400

minus1200

minus1000

minus800

minus600

minus400

minus200

0

Δfnn

(Hz)

n=

over

tone

s

(a)

0

100

200

300

400

500

600

700

800

900

706010 50403020320 1 4 5 6 7 98

0 50 100 150 200 250 300Time (min)

N = 3

N = 5

N = 7

N = 9

N = 11

N = overtone

Δen

ergy

diss

ipat

ion

(10minus6)

(b)



2is similar to






2values with



119879







Volume (PEG400)




0 99970 0000640 1E125 108653 0000727 5E1010 110887 0000995 5E1020 111751 0001315 600030 112029 0002032 300040 112109 0003137 80050 112145 0004813 50060 112160 0007697 33070 112170 0011300 250





2 The experimental







0 10 20 30 40 50 60 70 80980

1000

1020

1040

1060

1080

1100

1120

1140


Flui

d de

nsity

(kgmiddot

mminus3)

(a)

0 10 20 30 40 50 60 70 800000

0001

0002

0003

0004

0005

0006

0007

0008


DC

visc

osity

(Pamiddot

s)

(b)


15 20 25 30 35 40 45

20

21

22

23

24

25

Sign

atur

e 2 (M

Hz)



0510203040506070



2





0 10 20 30 40 50 60 70 80100

1000

10000

100000


log f

T(M

Hz)






4 Conclusions









2






Acknowledgments


References
















































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of




1and 119878





1198781=

1003816100381610038161003816Δ1198911003816100381610038161003816

Δ119877 (1)







1198782=

1003816100381610038161003816Δ1198911003816100381610038161003816

119873Δ119863=1198911119880

2 (2)


2 the value for





2was then








2values

















120578119871=120578DC

(1 + 119895120596120591)120573 (3)





119866119891=

119894120596120578119891

1 + 119894120596120591 (4)




Quartz parameters

Fluid

Admittance (Y)

Freq resis

Equiv circuit

Zero matrix (Matz)

Signature S2

parameters







2can more






119904 and 119877 119871 and 119862

119904yield




Quartz

Liquid

L

R

Cp Cs

L liq

Rliq



119880119871)


2for loading under







Volume (PEG400)

3rdovertone

5thovertone

7thovertone

9thovertone

0 2397 2351 2394 24155 2420 2415 2380 245010 2445 2389 2436 245320 2443 2390 2396 242130 2419 2378 2365 238340 2402 2320 2327 230350 2382 2291 2267 223660 2352 2195 2200 213870 2296 2184 2137 2011



119879120591 = 1 By changing


120578119871=120578DC

(1 + 119895(119891119891119905))120573 (5)






2changed




2decreased as



0 50 100 150 200 250 300

7060504030201032

Time (min)

0 1 4 5 6 7 98

N = 3

N = 5

N = 7

N = 9

N = 11

N = overtone

minus2000

minus1800

minus1600

minus1400

minus1200

minus1000

minus800

minus600

minus400

minus200

0

Δfnn

(Hz)

n=

over

tone

s

(a)

0

100

200

300

400

500

600

700

800

900

706010 50403020320 1 4 5 6 7 98

0 50 100 150 200 250 300Time (min)

N = 3

N = 5

N = 7

N = 9

N = 11

N = overtone

Δen

ergy

diss

ipat

ion

(10minus6)

(b)



2is similar to






2values with



119879







Volume (PEG400)




0 99970 0000640 1E125 108653 0000727 5E1010 110887 0000995 5E1020 111751 0001315 600030 112029 0002032 300040 112109 0003137 80050 112145 0004813 50060 112160 0007697 33070 112170 0011300 250





2 The experimental







0 10 20 30 40 50 60 70 80980

1000

1020

1040

1060

1080

1100

1120

1140


Flui

d de

nsity

(kgmiddot

mminus3)

(a)

0 10 20 30 40 50 60 70 800000

0001

0002

0003

0004

0005

0006

0007

0008


DC

visc

osity

(Pamiddot

s)

(b)


15 20 25 30 35 40 45

20

21

22

23

24

25

Sign

atur

e 2 (M

Hz)



0510203040506070



2





0 10 20 30 40 50 60 70 80100

1000

10000

100000


log f

T(M

Hz)






4 Conclusions









2






Acknowledgments


References
















































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of







120578119871=120578DC

(1 + 119895120596120591)120573 (3)





119866119891=

119894120596120578119891

1 + 119894120596120591 (4)




Quartz parameters

Fluid

Admittance (Y)

Freq resis

Equiv circuit

Zero matrix (Matz)

Signature S2

parameters







2can more






119904 and 119877 119871 and 119862

119904yield




Quartz

Liquid

L

R

Cp Cs

L liq

Rliq



119880119871)


2for loading under







Volume (PEG400)

3rdovertone

5thovertone

7thovertone

9thovertone

0 2397 2351 2394 24155 2420 2415 2380 245010 2445 2389 2436 245320 2443 2390 2396 242130 2419 2378 2365 238340 2402 2320 2327 230350 2382 2291 2267 223660 2352 2195 2200 213870 2296 2184 2137 2011



119879120591 = 1 By changing


120578119871=120578DC

(1 + 119895(119891119891119905))120573 (5)






2changed




2decreased as



0 50 100 150 200 250 300

7060504030201032

Time (min)

0 1 4 5 6 7 98

N = 3

N = 5

N = 7

N = 9

N = 11

N = overtone

minus2000

minus1800

minus1600

minus1400

minus1200

minus1000

minus800

minus600

minus400

minus200

0

Δfnn

(Hz)

n=

over

tone

s

(a)

0

100

200

300

400

500

600

700

800

900

706010 50403020320 1 4 5 6 7 98

0 50 100 150 200 250 300Time (min)

N = 3

N = 5

N = 7

N = 9

N = 11

N = overtone

Δen

ergy

diss

ipat

ion

(10minus6)

(b)



2is similar to






2values with



119879







Volume (PEG400)




0 99970 0000640 1E125 108653 0000727 5E1010 110887 0000995 5E1020 111751 0001315 600030 112029 0002032 300040 112109 0003137 80050 112145 0004813 50060 112160 0007697 33070 112170 0011300 250





2 The experimental







0 10 20 30 40 50 60 70 80980

1000

1020

1040

1060

1080

1100

1120

1140


Flui

d de

nsity

(kgmiddot

mminus3)

(a)

0 10 20 30 40 50 60 70 800000

0001

0002

0003

0004

0005

0006

0007

0008


DC

visc

osity

(Pamiddot

s)

(b)


15 20 25 30 35 40 45

20

21

22

23

24

25

Sign

atur

e 2 (M

Hz)



0510203040506070



2





0 10 20 30 40 50 60 70 80100

1000

10000

100000


log f

T(M

Hz)






4 Conclusions









2






Acknowledgments


References
















































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



Quartz

Liquid

L

R

Cp Cs

L liq

Rliq



119880119871)


2for loading under







Volume (PEG400)

3rdovertone

5thovertone

7thovertone

9thovertone

0 2397 2351 2394 24155 2420 2415 2380 245010 2445 2389 2436 245320 2443 2390 2396 242130 2419 2378 2365 238340 2402 2320 2327 230350 2382 2291 2267 223660 2352 2195 2200 213870 2296 2184 2137 2011



119879120591 = 1 By changing


120578119871=120578DC

(1 + 119895(119891119891119905))120573 (5)






2changed




2decreased as



0 50 100 150 200 250 300

7060504030201032

Time (min)

0 1 4 5 6 7 98

N = 3

N = 5

N = 7

N = 9

N = 11

N = overtone

minus2000

minus1800

minus1600

minus1400

minus1200

minus1000

minus800

minus600

minus400

minus200

0

Δfnn

(Hz)

n=

over

tone

s

(a)

0

100

200

300

400

500

600

700

800

900

706010 50403020320 1 4 5 6 7 98

0 50 100 150 200 250 300Time (min)

N = 3

N = 5

N = 7

N = 9

N = 11

N = overtone

Δen

ergy

diss

ipat

ion

(10minus6)

(b)



2is similar to






2values with



119879







Volume (PEG400)




0 99970 0000640 1E125 108653 0000727 5E1010 110887 0000995 5E1020 111751 0001315 600030 112029 0002032 300040 112109 0003137 80050 112145 0004813 50060 112160 0007697 33070 112170 0011300 250





2 The experimental







0 10 20 30 40 50 60 70 80980

1000

1020

1040

1060

1080

1100

1120

1140


Flui

d de

nsity

(kgmiddot

mminus3)

(a)

0 10 20 30 40 50 60 70 800000

0001

0002

0003

0004

0005

0006

0007

0008


DC

visc

osity

(Pamiddot

s)

(b)


15 20 25 30 35 40 45

20

21

22

23

24

25

Sign

atur

e 2 (M

Hz)



0510203040506070



2





0 10 20 30 40 50 60 70 80100

1000

10000

100000


log f

T(M

Hz)






4 Conclusions









2






Acknowledgments


References
















































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



0 50 100 150 200 250 300

7060504030201032

Time (min)

0 1 4 5 6 7 98

N = 3

N = 5

N = 7

N = 9

N = 11

N = overtone

minus2000

minus1800

minus1600

minus1400

minus1200

minus1000

minus800

minus600

minus400

minus200

0

Δfnn

(Hz)

n=

over

tone

s

(a)

0

100

200

300

400

500

600

700

800

900

706010 50403020320 1 4 5 6 7 98

0 50 100 150 200 250 300Time (min)

N = 3

N = 5

N = 7

N = 9

N = 11

N = overtone

Δen

ergy

diss

ipat

ion

(10minus6)

(b)



2is similar to






2values with



119879







Volume (PEG400)




0 99970 0000640 1E125 108653 0000727 5E1010 110887 0000995 5E1020 111751 0001315 600030 112029 0002032 300040 112109 0003137 80050 112145 0004813 50060 112160 0007697 33070 112170 0011300 250





2 The experimental







0 10 20 30 40 50 60 70 80980

1000

1020

1040

1060

1080

1100

1120

1140


Flui

d de

nsity

(kgmiddot

mminus3)

(a)

0 10 20 30 40 50 60 70 800000

0001

0002

0003

0004

0005

0006

0007

0008


DC

visc

osity

(Pamiddot

s)

(b)


15 20 25 30 35 40 45

20

21

22

23

24

25

Sign

atur

e 2 (M

Hz)



0510203040506070



2





0 10 20 30 40 50 60 70 80100

1000

10000

100000


log f

T(M

Hz)






4 Conclusions









2






Acknowledgments


References
















































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



0 10 20 30 40 50 60 70 80980

1000

1020

1040

1060

1080

1100

1120

1140


Flui

d de

nsity

(kgmiddot

mminus3)

(a)

0 10 20 30 40 50 60 70 800000

0001

0002

0003

0004

0005

0006

0007

0008


DC

visc

osity

(Pamiddot

s)

(b)


15 20 25 30 35 40 45

20

21

22

23

24

25

Sign

atur

e 2 (M

Hz)



0510203040506070



2





0 10 20 30 40 50 60 70 80100

1000

10000

100000


log f

T(M

Hz)






4 Conclusions









2






Acknowledgments


References
















































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of






2






Acknowledgments


References
















































VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of



VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of








Journal of










Volume 2014

RoboticsJournal of


Documents

Effect of a non‑newtonian load on signature S2 for quartz