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A remote query magnetostrictive viscosity sensor
Sensors and Actuators 80 Ž2000. 8–14 www.elsevier.nlrlocatersna
A remote query magnetostrictive viscosity sensor Plamen G. Stoyanov, Craig A. Grimes
)
Center for Applied Sensor Technology, Department of Electrical Engineering, 453 Anderson Hall, The UniÕersity of Kentucky, Lexington, KY 40506, USA Received 18 February 1999; received in revised form 2 August 1999; accepted 15 September 1999
Abstract Magnetically soft, magnetostrictive metallic glass ribbons are used as in-situ remote query viscosity sensors. When immersed in a liquid, changes in the resonant frequency of the ribbon-like sensors are shown to correlate with the square root of the liquid viscosity and density product. An elastic wave model is presented that describes the sensor response as a function of the frictional forces acting upon the sensor surface. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Magnetoelastic; Magnetostriction; Viscosity sensor; TSM; Remote query
1. Introduction Acoustic wave microsensors are widely used for measuring small changes in mass, temperature, viscosity, density and ionic conductivity of a medium in contact with the sensor surface; see, for example, Refs. w1,2x and the references therein. Despite the outstanding performance of these microsensors, for example, a quartz crystal oscillator can detect mass accumulation on the sensor surface corresponding to a few percent of a monolayer coverage, applications are limited by the necessity of providing electrical connections to the sensor head in order to excite an acoustic wave and to detect the response signal. This limitation rules out in-situ experiments, such as testing the environmental conditions inside sealed, opaque containers, and biological in vivo experiments such as monitoring of gastric pH or bloodstream glucose levels. One way of circumventing the constraint of needing electrical connections is to use a magnetostrictive, rather than piezoelectric, substrate wherein acoustic or elastic waves can be excited by an external AC magnetic field and the response monitored by a pick-up coil located outside the test area. An excellent candidate for a magnetostrictive sensor platform is a whole class of amorphous metallic glass ribbons called Metglasse. 1 These ribbons ) Corresponding author. Tel.: q1-606-257-1300, ext. 273; fax: q1606-257-3092; e-mail: [email protected] 1 Metglase is a trademark of Allied Signal.
of amorphous iron- and cobalt-based alloys have been shown to exhibit remarkable magnetoelastic properties, especially after a suitable heat treatment in a transverse DC magnetic field to induce a very low anisotropy w3–5x. These properties make these ribbons suitable for a variety of applications, such as position sensors w5x, anti-theft markers w6x, and strain sensors w7x. The operation of these devices is based on the excitation of a longitudinal elastic standing wave by an applied small AC magnetic field at the mechanical resonance frequency of the sensor superimposed, and parallel to, a much stronger DC magnetic field the purpose of which is to select the ‘‘operating point’’ on the sensor’s magnetization curve Žincluding a complete turn-off in the case of anti-theft markers.. This DC field can be supplied either by an external coil, or by placement of a magnetically hard piece of material adjacent to the sensor. The phase velocity of the elastic wave and, hence, its resonant frequency, is dependent on the density, Young’s modulus, and Poisson ratio of the sensor w8x, the characteristics of the medium in contact with the sensor surface, and on the details of the interfacial interaction between the ambient medium and the sensor surface. Some of the factors governing this interaction whereby the phase velocity is changed are surface roughness w9x, presence of surface stress w10x, and pressure. Additional factors are to be considered when the sensor is immersed in a liquid, including the strength of the interfacial molecular bond w11x, surface wetting w12x, liquid density, viscosity, and surface free energy w13x.
0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 9 . 0 0 2 8 8 - 5
P.G. StoyanoÕ, C.A. Grimesr Sensors and Actuators 80 (2000) 8–14
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These various factors need to be considered to obtain a reliable interpretation of the observed resonance frequency shifts. In this paper, we demonstrate the use of magnetically soft, magnetostrictive Metglas ribbons as remote query viscosity and mass sensors; a theoretical model is first presented to describe the sensor operation.
2. The model Notation d thickness of the sensor ribbon E Young’s modulus of the sensor material Fy , Fz components of the external force per unit area of the sensor surface L length of the sensor s velocity of an oscillating surface ui the ith component of the particle displacement vector Õ fluid velocity d transverse wave penetration depth in liquid h coefficient of dynamic viscosity of the liquid rs sensor material density rl density of the liquid s Poisson ratio of the sensor material f 0 , fn resonant frequency of a bare and loaded sensor, respectively v 0 , v n angular resonant frequency of a bare and loaded sensor, respectively Ž v s 2p f . The theoretical model is based on the equation of longitudinal vibratory motion of a thin elastic plate Žthe sensor. in the presence of a dissipative force, namely, the shear force acting on the basal plane of the sensor when immersed in a liquid. For a thin, homogenous elastic plate centered at the origin of a Cartesian coordinate system and oriented in the yz-plane, see Fig. 1, in the presence of external forces acting in the same plane the equations of equilibrium are w8x: Ed
E2 u z
1
1ys 2 Ez2
Ed
2 Ž 1 y s . E zE y E2 u y
1 1ys 1
q
q
E2 u y
1 q
1
2
Ey
2
2Ž 1 q s . E y 2
1 q
E2 u z
2 Ž 1 y s . E zE y
Ž 1a . E2 u y
2Ž 1 q s . E z q Fy s 0.
with yr dŽE 2 u zrEt 2 . and yr dŽE 2 u yrEt 2 ., respectively. For a plane wave propagating in the y-direction the displacement vectors are independent of z leaving:
rs rs
E2 u z Et 2 E2 u y Et 2
E s
Ž 2.
2Ž 1 q s . E y 2 E2 u y
E s
E2 u z
Ž 3.
1ys 2 E y2
Eqs. Ž2. and Ž3. show that the frequencies of the in-plane longitudinal and transversal waves are different and, hence, we can exclude the transversal wave from further consideration.
E2 u z
q Fz s 0
Fig. 1. A magnetostrictive thin film planar sensor immersed in liquid and located between two fixed plates. Vibrations in the basal plane due to incident AC magnetic field excite a transversal wave propagating away from the resonator surface.
2.1. Effect of a mass load If a mass D m, which is much less than the mass of the sensor M, is evenly deposited on the plate-like surface of the sensor, Eq. Ž3. is modified as follows:
2
Ž 1b .
The equations of motion ŽEOM., for a sensor in air, are obtained from the above equations by replacing Fz and Fy
M q D m E2 u y Ad
Et 2
E s
E2 u y
1ys 2 E y2
Ž 4.
where A is the surface area of the sensor, and d the thickness.
P.G. StoyanoÕ, C.A. Grimesr Sensors and Actuators 80 (2000) 8–14
10
The sensor will exhibit magnetostrictive vibrations at almost any frequency of the driving AC magnetic field. However, these vibrations are most pronounced at a specific frequency, corresponding to its mechanical resonance, as determined by both the sensor dimensions and material properties. We seek a standing wave solution to Eq. Ž4. in the form: np y u s 2 Beyi v n t cos Ž 5. L where v n denotes the set of the longitudinal resonant frequencies of the sensor, including higher order harmonics, and B is a complex number. Substituting Eq. Ž5. into Eq. Ž4., then taking the real part, results in an expression that describes the resonant radian frequency of the mass loaded sensor: 1 Ad E np 2 1 v n2 s s v2 Ž 6. Dm M 1ys 2 L Dm 0 1q 1q M M where v 0 denotes resonant radian frequency of the unloaded sensor. For small mass loads Eq. Ž6. reduces to: f0 D m D fsy Ž 7. 2 M where the frequency shift is downwards, D f s f n y f 0 - 0, and we are concerned with the fundamental resonant frequency due to its larger amplitude. The resonant frequency of the magnetoelastic sensor shifts linearly per mass load, just as it does for surface acoustic wave devices w1,2x.
ž /
In the presence of a viscous fluid surrounding the vibrating plate-like sensor, the resonant frequency of the sensor Žand associated harmonics. will be shifted lower due to the dissipative character of the shear forces associated with liquid viscosity. The theoretical model to describe this effect is most concise if we consider the motion of an incompressible fluid bounded by two infinite, parallel-oriented surfaces, one of which is fixed and the other oscillating in its own plane w14x. Let the oscillating surface be the yz-plane, with the vibrations occurring in the y-direction, and the fixed surface be parallel to it and shifted a distance h along the positive x-axis. The velocity of the oscillating surface can be described as s y s s s s0 eyi v t where s0 is a complex constant that can be made real by a proper choice of the time origin. The fluid velocity must satisfy the boundary conditions Õ y s s for x s 0 Ž Õ x and Õz are zero. and Õ y s 0 for x s h. Under these assumptions, the equation of motion of a viscous fluid ŽNavier–Stokes equation. reduces to a simple form:
h E2 Õ s
Et
rl Ex2
Õss
Ž 8.
sin k Ž h y x .
sin kx where k s ŽŽ1 q i .rŽ d .., i s 'y 1 , and
ds
(
2h
Ž 9.
Ž 10 .
rl v
is the depth of penetration into the fluid of the perturbation, caused by the oscillating surface, or the velocity amplitude damping constant. A transversal elastic wave is generated at the vibrating surface which propagates in the fluid, in the x-direction towards the steady plate. The frictional force Žor the shear stress. per unit area of the vibrating plate is related to the shear strain rate ŽEÕrE x . at its surface by the dynamic viscosity coefficient, h , through Newton’s law: Fy s h Ž EÕrE x . xs 0 s yRe Ž h ks cot kh .
Ž 11 .
where Re denotes the real part. The force expression for Fy is inserted into Eq. Ž3. to describe a vibrating thin elastic plate Žthe sensor. immersed in a liquid, sandwiched between two infinitely large, parallel fixed surfaces spaced equidistant from the vibrating sensor, as shown in Fig. 1: E 2 Uy Et
2.2. Effect of Õiscosity
EÕ
The periodic solution that we seek is in the form Õ s Ž A sin kx q B cos kx . eyi v t. Substituting this into Eq. Ž8. and determining constants A and B from the boundary conditions, the following expression is found for the fluid velocity as a function of distance from the vibrating plate:
2
E
E2 u
1
s
rs 1 y s
2
Ey
2
y
2h k Eu y
rs d Et
cot kh
Ž 12 .
The factor of 2 in the second term on the right-hand-side ŽRHS. reflects the presence of two fixed surfaces. To be mathematically precise, the expression for Fy must be modified to account for the drag forces acting on the edges of the vibrating plate-like sensor. However, since the plate thickness is negligibly small compared with the lateral dimensions Žillustrative sensor dimensions are f 0.01 = 30 = 5 mm. the compression waves generated by the front and back edges have little impact on the plate motion. As for the side edges, those parallel to the direction of vibration, their presence effectively amounts to increasing the planar area by, approximately, the product d L w14x, a quantity f 0.01% of the total plate area. Therefore, Eq. Ž12. is valid for thin sensors Žplates. that have relatively large surface areas. We look for a solution to Eq. Ž12. in the form of Eq. Ž5.; taking the real part the resulting dispersion relation is:
v n2 s
np
E
ž /
rs Ž 1 y s 2 . y
2
L
2hv n sinh Ž 2 hrd . y sin Ž 2 hrd .
drs d cosh Ž 2 hrd . y cos Ž 2 hrd . s Ž v0 qD v .
2
Ž 13 .
P.G. StoyanoÕ, C.A. Grimesr Sensors and Actuators 80 (2000) 8–14
where D v s v n y v 0 - 0. The first term on the RHS represents the square of the nth resonant frequency of the resonator in an inviscid fluid, e.g., air; the second term reflects the influence of the shear forces acting on both solid faces. No assumptions have been made about the viscosity levels of the tested fluid; Eq. Ž13. is equally applicable to predicting the resonator response to both highly viscous and almost inviscid fluids. These two extremes, however, deserve further consideration. 2.2.1. Case 1: Highly Õiscous fluid (2h r d < 1) Keeping only the terms linear in D vrv 0 we obtain: Dv
v0
sy
1 rl h 3 rs d
or D f s y
1 3
f0
rl h rs d
.
Ž 14 .
This formula is almost identical with the expression for the solid mass load ŽEq. Ž7.. apart from the smaller numerical constant. In this limit, the fluid density r l can be measured, but not the viscosity. This result is to be expected since the fixed plates are, in effect, so close to the resonator surfaces that they frustrate the boundary layers responsible for the viscous action. As the attenuation depth d is large compared with h, the whole liquid layer oscillates synchronously with the resonator, so that it behaves as if there were a solidified liquid layer of mass r l h per unit area loaded on the resonator face. Therefore, in the limit of highly viscous fluids the model exhibits the proper behavior for deposition of a solid onto the sensor surface. However, for solid mass loads Eq. Ž7. is appropriate, rather than Eq. Ž14., since the numerical constant in the latter originates from the oscillating factor in the second term of Eq. Ž13. which is present only in the liquid phase.
11
can be determined from the slope of the frequency shift vs. square root of viscosity plot Žsee Eq. Ž15... Furthermore, liquid density and viscosity effects on the magnetostrictive sensor can be separated following the approach described by Hermann et al. w19x. The model presented here does not account for any effects at the solidrliquid interface. It assumes an ideally smooth surface and a homogenous dynamic viscosity coefficient throughout the liquid, including at the sensor surface. However, as observed by Pechel and Adlfinger w20x, and later experimentally demonstrated by the same authors w21,22x, liquid viscosity can be significantly higher at the interface with solid surfaces. In the case of water w21,22x, at 208C, the interfacial viscosity was found to be 5.4 times greater than the bulk fluid viscosity. Nevertheless, although important when interfacial interactions are the subject of interest, these considerations do not have a crucial importance in viscosity sensing applications since the sensor response can be empirically calibrated. Yet, it is interesting to note that increased sensor surface roughness can effectively switch the operational regime from an almost inviscid Žliquid-like. one, to that of a highly viscous Žsolid-like. one, making the frequency shift directly proportional to the amount of the liquid mass trapped in the cavities of the roughened surface and, therefore, vibrating synchronously with the resonator. Schumacher et al. w9,23x treated the liquid entrapments in a roughened surface made up from semicylinders as a rigidly attached liquid layer of height Dr2, D being the height of a semicylinder. They found that under this condition the frequency shift is proportional to D m s r l Dr2, the mass per unit area of the equivalent rigid
2.2.2. Case 2: Almost inÕiscid fluid (2h r d 4 1) Keeping only the linear terms in D vrv 0 , the dispersion relation Eq. Ž13. is reduced to:
v n2 s v 02 y
2hv n
rs d d
,
From which we find: D fsy
(p f
0
2prs d
Ž hr l .
1r2
Ž 15 .
For this viscosity regime, the frequency shift is proportional to the square root of the liquid viscosity and density product. The functional dependence of D f on hr l in this limit is the same as in the liquid phase theories of TSM acoustic wave quartz sensors w11,15–18x. Measurement of viscosity in this case requires a prior knowledge of the liquid density. However, it should be noted that for many fluids the density remains essentially constant while viscosity rapidly changes w15,16x. For such liquids, a direct measurement of the viscosity is obtained. Liquid density
Fig. 2. The resonator surface roughness can be incorporated into the model through the concept of an effective rigid layer w9,22x. The modified boundary conditions for the velocity of the transversal wave propagating in the liquid are Õ y s s for x s t and Õ y s 0 for x s h Žsee text..
12
P.G. StoyanoÕ, C.A. Grimesr Sensors and Actuators 80 (2000) 8–14
layer. Using the approach of Schumacher et al., it is not difficult to modify the present theory to incorporate the resonator surface roughness. All that needs to be done is to alter the boundary conditions for the transverse wave propagating in the liquid, see Fig. 2, so that Õ y s s for x s t Ž Õ x and Õz are zero. and Õ y s 0 for x s h, and then account for the equivalent rigid layer of thickness t through the use of Eq. Ž7.. Other interfacial effects, such as selective bonding to the solid surface, may be taken into account in a similar manner.
3. Experimental results and discussion The samples used in this work were highly magnetostrictive amorphous ribbons of Metglas 2826 MB alloy, 3 7 .5 = 1 2 .5 = 0 .0 3 0 m m 3 o f c o m p o sitio n Fe 40 Ni 38 Mo 4 B18 , available from Allied Signal. The saturation magnetic induction is 0.88 Tesla Žas-cast. and the saturation magnetostriction is 1.2 = 10y5 . The samples were tested as received; no additional heat treatment was done. X-ray diffraction experiments confirmed the amorphous structure of the material. The sensors were characterized using a magnetoelastic resonance test fixture, as shown schematically in Fig. 3. Referring to Fig. 3, a sinusoidal AC voltage from the signal generator is amplified and applied to a pair of
Fig. 3. Schematic drawing of the magnetostrictive sensor test set-up.
Helmholtz coils, producing a RMS magnetic field of 55 mOe that is superimposed on a 5.5 Oe DC magnetic field. The sample is positioned lengthwise in a 350 turn 40-ga wire pick-up coil of 16 cm2 rectangular cross-section. The voltage from the pick-up coil is preamplified and fed into a dual-channel lock-in amplifier tracking the signal generator frequency, and eventually into the computer controlling the experiment. A typical frequency response spectrum of a bare Žnonloaded. sensor tested in air and in a 1% solution of polyethilenimine in water Žroom temperature. is shown in Fig. 4. Note that we are not concerned with the relative amplitude of the responses, rather the location of the resonant frequency peaks as indicated on Fig. 4. The viscosity measurements were carried out in a specially designed test trough in which the resonator was supported along its transversal centerline, thus avoiding any frustration of the fundamental vibration mode, and positioned equidistantly 2 mm from two parallel fixed plates, thus realizing the conditions shown in Fig. 1. The value of d for water Ždynamic viscosity 0.001 Nsrm2 . is 2.4 mm; for castor oil Ždynamic viscosity of 0.985 Nsrm2 . it is 80 mm. Since the fluid film thickness h in the test trough is 2 mm, it is evident that almost all fluids can be considered almost inviscid in the context of this model so that Eq. Ž15. can be used rather than Eq. Ž13.. It is important to note, however, that while the test fixture was used for precise comparison to theory, the sensors appeared to work equally well by simply placing them in a liquid container. Because of the substantial temperature dependence of the viscosity, the ambient temperature was constantly monitored throughout the experiments. The plots of the resonant frequency shift vs. the square root of the viscosity and density product for glucose dissolved in phosphate buffered saline ŽPBS. and polyŽethyleneimine. dissolved in water are shown in Fig. 5. The concentration range of the Glucose solutions ranged from 10 to 700 grl, with the upper limit being close to saturation. The polyŽethyleneimine. solutions ranged from 1% to 11% concentration; beyond that range the determination of the resonant peak position becomes unreliable due to damping of the magnetoelastic response. The sensor response to both analytes is almost identical. The slope seen in Fig. 5 is approximately twice as large as that predicted by Eq. Ž15., suggesting higher viscosities. It is our belief that the key to this discrepancy has to be sought in the difference between the fluid viscosities at the solid–liquid interface and in the bulk liquid. As noted in the theoretical discussion above, there is experimental evidence that the ratio of these two viscosities in the case of water is 5.4 w21,22x; as '5.4 f 2.3, this alone is enough to account for the observed discrepancy of our experimental results with theory. The surface topography of the sensor may also play an important role. The average surface roughness of the rougher face of the magnetostrictive ribbon, that which is exposed to air during the quench-
P.G. StoyanoÕ, C.A. Grimesr Sensors and Actuators 80 (2000) 8–14
13
Fig. 4. Response spectrum of a 2826MB alloy Metglas sensor tested in air and in 1% solution of polyŽethyleneimine. in water at room temperature.
ing process, is about 0.4 mm, which forms a significant fraction of the boundary layer at the solid surface and is one-sixth of the transverse wave penetration depth d in water. In addition, the presence of macroscale surface irregularities found on our samples, such as 2 to 3 mm
deep wells, would also contribute towards seemingly higher viscosities. It will be appreciated, however, that the linearity of the plots shown in Fig. 5 guarantees the excellent performance of these magnetostrictive ribbons as viscosity sensors after an appropriate calibration.
Fig. 5. Resonant frequency shift vs. square root of viscosity and density product Žunitss kg my2 sy1r2 . for solutions of glucose in phosphate buffered saline, and polyŽethyleneimine. in water.
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P.G. StoyanoÕ, C.A. Grimesr Sensors and Actuators 80 (2000) 8–14
4. Conclusions It is shown that sensors made of magnetostrictive Metglas ribbons can be reliably used as remote query viscosity sensors. The sensors are passive, requiring no internal power supply, and require no physical connection or specific orientation for signal telemetry. A mathematical model predicting the sensor response to a mass load and in liquid is presented based on the equations of equilibrium of a thin plate and an expression for the friction force acting on the sensor surface. This model does not include interfacial interactions, does not impose any constraints on the tested viscosity range and in the limiting case of low viscosity fluids contains some of the already existing theoretical results for TSM resonators. In the limit of very viscous fluids, the model correctly converges to the proper behavior for solid deposits; in this limit, the sensor can measure only the fluid density. A significant advantage of this sensor technology is that the resonant frequency does not shift with sensor orientation relative to the pickup coil, allowing great flexibility in application of the sensor technology. This is in contrast, for example, with remote query sensors based on magnetostatic coupling w24,25x that obtain environmental information using correlations with the measured amplitude response, or the presence of higher order harmonics, of the sensor in response to a time varying magnetic field. Such amplitude-based sensors require a known orientation with respect to the pickup coil. It is our hope that this new application of magnetostrictive materials to remote query sensor technology will open a new perspective for sensor development allowing accurate measurements in situations where no electrical connections to the sensor element are possible or desirable. Acknowledgements Support to this work by the Life Sciences Division of the National Aeronautics and Space Administration of the United States of America under grant NAG5-4594, by the National Institutes of Health under contract 1-R21GM057240-01, and by the National Science Foundation under contract ECS-9701733, is gratefully acknowledged. References w1x J.W. Grate, S.J. Martin, R.M. White, Acoustic TSM, SAW, FPW and APM wave microsensors, Part I, Analytical Chemistry 65 Ž21. Ž1993. 940A–948A. w2x J.W. Grate, S.J. Martin, R.M. White, Acoustic TSM, SAW, FPW and APM wave microsensors, Part II, Analytical Chemistry 65 Ž22. Ž1993. 987A–996A.
w3x E. du Tremolet de Lacheisserie, Magnetoelastic properties of amorphous alloys, J. Magn. Magn. Mater. 25 Ž1982. 251–270. w4x P.M. Anderson III, Magnetomechanical coupling, D E effect, and permeability in FeSiB and FeNiMoB alloys, J. Appl. Phys. 53 Ž1982. 8101–8103. w5x J.M. Barandiaran, J. Gutierrez, Magnetoelastic sensors based on soft amorphous magnetic alloys, Sensors and Actuators A 59 Ž1997. 38–42. w6x J. Ryan Jr., Antishoplifting labels, Scientific American ŽMay 1997. 120. w7x E.E. Mitchell, R. DeMoyer, J. Vranish, A new Metglas sensor, IEEE Trans. Ind. Electron. IEr33 Ž2. Ž1986. 166–170. w8x L.D. Landaum, E.M. Lifshitz, Theory of Elasticity, 3rd edn., Pergamon, 1986, Chap. 2. w9x R. Schumacher, The quartz microbalance: a novel approach to the in-situ investigation of interfacial phenomena at the solidrliquid junction, Angew. Chem., Int. Ed. Engl. 29 Ž1990. 329–343. w10x K.E. Heusler, A. Grzegorzewski, L. Jackel, J. Pietrucha, Measurements of mass and surface stress at one electrode of a quartz oscillator, Deut. Bunsenges. Phys. Chem. 92 Ž1988. 1218–1225. w11x H.E. Hager, Fluid property evaluation by piezoelectric crystals operating in the thickness shear mode, Chem. Eng. Commun. 43 Ž1986. 25–38. w12x S-Z. Yao, T-A. Zhou, Dependence of oscillation frequency of a piezoelectric crystal on the physical properties of liquid, Anal. Chim. Acta 212 Ž1988. 61–72. w13x M. Thompson, C.L. Arthur, G.K. Dhaliwal, Liquid-phase piezoelectric and acoustic transmission studies of interfacial immunochemistry, Anal. Chem. 58 Ž1986. 1206–1209. w14x L.D. Landau, E.M. Lifshitz, Fluid Mechanics, 2nd edn., Pergamon, 1987, Chap. 2. w15x K.K. Kanazawa, J.G. Gordon, The oscillation frequency of a quartz resonator in contact with a liquid, Anal. Chim. Acta 175 Ž1985. 99–105. w16x S. Bruckenstein, M. Shay, Experimental aspects of use of the quartz crystal microbalance in solution, Electrochim. Acta 30 Ž1985. 1295– 1300. w17x H. Miramatsu, E. Tamyia, I. Karube, Computation of equivalent-circuit parameters of quartz crystals in contact with liquids and study of liquid properties, Anal. Chem. 60 Ž1988. 2142–2146. w18x Z.A. Shana, D.E. Radtke, U.R. Kelkar, F. Josse, D.T. Haworth, Theory and application of a quartz resonator as a sensor for viscous liquids, Anal. Chim. Acta 231 Ž1990. 317–320. w19x F. Herrmann, D. Hahn, S. Buttgenbach, Separation of density and viscosity influence on liquid-loaded surface acoustic wave devices, Appl. Phys. Lett. 74 Ž1999. 3410–3412. w20x G. Pechel, K.H. Adlfinger, Viskositatsanomalien in flussigkeitsgrenzzonen, Z. Naturforsch. 24a Ž1969. 1113–1116. w21x K.H. Adlfinger, G. Pechel, Viscosity anomalies in liquid surface zones, Part II, Deut. Bunsenges. Phys. Chem. 74 Ž1970. 347–350. w22x K.H. Adlfinger, G. Pechel, Viscosity anomalies in liquid surface zones, Part III, Deut. Bunsenges. Phys. Chem. 74 Ž1970. 351–357. w23x R. Schumacher, G. Borges, K.K. Kanazawa, The quartz microbalance: a sensitive tool to probe surface reconstructions on gold electrodes in liquid, Surf. Sci. 163 Ž1985. L621–L626. w24x C.A. Grimes, P.G. Stoyanov, Y. Liu, C. Tong, K.G. Ong, K. Loiselle, M. Shaw, S.A. Doherty, W.R. Seitz, A magnetostatic-coupling based remote query sensor for environmental monitoring, J. Phys. D 32 Ž1999. 1329–1335. w25x P.G. Stoyanov, S.A. Doherty, C.A. Grimes, W. R Seitz, A remotely interrogatable sensor for chemical monitoring, IEEE Trans. Magn. 34 Ž1998. 1315–1317.
A remote query magnetostrictive viscosity sensor Plamen G. Stoyanov, Craig A. Grimes
)
Center for Applied Sensor Technology, Department of Electrical Engineering, 453 Anderson Hall, The UniÕersity of Kentucky, Lexington, KY 40506, USA Received 18 February 1999; received in revised form 2 August 1999; accepted 15 September 1999
Abstract Magnetically soft, magnetostrictive metallic glass ribbons are used as in-situ remote query viscosity sensors. When immersed in a liquid, changes in the resonant frequency of the ribbon-like sensors are shown to correlate with the square root of the liquid viscosity and density product. An elastic wave model is presented that describes the sensor response as a function of the frictional forces acting upon the sensor surface. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Magnetoelastic; Magnetostriction; Viscosity sensor; TSM; Remote query
1. Introduction Acoustic wave microsensors are widely used for measuring small changes in mass, temperature, viscosity, density and ionic conductivity of a medium in contact with the sensor surface; see, for example, Refs. w1,2x and the references therein. Despite the outstanding performance of these microsensors, for example, a quartz crystal oscillator can detect mass accumulation on the sensor surface corresponding to a few percent of a monolayer coverage, applications are limited by the necessity of providing electrical connections to the sensor head in order to excite an acoustic wave and to detect the response signal. This limitation rules out in-situ experiments, such as testing the environmental conditions inside sealed, opaque containers, and biological in vivo experiments such as monitoring of gastric pH or bloodstream glucose levels. One way of circumventing the constraint of needing electrical connections is to use a magnetostrictive, rather than piezoelectric, substrate wherein acoustic or elastic waves can be excited by an external AC magnetic field and the response monitored by a pick-up coil located outside the test area. An excellent candidate for a magnetostrictive sensor platform is a whole class of amorphous metallic glass ribbons called Metglasse. 1 These ribbons ) Corresponding author. Tel.: q1-606-257-1300, ext. 273; fax: q1606-257-3092; e-mail: [email protected] 1 Metglase is a trademark of Allied Signal.
of amorphous iron- and cobalt-based alloys have been shown to exhibit remarkable magnetoelastic properties, especially after a suitable heat treatment in a transverse DC magnetic field to induce a very low anisotropy w3–5x. These properties make these ribbons suitable for a variety of applications, such as position sensors w5x, anti-theft markers w6x, and strain sensors w7x. The operation of these devices is based on the excitation of a longitudinal elastic standing wave by an applied small AC magnetic field at the mechanical resonance frequency of the sensor superimposed, and parallel to, a much stronger DC magnetic field the purpose of which is to select the ‘‘operating point’’ on the sensor’s magnetization curve Žincluding a complete turn-off in the case of anti-theft markers.. This DC field can be supplied either by an external coil, or by placement of a magnetically hard piece of material adjacent to the sensor. The phase velocity of the elastic wave and, hence, its resonant frequency, is dependent on the density, Young’s modulus, and Poisson ratio of the sensor w8x, the characteristics of the medium in contact with the sensor surface, and on the details of the interfacial interaction between the ambient medium and the sensor surface. Some of the factors governing this interaction whereby the phase velocity is changed are surface roughness w9x, presence of surface stress w10x, and pressure. Additional factors are to be considered when the sensor is immersed in a liquid, including the strength of the interfacial molecular bond w11x, surface wetting w12x, liquid density, viscosity, and surface free energy w13x.
0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 9 . 0 0 2 8 8 - 5
P.G. StoyanoÕ, C.A. Grimesr Sensors and Actuators 80 (2000) 8–14
9
These various factors need to be considered to obtain a reliable interpretation of the observed resonance frequency shifts. In this paper, we demonstrate the use of magnetically soft, magnetostrictive Metglas ribbons as remote query viscosity and mass sensors; a theoretical model is first presented to describe the sensor operation.
2. The model Notation d thickness of the sensor ribbon E Young’s modulus of the sensor material Fy , Fz components of the external force per unit area of the sensor surface L length of the sensor s velocity of an oscillating surface ui the ith component of the particle displacement vector Õ fluid velocity d transverse wave penetration depth in liquid h coefficient of dynamic viscosity of the liquid rs sensor material density rl density of the liquid s Poisson ratio of the sensor material f 0 , fn resonant frequency of a bare and loaded sensor, respectively v 0 , v n angular resonant frequency of a bare and loaded sensor, respectively Ž v s 2p f . The theoretical model is based on the equation of longitudinal vibratory motion of a thin elastic plate Žthe sensor. in the presence of a dissipative force, namely, the shear force acting on the basal plane of the sensor when immersed in a liquid. For a thin, homogenous elastic plate centered at the origin of a Cartesian coordinate system and oriented in the yz-plane, see Fig. 1, in the presence of external forces acting in the same plane the equations of equilibrium are w8x: Ed
E2 u z
1
1ys 2 Ez2
Ed
2 Ž 1 y s . E zE y E2 u y
1 1ys 1
q
q
E2 u y
1 q
1
2
Ey
2
2Ž 1 q s . E y 2
1 q
E2 u z
2 Ž 1 y s . E zE y
Ž 1a . E2 u y
2Ž 1 q s . E z q Fy s 0.
with yr dŽE 2 u zrEt 2 . and yr dŽE 2 u yrEt 2 ., respectively. For a plane wave propagating in the y-direction the displacement vectors are independent of z leaving:
rs rs
E2 u z Et 2 E2 u y Et 2
E s
Ž 2.
2Ž 1 q s . E y 2 E2 u y
E s
E2 u z
Ž 3.
1ys 2 E y2
Eqs. Ž2. and Ž3. show that the frequencies of the in-plane longitudinal and transversal waves are different and, hence, we can exclude the transversal wave from further consideration.
E2 u z
q Fz s 0
Fig. 1. A magnetostrictive thin film planar sensor immersed in liquid and located between two fixed plates. Vibrations in the basal plane due to incident AC magnetic field excite a transversal wave propagating away from the resonator surface.
2.1. Effect of a mass load If a mass D m, which is much less than the mass of the sensor M, is evenly deposited on the plate-like surface of the sensor, Eq. Ž3. is modified as follows:
2
Ž 1b .
The equations of motion ŽEOM., for a sensor in air, are obtained from the above equations by replacing Fz and Fy
M q D m E2 u y Ad
Et 2
E s
E2 u y
1ys 2 E y2
Ž 4.
where A is the surface area of the sensor, and d the thickness.
P.G. StoyanoÕ, C.A. Grimesr Sensors and Actuators 80 (2000) 8–14
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The sensor will exhibit magnetostrictive vibrations at almost any frequency of the driving AC magnetic field. However, these vibrations are most pronounced at a specific frequency, corresponding to its mechanical resonance, as determined by both the sensor dimensions and material properties. We seek a standing wave solution to Eq. Ž4. in the form: np y u s 2 Beyi v n t cos Ž 5. L where v n denotes the set of the longitudinal resonant frequencies of the sensor, including higher order harmonics, and B is a complex number. Substituting Eq. Ž5. into Eq. Ž4., then taking the real part, results in an expression that describes the resonant radian frequency of the mass loaded sensor: 1 Ad E np 2 1 v n2 s s v2 Ž 6. Dm M 1ys 2 L Dm 0 1q 1q M M where v 0 denotes resonant radian frequency of the unloaded sensor. For small mass loads Eq. Ž6. reduces to: f0 D m D fsy Ž 7. 2 M where the frequency shift is downwards, D f s f n y f 0 - 0, and we are concerned with the fundamental resonant frequency due to its larger amplitude. The resonant frequency of the magnetoelastic sensor shifts linearly per mass load, just as it does for surface acoustic wave devices w1,2x.
ž /
In the presence of a viscous fluid surrounding the vibrating plate-like sensor, the resonant frequency of the sensor Žand associated harmonics. will be shifted lower due to the dissipative character of the shear forces associated with liquid viscosity. The theoretical model to describe this effect is most concise if we consider the motion of an incompressible fluid bounded by two infinite, parallel-oriented surfaces, one of which is fixed and the other oscillating in its own plane w14x. Let the oscillating surface be the yz-plane, with the vibrations occurring in the y-direction, and the fixed surface be parallel to it and shifted a distance h along the positive x-axis. The velocity of the oscillating surface can be described as s y s s s s0 eyi v t where s0 is a complex constant that can be made real by a proper choice of the time origin. The fluid velocity must satisfy the boundary conditions Õ y s s for x s 0 Ž Õ x and Õz are zero. and Õ y s 0 for x s h. Under these assumptions, the equation of motion of a viscous fluid ŽNavier–Stokes equation. reduces to a simple form:
h E2 Õ s
Et
rl Ex2
Õss
Ž 8.
sin k Ž h y x .
sin kx where k s ŽŽ1 q i .rŽ d .., i s 'y 1 , and
ds
(
2h
Ž 9.
Ž 10 .
rl v
is the depth of penetration into the fluid of the perturbation, caused by the oscillating surface, or the velocity amplitude damping constant. A transversal elastic wave is generated at the vibrating surface which propagates in the fluid, in the x-direction towards the steady plate. The frictional force Žor the shear stress. per unit area of the vibrating plate is related to the shear strain rate ŽEÕrE x . at its surface by the dynamic viscosity coefficient, h , through Newton’s law: Fy s h Ž EÕrE x . xs 0 s yRe Ž h ks cot kh .
Ž 11 .
where Re denotes the real part. The force expression for Fy is inserted into Eq. Ž3. to describe a vibrating thin elastic plate Žthe sensor. immersed in a liquid, sandwiched between two infinitely large, parallel fixed surfaces spaced equidistant from the vibrating sensor, as shown in Fig. 1: E 2 Uy Et
2.2. Effect of Õiscosity
EÕ
The periodic solution that we seek is in the form Õ s Ž A sin kx q B cos kx . eyi v t. Substituting this into Eq. Ž8. and determining constants A and B from the boundary conditions, the following expression is found for the fluid velocity as a function of distance from the vibrating plate:
2
E
E2 u
1
s
rs 1 y s
2
Ey
2
y
2h k Eu y
rs d Et
cot kh
Ž 12 .
The factor of 2 in the second term on the right-hand-side ŽRHS. reflects the presence of two fixed surfaces. To be mathematically precise, the expression for Fy must be modified to account for the drag forces acting on the edges of the vibrating plate-like sensor. However, since the plate thickness is negligibly small compared with the lateral dimensions Žillustrative sensor dimensions are f 0.01 = 30 = 5 mm. the compression waves generated by the front and back edges have little impact on the plate motion. As for the side edges, those parallel to the direction of vibration, their presence effectively amounts to increasing the planar area by, approximately, the product d L w14x, a quantity f 0.01% of the total plate area. Therefore, Eq. Ž12. is valid for thin sensors Žplates. that have relatively large surface areas. We look for a solution to Eq. Ž12. in the form of Eq. Ž5.; taking the real part the resulting dispersion relation is:
v n2 s
np
E
ž /
rs Ž 1 y s 2 . y
2
L
2hv n sinh Ž 2 hrd . y sin Ž 2 hrd .
drs d cosh Ž 2 hrd . y cos Ž 2 hrd . s Ž v0 qD v .
2
Ž 13 .
P.G. StoyanoÕ, C.A. Grimesr Sensors and Actuators 80 (2000) 8–14
where D v s v n y v 0 - 0. The first term on the RHS represents the square of the nth resonant frequency of the resonator in an inviscid fluid, e.g., air; the second term reflects the influence of the shear forces acting on both solid faces. No assumptions have been made about the viscosity levels of the tested fluid; Eq. Ž13. is equally applicable to predicting the resonator response to both highly viscous and almost inviscid fluids. These two extremes, however, deserve further consideration. 2.2.1. Case 1: Highly Õiscous fluid (2h r d < 1) Keeping only the terms linear in D vrv 0 we obtain: Dv
v0
sy
1 rl h 3 rs d
or D f s y
1 3
f0
rl h rs d
.
Ž 14 .
This formula is almost identical with the expression for the solid mass load ŽEq. Ž7.. apart from the smaller numerical constant. In this limit, the fluid density r l can be measured, but not the viscosity. This result is to be expected since the fixed plates are, in effect, so close to the resonator surfaces that they frustrate the boundary layers responsible for the viscous action. As the attenuation depth d is large compared with h, the whole liquid layer oscillates synchronously with the resonator, so that it behaves as if there were a solidified liquid layer of mass r l h per unit area loaded on the resonator face. Therefore, in the limit of highly viscous fluids the model exhibits the proper behavior for deposition of a solid onto the sensor surface. However, for solid mass loads Eq. Ž7. is appropriate, rather than Eq. Ž14., since the numerical constant in the latter originates from the oscillating factor in the second term of Eq. Ž13. which is present only in the liquid phase.
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can be determined from the slope of the frequency shift vs. square root of viscosity plot Žsee Eq. Ž15... Furthermore, liquid density and viscosity effects on the magnetostrictive sensor can be separated following the approach described by Hermann et al. w19x. The model presented here does not account for any effects at the solidrliquid interface. It assumes an ideally smooth surface and a homogenous dynamic viscosity coefficient throughout the liquid, including at the sensor surface. However, as observed by Pechel and Adlfinger w20x, and later experimentally demonstrated by the same authors w21,22x, liquid viscosity can be significantly higher at the interface with solid surfaces. In the case of water w21,22x, at 208C, the interfacial viscosity was found to be 5.4 times greater than the bulk fluid viscosity. Nevertheless, although important when interfacial interactions are the subject of interest, these considerations do not have a crucial importance in viscosity sensing applications since the sensor response can be empirically calibrated. Yet, it is interesting to note that increased sensor surface roughness can effectively switch the operational regime from an almost inviscid Žliquid-like. one, to that of a highly viscous Žsolid-like. one, making the frequency shift directly proportional to the amount of the liquid mass trapped in the cavities of the roughened surface and, therefore, vibrating synchronously with the resonator. Schumacher et al. w9,23x treated the liquid entrapments in a roughened surface made up from semicylinders as a rigidly attached liquid layer of height Dr2, D being the height of a semicylinder. They found that under this condition the frequency shift is proportional to D m s r l Dr2, the mass per unit area of the equivalent rigid
2.2.2. Case 2: Almost inÕiscid fluid (2h r d 4 1) Keeping only the linear terms in D vrv 0 , the dispersion relation Eq. Ž13. is reduced to:
v n2 s v 02 y
2hv n
rs d d
,
From which we find: D fsy
(p f
0
2prs d
Ž hr l .
1r2
Ž 15 .
For this viscosity regime, the frequency shift is proportional to the square root of the liquid viscosity and density product. The functional dependence of D f on hr l in this limit is the same as in the liquid phase theories of TSM acoustic wave quartz sensors w11,15–18x. Measurement of viscosity in this case requires a prior knowledge of the liquid density. However, it should be noted that for many fluids the density remains essentially constant while viscosity rapidly changes w15,16x. For such liquids, a direct measurement of the viscosity is obtained. Liquid density
Fig. 2. The resonator surface roughness can be incorporated into the model through the concept of an effective rigid layer w9,22x. The modified boundary conditions for the velocity of the transversal wave propagating in the liquid are Õ y s s for x s t and Õ y s 0 for x s h Žsee text..
12
P.G. StoyanoÕ, C.A. Grimesr Sensors and Actuators 80 (2000) 8–14
layer. Using the approach of Schumacher et al., it is not difficult to modify the present theory to incorporate the resonator surface roughness. All that needs to be done is to alter the boundary conditions for the transverse wave propagating in the liquid, see Fig. 2, so that Õ y s s for x s t Ž Õ x and Õz are zero. and Õ y s 0 for x s h, and then account for the equivalent rigid layer of thickness t through the use of Eq. Ž7.. Other interfacial effects, such as selective bonding to the solid surface, may be taken into account in a similar manner.
3. Experimental results and discussion The samples used in this work were highly magnetostrictive amorphous ribbons of Metglas 2826 MB alloy, 3 7 .5 = 1 2 .5 = 0 .0 3 0 m m 3 o f c o m p o sitio n Fe 40 Ni 38 Mo 4 B18 , available from Allied Signal. The saturation magnetic induction is 0.88 Tesla Žas-cast. and the saturation magnetostriction is 1.2 = 10y5 . The samples were tested as received; no additional heat treatment was done. X-ray diffraction experiments confirmed the amorphous structure of the material. The sensors were characterized using a magnetoelastic resonance test fixture, as shown schematically in Fig. 3. Referring to Fig. 3, a sinusoidal AC voltage from the signal generator is amplified and applied to a pair of
Fig. 3. Schematic drawing of the magnetostrictive sensor test set-up.
Helmholtz coils, producing a RMS magnetic field of 55 mOe that is superimposed on a 5.5 Oe DC magnetic field. The sample is positioned lengthwise in a 350 turn 40-ga wire pick-up coil of 16 cm2 rectangular cross-section. The voltage from the pick-up coil is preamplified and fed into a dual-channel lock-in amplifier tracking the signal generator frequency, and eventually into the computer controlling the experiment. A typical frequency response spectrum of a bare Žnonloaded. sensor tested in air and in a 1% solution of polyethilenimine in water Žroom temperature. is shown in Fig. 4. Note that we are not concerned with the relative amplitude of the responses, rather the location of the resonant frequency peaks as indicated on Fig. 4. The viscosity measurements were carried out in a specially designed test trough in which the resonator was supported along its transversal centerline, thus avoiding any frustration of the fundamental vibration mode, and positioned equidistantly 2 mm from two parallel fixed plates, thus realizing the conditions shown in Fig. 1. The value of d for water Ždynamic viscosity 0.001 Nsrm2 . is 2.4 mm; for castor oil Ždynamic viscosity of 0.985 Nsrm2 . it is 80 mm. Since the fluid film thickness h in the test trough is 2 mm, it is evident that almost all fluids can be considered almost inviscid in the context of this model so that Eq. Ž15. can be used rather than Eq. Ž13.. It is important to note, however, that while the test fixture was used for precise comparison to theory, the sensors appeared to work equally well by simply placing them in a liquid container. Because of the substantial temperature dependence of the viscosity, the ambient temperature was constantly monitored throughout the experiments. The plots of the resonant frequency shift vs. the square root of the viscosity and density product for glucose dissolved in phosphate buffered saline ŽPBS. and polyŽethyleneimine. dissolved in water are shown in Fig. 5. The concentration range of the Glucose solutions ranged from 10 to 700 grl, with the upper limit being close to saturation. The polyŽethyleneimine. solutions ranged from 1% to 11% concentration; beyond that range the determination of the resonant peak position becomes unreliable due to damping of the magnetoelastic response. The sensor response to both analytes is almost identical. The slope seen in Fig. 5 is approximately twice as large as that predicted by Eq. Ž15., suggesting higher viscosities. It is our belief that the key to this discrepancy has to be sought in the difference between the fluid viscosities at the solid–liquid interface and in the bulk liquid. As noted in the theoretical discussion above, there is experimental evidence that the ratio of these two viscosities in the case of water is 5.4 w21,22x; as '5.4 f 2.3, this alone is enough to account for the observed discrepancy of our experimental results with theory. The surface topography of the sensor may also play an important role. The average surface roughness of the rougher face of the magnetostrictive ribbon, that which is exposed to air during the quench-
P.G. StoyanoÕ, C.A. Grimesr Sensors and Actuators 80 (2000) 8–14
13
Fig. 4. Response spectrum of a 2826MB alloy Metglas sensor tested in air and in 1% solution of polyŽethyleneimine. in water at room temperature.
ing process, is about 0.4 mm, which forms a significant fraction of the boundary layer at the solid surface and is one-sixth of the transverse wave penetration depth d in water. In addition, the presence of macroscale surface irregularities found on our samples, such as 2 to 3 mm
deep wells, would also contribute towards seemingly higher viscosities. It will be appreciated, however, that the linearity of the plots shown in Fig. 5 guarantees the excellent performance of these magnetostrictive ribbons as viscosity sensors after an appropriate calibration.
Fig. 5. Resonant frequency shift vs. square root of viscosity and density product Žunitss kg my2 sy1r2 . for solutions of glucose in phosphate buffered saline, and polyŽethyleneimine. in water.
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P.G. StoyanoÕ, C.A. Grimesr Sensors and Actuators 80 (2000) 8–14
4. Conclusions It is shown that sensors made of magnetostrictive Metglas ribbons can be reliably used as remote query viscosity sensors. The sensors are passive, requiring no internal power supply, and require no physical connection or specific orientation for signal telemetry. A mathematical model predicting the sensor response to a mass load and in liquid is presented based on the equations of equilibrium of a thin plate and an expression for the friction force acting on the sensor surface. This model does not include interfacial interactions, does not impose any constraints on the tested viscosity range and in the limiting case of low viscosity fluids contains some of the already existing theoretical results for TSM resonators. In the limit of very viscous fluids, the model correctly converges to the proper behavior for solid deposits; in this limit, the sensor can measure only the fluid density. A significant advantage of this sensor technology is that the resonant frequency does not shift with sensor orientation relative to the pickup coil, allowing great flexibility in application of the sensor technology. This is in contrast, for example, with remote query sensors based on magnetostatic coupling w24,25x that obtain environmental information using correlations with the measured amplitude response, or the presence of higher order harmonics, of the sensor in response to a time varying magnetic field. Such amplitude-based sensors require a known orientation with respect to the pickup coil. It is our hope that this new application of magnetostrictive materials to remote query sensor technology will open a new perspective for sensor development allowing accurate measurements in situations where no electrical connections to the sensor element are possible or desirable. Acknowledgements Support to this work by the Life Sciences Division of the National Aeronautics and Space Administration of the United States of America under grant NAG5-4594, by the National Institutes of Health under contract 1-R21GM057240-01, and by the National Science Foundation under contract ECS-9701733, is gratefully acknowledged. References w1x J.W. Grate, S.J. Martin, R.M. White, Acoustic TSM, SAW, FPW and APM wave microsensors, Part I, Analytical Chemistry 65 Ž21. Ž1993. 940A–948A. w2x J.W. Grate, S.J. Martin, R.M. White, Acoustic TSM, SAW, FPW and APM wave microsensors, Part II, Analytical Chemistry 65 Ž22. Ž1993. 987A–996A.
w3x E. du Tremolet de Lacheisserie, Magnetoelastic properties of amorphous alloys, J. Magn. Magn. Mater. 25 Ž1982. 251–270. w4x P.M. Anderson III, Magnetomechanical coupling, D E effect, and permeability in FeSiB and FeNiMoB alloys, J. Appl. Phys. 53 Ž1982. 8101–8103. w5x J.M. Barandiaran, J. Gutierrez, Magnetoelastic sensors based on soft amorphous magnetic alloys, Sensors and Actuators A 59 Ž1997. 38–42. w6x J. Ryan Jr., Antishoplifting labels, Scientific American ŽMay 1997. 120. w7x E.E. Mitchell, R. DeMoyer, J. Vranish, A new Metglas sensor, IEEE Trans. Ind. Electron. IEr33 Ž2. Ž1986. 166–170. w8x L.D. Landaum, E.M. Lifshitz, Theory of Elasticity, 3rd edn., Pergamon, 1986, Chap. 2. w9x R. Schumacher, The quartz microbalance: a novel approach to the in-situ investigation of interfacial phenomena at the solidrliquid junction, Angew. Chem., Int. Ed. Engl. 29 Ž1990. 329–343. w10x K.E. Heusler, A. Grzegorzewski, L. Jackel, J. Pietrucha, Measurements of mass and surface stress at one electrode of a quartz oscillator, Deut. Bunsenges. Phys. Chem. 92 Ž1988. 1218–1225. w11x H.E. Hager, Fluid property evaluation by piezoelectric crystals operating in the thickness shear mode, Chem. Eng. Commun. 43 Ž1986. 25–38. w12x S-Z. Yao, T-A. Zhou, Dependence of oscillation frequency of a piezoelectric crystal on the physical properties of liquid, Anal. Chim. Acta 212 Ž1988. 61–72. w13x M. Thompson, C.L. Arthur, G.K. Dhaliwal, Liquid-phase piezoelectric and acoustic transmission studies of interfacial immunochemistry, Anal. Chem. 58 Ž1986. 1206–1209. w14x L.D. Landau, E.M. Lifshitz, Fluid Mechanics, 2nd edn., Pergamon, 1987, Chap. 2. w15x K.K. Kanazawa, J.G. Gordon, The oscillation frequency of a quartz resonator in contact with a liquid, Anal. Chim. Acta 175 Ž1985. 99–105. w16x S. Bruckenstein, M. Shay, Experimental aspects of use of the quartz crystal microbalance in solution, Electrochim. Acta 30 Ž1985. 1295– 1300. w17x H. Miramatsu, E. Tamyia, I. Karube, Computation of equivalent-circuit parameters of quartz crystals in contact with liquids and study of liquid properties, Anal. Chem. 60 Ž1988. 2142–2146. w18x Z.A. Shana, D.E. Radtke, U.R. Kelkar, F. Josse, D.T. Haworth, Theory and application of a quartz resonator as a sensor for viscous liquids, Anal. Chim. Acta 231 Ž1990. 317–320. w19x F. Herrmann, D. Hahn, S. Buttgenbach, Separation of density and viscosity influence on liquid-loaded surface acoustic wave devices, Appl. Phys. Lett. 74 Ž1999. 3410–3412. w20x G. Pechel, K.H. Adlfinger, Viskositatsanomalien in flussigkeitsgrenzzonen, Z. Naturforsch. 24a Ž1969. 1113–1116. w21x K.H. Adlfinger, G. Pechel, Viscosity anomalies in liquid surface zones, Part II, Deut. Bunsenges. Phys. Chem. 74 Ž1970. 347–350. w22x K.H. Adlfinger, G. Pechel, Viscosity anomalies in liquid surface zones, Part III, Deut. Bunsenges. Phys. Chem. 74 Ž1970. 351–357. w23x R. Schumacher, G. Borges, K.K. Kanazawa, The quartz microbalance: a sensitive tool to probe surface reconstructions on gold electrodes in liquid, Surf. Sci. 163 Ž1985. L621–L626. w24x C.A. Grimes, P.G. Stoyanov, Y. Liu, C. Tong, K.G. Ong, K. Loiselle, M. Shaw, S.A. Doherty, W.R. Seitz, A magnetostatic-coupling based remote query sensor for environmental monitoring, J. Phys. D 32 Ž1999. 1329–1335. w25x P.G. Stoyanov, S.A. Doherty, C.A. Grimes, W. R Seitz, A remotely interrogatable sensor for chemical monitoring, IEEE Trans. Magn. 34 Ž1998. 1315–1317.