Ultrasonics in food engineering. Part I: Introduction and experimental methods

Journal of Food Engineering 8 1988) 2 17-245

Ultrasonics in Food Engineering. Part I: Introduction and Experimental Methods M. J. W. Povey & D. J. McClements Procter Department

of Food Science, The University, Leeds LS2 9JT, UK

(Received 20 October 1986; revised version received 7 October 1988: accepted 7 November 1988)

ABSTRACT The basic ideas underlying the use of ultrasound in non-destructive testing are reviewed with a special emphasis on their relevance to food engineering. Sound velocity is a valuable engineering tool because of its relative ease of measurement, ease of interpretation of the consequent data and its greater accuracy than attenuation measurements. It is a non-destructive, non-invasive, non-intrusive technique. Low-intensity applications are reviewed and their potential in the measurement of physical properties is emphasised. Such measurements include the determination of adiabatic compressibility, rigidity and, in two-phase systems, particle size and dispersed-_vhase volume fraction. Experimental techniques which the authors have found useful for measurements in food systems are described and the accuracy of available techniques is compared.

NOTATION

d

f” G Z K

“p, Journal

Radius (m) Cross-sectional area of the rod (m’) Pipe diameter (m) Young’s modulus (N m-?) Frequency (MHZ) Rigidity modulus (N m-*) Intensity (kW m-*) Bulk modulus (N m-‘) Experimentally determined constraint in the Rao equation Absolute pressure (MPa) 217 of Food

Engineering

0260-8774/88/$03.50

Publishers Ltd, England. Printed in Great Britain

- 0

1989

Elsevier

Science

218 P

R S

T ?;b 211 v, V X z

p”

r 6

A 1 E’ E” ‘Is 8 ;1 P PO Pf

; @Ill w aIll

M. J. W. Povey, D. J. McClements

Pressure deviation

due to the passage of the ultrasound

(MPa) Reflection coefficient Temperature deviation due to the passage of the ultraTemperature deviation owing to the passage of the ultrasound (K) Absolute temperature (K) Velocity of compressional ultrasound (m s - ’ ) Velocity of shear ultrasound (m s- ’ ) Velocity of fluid flow or speed of scatterer (m s - ’ ) Distance travelled by the pulse (m) Specific acoustical impedance, i.e. the ratio of the pressure to the particle velocity arising from the passage of the ultrasound (MPa.s m-‘) Attenuation coefficient for ultrasound (Nepers m- ‘) The adiabatic compressibility (N-l m-‘); this is the inverse of the bulk modulus K Shear wave skin depth [ = (v,/nfp )- 1/2] (m) An infinitesimally small change in the quantity immediately to the right of this symbol A small but finite change in the quantity immediately to the right of this symbol Particle displacement (run) Particle velocity (mm s - ’ ) Particle acceleration (km s - ‘) Shear viscosity (Pa s) Angle of ultrasound propagation direction with respect to fluid flow Ultrasound wavelength (m) Density in the presence of the ultrasound (kg m- ‘) Static density (kg m-“) Fluid density surrounding a bubble of gas (kg m-j) Transmission coefficient Volume fraction of dispersed phase Molar volume (m3 kg- ’ mall ’ ) Ultrasound frequency in the form 2nf(radians s- ‘) Resonant frequency of an air bubble (radians s - ’ )

INTRODUCTION Ultrasonics has been used in the food industry for many years for various purposes, chief amongst which are emulsification (Sajas et al.,

Ultrasonicsin food engineering - 1 1978),

219

cleaning (Lambert, 1982) and animal backfat thickness estimation (Lister, 1984). There is now a growing interest in the use of ultrasonics (Agricultural Research Council, 1982; Food and Drink Federation, 1985) to provide data on the bulk properties of food materials, in-line, and non-intrusively. Karl Graff ( 198 1 ), in his review of the history of ultrasonics, noted that ‘no reference has been found to the study of inaudible acoustic phenomena by pre-nineteenth century investigators’. It was the discovery that pitch was related to frequency which led, in the mid-l 9th century, to the establishment of a limit of audibility of the human ear at about 16 kHz. Ultrasonics technology was first developed as a means of submarine detection in World War I, and developments in this area have continued to the present day (Kinsler et al., 1982). In the inter-war years investigation into the effects of high-intensity ultrasonics began, which have culminated in the ultrasonic cleaning, cell disruption and emulsification equipment now found in laboratories and a few factories. These high-intensity applications are characterised by relatively low frequencies, up to about 100 kHz, by continuous (as distinct from pulsed) operation and by power levels from 10 kW m-’ upwards. Recently, high-power ultrasonics has found increasing use for promoting chemical reactions, acquiring the name ‘Sonochemistry’ in the process (Mason, 1987). Applications of high-intensity ultrasonics are beyond the scope of this review and interested readers are referred to Puskar (1982) for a review of the subject. Although superficially the two techniques appear to have a great deal in common, in fact they involve different technologies and physical principles. Ultrasonic techniques for non-destructive testing (NDT) of metals were based on developments in radar electronics in World War II, and these advances also made possible the imaging techniques on which much of present-day medical ultrasonics rely (Wells, 1977). The recent rapid reduction in the cost of sophisticated electronic equipment has accelerated the trend towards the integration of ultrasonic sensors into complex data-processing systems. Ultrasonics NDT is characterised by high frequencies (between O-1 and 20 MHz), pulsed operation and lower power levels ( G 100 mW) than ‘High Power’ ultrasonics. As the term NDT implies, this lower-power ultrasonics leaves the system unchanged. A major technical development of the 196Os, the Surface Acoustic Wave (SAW) device has found uses in electronics and bioelectronics (see, e.g. Wohltjen & Dessy, 1979a-c). The SAW device uses ultrasonic waves propagating along the surface of a plate of piezo-electric material such as quartz or lithium niobate. The device is incorporated into a resonant circuit which is extremely sensitive to changes in the condition of the surface. If the surface of the SAW is coated with a gel containing an

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M. J. W. Povey. D. J. McClements

enzyme, small changes due to the interaction of the enzyme with the biological system being monitored are detected as changes in the resonant frequency of the SAW, and the SAW forms an extremely sensitive bio-sensor. In-line ultrasonic measurements on food systems make special demands of the ultrasonicist. Foods are generally more complex than the usual range of materials presented to automated ultrasonic systems. Although even the most complex of electronic systems can be environmentally protected, their sensors must withstand factory cleaning and maintenance. Furthermore, the sample temperature and properties and method of presentation to the sensor may depart from the laboratory ideal. Ultrasonics, however, lends itself well to translation from the laboratory to in-line factory application (Papadakis, 1976) but a thorough understanding of the sources of degradation of accuracy on transfer from laboratory to factory is necessary. Ultrasonic techniques have the advantage of relatively low cost and robust probes and associated electronics, a reasonably well-established theory of the interaction between acoustic fields and matter, indifference to hostile environments, for example corrosive or hot materials, and accessibility to materials opaque to light. Ultrasonic radiation also has fewer hazards associated with it than most other forms of radiation. However, some concern has been expressed at possible risks from high-power applications, and the actual hazard level associated with ultrasonics has not yet been established (Apfel, 198 1; Carstensen, 1982). Food ultrasonics represents a new area of application, possibly rivalling medical ultrasonics (Wells, 1977) and NDT of metals (Papadakis, 1976) in importance, and provides the food engineer with a new source of information about the properties of materials being processed. When used in conjunction with other physical measurements, for example density, elastic modulus can be measured.

ULTRASONIC

PROPAGATION THROUGH MEDIA

VISCOELASTIC

A comprehensive review of ultrasonic propagation and developments in ultrasonic techniques is contained in the series Physical Acoustics by Mason and later Mason & Thurston (1964-84). A review can be found in Edmonds ( 198 1). Ultrasonics are high-frequency ( > 16 kHz) mechanical waves. These waves travel either through the buIk of a material or on its surface at a velocity which is characteristic of the nature of the wave under con-

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331

sideration and the material through which it is propagating. Unless stated otherwise in this review, only one type of mechanical wave will be considered; this is the compressional or longitudinal wave. This is because compressional waves are the easiest to generate and detect and are thus by far the most widely used. They consist of a succession of compressions and rarefactions which vary both in time and space, the material displacement being in the same direction as that in which the wave is propagating. The velocity of propagation, L’,, in a solid material is related to the elastic moduli of the material and its density, p, by the relationship I,, =((K +4G/3}/p)‘Q’

(1)

where K is the bulk modulus and G is the rigidity modulus. A derivation of this expression is given in Kinsler et al. (1982), which also gives an introduction to the theory of ultrasonic propagation. For most purposes, it is only necessary to appreciate that a measurement of ultrasonic velocity provides information about the ratio of an elastic modulus to the density of the material through which the wave propagates. Thus independent measurements of density and velocity enable a value of the combined elastic moduli (K + 4G/3) to be determined. As a liquid has no rigidity, eqn ( 1) simplifies to 2’1 =

(K/p)“’

In many food systems, such as gels, the rigidity modulus G is much smaller than the bulk modulus, K, and eqn (2) also provides a good approximation for these systems. In some particularly rigid foods, a different type of ultrasonic wave may propagate, called a shear wave, in which the material moves transversely to the direction of propagation of the wave, inducing a shearing action in the material. The velocity of propagation is generally less than that of a compressional wave and is given by (3) where v, is the shear wave propagation velocity. The simplest experimental arrangement, described by Pellam & Galt ( 1946), is depicted in Fig. 1. A short-duration ( = 1 ,M.) pulse of ultrasound is introduced by a transducer into the liquid contained in the cuvette. The pulse travels through the liquid at the velocity of sound, to be detected subsequently on reflection by the transducer acting as a receiver. The pulse will undergo multiple reflections within the cuvette so that a series of ‘echoes’, as depicted in Fig. l(b), is detected. The time lapse between emission of the pulse and receipt of the subsequent echoes

M. J. W. Povey,

137

I__

D. McClements

rlOcm_I Echo

Peak

?Lz%iz

ia) Fig. 1.

A

B

2Dcm

C

4Ocm

D

60cm

pattern

E

80cm

b)

Ultrasonic pulse propagation within a glass cuvette using pulse reflection: (a) transducer and cell and (b) resultant echo pattern.

depends on the velocity of sound and the distance travelled by the pulse. The first reference to this, the simplest way of determining the velocity of sound, was by Colladon & Sturm (1827). This technique is also called, descriptively, ‘pitch and catch. The pulse echo experiment illustrates a feature important in many ultrasonic measurements. The velocity may simply be calculated from a time and a distance measurement. Any error in velocity estimation arises from errors in the measurement of these two quantities. The echo amplitude decreases due to absorption of sound in the liquid, to diffraction, interference, losses through the walls, at the bond between the transducer and the cuvette and to phase cancellation errors in the transducer itself. So, although the attenuation coefficient due to absorption in the liquid may be estimated, it is much more difficult to separate the contribution to the overall signal loss due to intrinsic absorption in the liquid from all the other sources of signal loss. Velocity measurements are therefore generally easier to make and are more accurate and reproducible than attenuation measurements. The linear approximation At low ultrasonic power levels, e.g. below c. 10 kW m- 2 in water at room temperature (Puskar, 1982), the signal amplitude is small enough for the strain to be linearly related to the stress. This means, amongst other things, that velocity will be independent of the ultrasonic power level and eqns (1) and (2) can be used to determine the elastic properties of materials at the small strains. However, examination of Table 1 (adapted from Edmonds ( 198 1)) shows that although the linear approximation (d/u, Q 0.1; T4 100 mK),

Ultrasonicsin food engineering - I

t-.

223

224

M. J. W. Povey, D. J. McClements

where E’is the particle velocity, is valid over a very wide range of power levels, local pressure intensities can easily reach 1 atm and particle accelerations can be large. Under these conditions cavitation, to which water is particularly prone, becomes likely, so that the ultrasonic technique may no longer be described as non-destructive. Although propagation conditions may still technically be linear, the conditions created by cavitation mean that the assumptions of the linear theory no longer apply. This can be a problem because the simplest solution to a lack of sensitivity in an application is to boost the power of the transmitter. Under these circumstances, apparatus which formerly worked in the linear region may produce nonlinear results. The symptoms of nonlinear propagation include the appearance of shock fronts, distortion of the pulse envelope so that the positive pressure part of the wave has a greater amplitude than the negative part and a dependence of velocity and attenuation on power levels. PROPAGATION

ACROSS

INTERFACES

When an ultrasonic wave reaches a boundary between two media of different acoustic properties (subscripted 1 and 2) some of the energy will be reflected. If the boundary dimensions normal to the propagation direction are much greater than the wavelength and the thickness is much less than the wavelength, then the reflection coefficient, R, for normal incidence will be:

R = (Z2 - ZJ2/(Z2 + Z,)’ and the transmission coefficient for normal incidence will be

t=l--R R and t are thus the fractions of the incident ultrasonic power that are reflected and transmitted respectively. Impedance matching to ensure that Z, and Z, are nearly equal is an important consideration when choosing a transducer for a given food, since if Z, and Z, are significantly different in value, then almost all the energy from the transducer will be reflected at the boundary and fail to enter the material. A similar condition exists within a heterogeneous sample consisting of materials of widely differing acoustic impedances. Velocity dispersions

of different frequencies

Many systems display a phenomenon called ‘dispersion’. In this case, different ultrasonic frequencies travel at different velocities. The overall

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result is for the initial wave packet to spread out with time, the lowerfrequency components of the wave pulse trailing behind the higherfrequency components. This makes meaningless the concept of a single velocity for the whole pulse in such circumstances. The velocity of the pulse packet is called the group velocity. The velocity of a singlefrequency component is called the phase velocity. Velocity of sound in gases and liquids The velocity as given by eqn (2) is simply a function of the bulk modulus and density. The equation in the case of gases and liquids has the more conventional form: u, = ( l//3p)“z where /3 is the adiabatic compressibility, which is simply the inverse of the bulk modulus K. This equation can be invalidated by the presence of any dispersed phase in the fluid. Velocity in rods and bars When the wavelength is long in comparison sion of the rod, the velocity of compressional u, = (E/p)‘/’

with the transverse dimenwaves is given by (5)

where E is Young’s modulus. In the intermediate case where the rod diameter is comparable in size with the wavelength, the rod acts as a waveguide and the ultrasound velocity is dependent on both the rod diameter and the frequency of the ultrasound. Velocity in dispersions The term dispersion, as used in this section, refers to a continuous phase within which a second phase is dispersed. Propagation in dispersed @stems has been reviewed by McClements & Povey ( 1987~) and those conclusions are briefly reviewed here. The simplest prescription has been given by Urick (1947), who substituted volume-averaged bulk values for the elastic modulus and density into the velocity equation VI =(1//3/O)“’

(6)

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M. J. W. Covey, D. J. McCIemerlts

where /I is the adiabatic compressibility of the material and p its density. The volume averages which are substituted into this equation are P=P1#+PJl-9) P=Pd+P2(1-9)

where the subscripts 1 and 2 refer to the dispersed and continuous phases respectively; $ is the volume fraction of the dispersed phase. A more general equation for dispersions has been given by Ament (1953). This equation applies provided the dispersed phase is rigid and the ultrasonic wavelength is much greater than the particle diameter. It accounts for viscoelastic scattering but not for thermal scattering and assumes that the particles do not interfere with one another. In this case, the following quantities are substituted into the velocity equation U, = ( l/ #dp)“C P=Po+z

where z= -[2a2#(1

-9)

Q].(Q’+A’)

Q=26(1-$)+9p,/(21’a)+3p2 A = 9p,( 1 + I’a)/( ~I’LI)~ d=p,-PI I- =(qF/nfp)-“z

Here I is the shear wave skin depth at which the amplitude has diminished to l/e of its original value; a, the particle radius; T]~,the shear viscosity; and subscripts 1 and 2 refer to the dispersed and continuous phases respectively. This formula is plotted in Fig. 2 in three-dimensional form to demonstrate that for the region where Ia = 1 then the velocity is frequency dependent and in those regions where this condition does not apply the velocity is frequency independent. Thus, in the region where Ta = 1, the possibility exists of particle-size determination by measuring ultrasonic velocity as a function of frequency. The Ament (1953) formula does not account for other scattering phenomena, such as thermal scattering (which is of importance in submicron water-oil emulsions). The viscoelastic scattering mechanism described by Ament involves motion of the scatterer relative to the fluid continuum in which it is suspended, due to the passage of the ultrasonic wave. In thermal scattering (McClements & Povey, 1989), differences in heat capacity and thermal diffusivity

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Fig. 2. A 3-dimensional plot of ultrasonic velocity against volume fraction $ and log(ra), where r is the shear wave skin depth and a is particle radius. The data are for a bromoform-in-water emulsion at 20°C: the plot is based on the Ament (1953) equation.

between the scatterer and the continuum be scattered.

cause the ultrasound

wave to

Velocity in systems containing bubbles

When p, 4 ,o? then resonant scattering occurs (Gaunaurd & Uberall, 198 1). Near the resonant frequency, given approximately by 0,

=(3p,

v,Z/p2a,)‘i’

the attenuation is sharply increased, and enhanced attenuation appears from zero frequency up to just above the resonant frequency, CO,.Here p, and LJ,are bubble density and ultrasound velocity in the gas bubble, px is the surrounding fluid density and a, is the bubble radius. The velocity is reduced below its value in the surrounding fluid and can be described by the Urick ( 1947) equation (eqn (6)) at frequencies below the resonant frequency, and is highly frequency dependent in the resonant region. At frequencies above the resonant the velocity is the same as in the continuum. At frequencies of the order of 1 MHz, for air in water, very small bubbles of the order of tens of microns in diameter can have large effects at very small volume fractions. This phenomenon is important in industrial ultrasonic applications where small quantities of air are frequently present. This suggests that ultrasonics could be a

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M. J. W. Povey, D. J. McClements

means of measuring the number and size of gas bubbles in liquids and solids. Velocity in concentrated dispersions Examples of such systems in foods include solid foams (aerated chocolate), sediments and slurries, and solid dispersions (sugar in chocolate). When the dispersed phase forms a significant fraction of the total volume, the Ament (1953) equation no longer applies and the Biot theory ( 1962~1,b) may be more appropriate. Biot developed a theory of sound propagation in concentrated dispersions in which the two phases may be interpenetrating. One of the phases is assumed to be fluid. The phases are treated in the first instance as independent, possessing their own equations of motion. The interactions between the phases are introduced as coupling terms between the equations. Whilst this approach cannot account for scattering and is therefore incomplete, it is the only one available for propagation in concentrated systems consisting of one fltid and one solid phase. Johnson & Plona ( 1982) derived an equation for velocity based on the Biot theory and indicate how liquid viscosity may be included in their formula. Scattering arising either from a large acoustical mismatch between the continuous and dispersed phases (as is the case for sugar in chocolate) or from resonant scattering, as described in the previous section for bubbles in water, will lead to a failure of the Ament (1953) model. Velocity of sound in mixtures A widely used empirical expression for the velocity of ultrasound in a mixture, ZI,, is that of Rao ( 1941) where, when mixing two liquids of ultrasound velocities 2/l1 and o, 2

where n is experimentally determined and a,,, is the molar volume (molecular weight divided by density). Discussion of the range of applicability of this and other formulae can be found in Gouw & Vlugter (1967). Javanaud & Rahalkar (1988) have suggested that the Urick equation (eqn (3)) is of use, and Apfel(1986) has applied the Urick concept to the prediction of composition of tissues from measurements of density, ultrasonic velocity and acoustic nonlinear parameter.

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Absorption of sound The most often quoted equation for attenuation, called classical equation: a = 2~%i(3~,~,)

a, in liquids is the so(7)

where o is the ultrasonic radial frequency ( = 24). This assumes that attenuation is solely a product of fluid flow associated with the passage of the ultrasound and the consequent friction owing to the shear viscosity of the liquid, vs. However, as Kinsler et al. (1982) pointed out, this is just one of many possible loss mechanisms. They divided loss mechanisms into three basic types, viscous losses, heat conduction losses and losses associated with molecular exchanges of energy. The attenuation in a wide range of liquids can be explained by these three mechanisms. Slutsky (1981), Lindsay (1982) and Jongen et al. (1986) should be referred to for a more detailed analysis. In fact, only attenuation in a monatomic gas is accurately described by the classical equation (eqn (7)). Attenuation in inhomogeneous media Inhomogeneities introduce the possibility of scattering. A variety of scattering mechanisms exist, the most important in foods being thermal and viscoelastic scattering, described earlier. Viscous and surface tension effects modify the scattering in the case of a liquid continuum. Scattering mechanisms in biological tissues were reviewed by Povey (1988), and this section can give only an outline of this most complicated of subjects. Resonant scattering can be important when there is a large density difference between two of the phases constituting the medium (see Gaunaurd & Uberall, 198 1). Resonant scattering is an example of strong scattering in which the magnitude of the scattered ultrasonic wave is of the same order as that of the incident wave. When all the energy incident on a scatterer is scattered, this may be regarded as a reflection. Distinguishing between weak and strong scattering is important because multiple scattering will have a much greater effect on the ultrasound velocity in the case of strong scattering. This will make the ultrasound velocity and attenuation a complicated function of the frequency and of the number and size of scatterers. In the weak scattering case, ultrasonic velocity is relatively unaffected by multiple scattering in media with quite high concentrations (between 15 and 30% by volume) of the scatterers. Examples of such systems were considered by McClements & Povey (1987a). Multiple scattering occurs when the ultrasound scattered by

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M. J. W. Povey, D. J. McClements

one particle then undergoes subsequent scattering and in consequence increases in importance as the concentration of scatters increases. Allegra & Hawley (1972) provided the most completely developed theory for the attenuation due to inhomogeneity in the case of weak, non-multiple scattering. Their treatment of the subject has been extended to more concentrated oil-water emulsions by McClements & Povey (in press) through the inclusion of multiple scattering. For concentrated dispersions no adequate theory exists. Multiple scattering, particle-particle interaction and hydrodynamic screening all combine to produce a theoretically complicated mechanism. In such systems a phenomenological approach such as that of Biot (19624 b) is all that is available. In the limit when the particle or inhomogeneity dimension is much greater than the ultrasound wavelength, each inhomogeneity must be treated as a distinct region, through which the wave will propagate as a bulk wave or reflected at the boundaries. Attenuation in solids In most homogeneous solids, at room temperature, the dominant absorption mechanism is thermal scattering, although in metals, electron scattering can dominate. Close to a change in phase in a material, such as the transition from liquid to solid which occurs at the melting point, molecular relaxation can be an important absorption mechanism, resulting in an attenuation peak. This description will be modified in the case of inhomogeneous solids, by a variety of the scattering mechanisms described above for the case of dispersions. In addition, the possibility of mode conversion exists, where a compressional wave can change to shear and vice versa. This may occur at boundaries if the angle of incidence of the wave is oblique. Attenuation in gels Although gels are solids, acoustically they behave more like liquids, due to their low rigidity and high but not infinite viscosity. Low shear wave velocities and high shear wave attenuation are characteristic of gels. Compressional wave propagation is normally indistinguishable from that in a liquid. Propagation in moving systems For an extensive review of this subject, see Lynnworth Sanderson (1982).

(1979) and

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Ultrasonics in food engineering - I

F/o wing systems The transit time of a pulse propagating through a moving fluid will be different from that expected from the relationship t = x/u,, where x is distance travelled by the pulse. If the fluid velocity in the direction of propagation is V, then the travel time will be reduced for downstream flow to x/( I/+ z+) and increased for upstream flow to x/( V- Us). By propagating ultrasound in the upstream and downstream directions simultaneously, the flow velocity of the liquid can be determined. If the respective pulse travel times are t, and t2 then, provided U, b V,

and

v= 2 x (t,

- t,)/( t2 + tJ2

In the case when fluid flows at an angle 8 to the ultrasound tion direction (see Fig. 3), the equations for velocity become t, - t2 =

so long as the ultrasound diameter.

s wxty

el v

t

& IY~

2 Vd cos 9/v,

velocity

I

Qi

d .l 2

propaga-

v, B Vcos 19.Here

d

is the pipe

Fig. 3. Ultrasonic determination of fluid flow velocity using two pulse transmission-time measurements. The probes are installed in the pipe wall because the angle must remain constant and signal losses in the pipe wall are eliminated.

When a sound source moves relative to the receiver (Fig. 4), the frequency of the received sound is changed, this phenomenon being known as the Doppler shift. The frequency change, Af, at a frequency fO is given by Af = 2 Vfo cos 8/v, where 19is the angle between the sound beam axis and the direction of movement of the source; V is the velocity of the source and v1 is the velocity of ultrasound. This frequency change is independent of the velocity of the fluid through which the sound propagates. A sound

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M. J. W. Povey, D. J. McClements

Fig. 4. Ultrasonic Doppler determination of fluid flow velocity. The probes are strapped to the pipe, using a fluid to couple the ultrasonic signal to the pipe wail and thence into the liquid. In this case, errors occur due to inaccurate information on the angle, and because the scatterers may not be moving at the same velocity as the fluid.

scatterer, entrained in a flowing fluid, acts as if it were the source of the sound and hence the velocity of the scatterer can be determined from the frequency change arising from its movement. This principle forms the basis for Doppler flowmeters but it should be emphasised that it is the velocity of the scatterer that is detected and this may be equal to or less than the fluid flow velocity. Scattering centres are generally present in liquids, the small changes in density arising from flow inhomogeneities being easily detectable. These inhomogeneities will scatter sound from different parts of the flow. When using pulsed ultrasound, the time between the generation of the pulse and the reception of the scattered ultrasound will depend on the distance x between the transducer and the scatterer. All the scatterers lying at a specific distance x from the transducer will return the ultrasound to the transducer in a time t = 2x/v. By selecting electronically only that part of the scattered ultrasound which arrives close to the time t, corresponding to the distance x, the flow rate in the region around x can be determined from its Doppler shift. A succession of return times can then be selected and the respective Doppler shifts measured to obtain the flow profile. Cross-correlation

In a flowing fluid, density variations usually occur owing to pressure variations arising from nonlinear flow or from entrained gas bubbles or some similar inhomogeneity. These inhomogeneities are usually distributed randomly. The flow rate can be determined from the motion of these inhomogeneities by means of two transducers spaced along the flow (Fig. 5). The signals from the two transducers are compared using a technique called cross-correlation (Lynnworth, 1979), which permits a time interval to be determined equivalent to the time for an inhomogeneity in the flow to pass from one transducer to the next. From this time and the known distance between the transducers, the flow velocity can be computed.

Ultrasonicsin food engineering - I

_ 2

1

L,At

j

V,=h

233

Fig. 5. Cross-correlation ultrasonic measurement of fluid flow velocity. The two probes need not be angled and can be strapped to the pipe. The technique relies on inhomogeneities in the flow which scatter ultrasound and are travelling at the same velocity as the flow.

ULTRASONIC

TECHNIQUES

A general review of ultrasonic techniques in the laboratory was given by Breazeale et al. (198 l), and one of industrial applications was given by Papadakis (1976). Velocity measurement The pulse echo technique The original descriptions of this technique were given by Firestone & Frederick (1946) and Pellam & Galt (1946). A system for making these measurements is depicted in Fig. 6. A schematic representation of the technique was given earlier in Fig. 1. Both velocity and attenuation can be measured. The method and its modifications are the lowest-cost route to ultrasonic measurements and can readily be automated. Equipment is commercially available but is designed for use in metals testing (Schlumberger-Sonatest, Mateval, Wells-Krautkramer and Diagnostic Sonar); direct application to food testing is often complicated. Problems

61 em_--__a_--

t

ansducer ample Fig. 6. Block diagram of the electronic equipment used in pulsed and continuous wave ultrasonic experiments: (a) pulse reflection and (b) radio-frequency burst and continuous wave transmission.

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M. J. W. Povey, D. J. McClements

can arise from the need to match the transducer to the food through adjustment of the acoustic impedance of the probes, difficulties in presenting the sample to the probes, temperature fluctuations in the material under investigation and high attenuation. The main method of determining the pulse transit time relies on detecting the start of the pulse. This technique can suffer from all of the sources of error described later in this review, particularly pulse broadening at the transducer-sample interface. Normally, the arrival time is determined by the detection of a certain percentage of the maximum reflected pulse amplitude. This can be done visually on an oscilloscope or automatically with a timer/counter with a variable trigger level. The timer/counter technique can be refined by using the incoming echo to trigger the outgoing pulse. This constitutes the ‘sing-around method’ in which the pulse-repetition frequency (prf) is inversely related to the velocity of sound. A continuous reading of velocity can be obtained in this way, provided the sample length is known. This technique forms the basis for most commercially available automatic, velocity-of-sound measuring equipment. The accuracy of the technique can be increased by introducing a calibrant into the flow. This method is suited to fluids. A liquid of accurately known velocity (measured by an interferometric technique) is introduced into the cell and the time of flight of a given echo is determined. The liquid should be of a similar acoustic impedance to that of the sample under investigation so that the pulse envelope is similar in the two cases. The receiver amplification is adjusted so that pulse height is the same and the delay time is read off. Errors arising from delays in the transducers, cell walls and electronic system can be eliminated by measuring the delay time between two subsequent echoes, rather than between the transmitter pulse and the first echo. This technique, allied with a calibration, gives the maximum accuracy quoted in Table 2 for the accuracy can be pulse echo technique. Delay time measurement improved by increasing the frequency or by using a cycle-by-cycle matching technique, in which the waveform of the echo is matched against an electronically delayed image of the waveform of the transmitted pulse. The authors have found the arrangements depicted in Fig. 6 to be sufficiently flexible for both pulse and interferometric techniques, and they give an accuracy of better than * O-5 m s-l for liquids. The transmitter is either a Hewlett-Packard 3312A Function Generator (Fig. 6b) or the spike generator of a Balteau-Sonatest UFDl. The function generator can produce sine-wave bursts at frequencies up to 15 MHz and containing one or more cycles. The frequency in the burst can be

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tuned to the resonant frequency of the transducer. Either SchlumbergerSonatest or Mateval highly damped immersion transducers are used in the arrangement shown in Fig. 1, as the whole cell-transducer arrangement is immersed in a thermostatically controlled water bath which also provides the acoustic coupling between the transducer and the glass cuvette. The cuvette is chosen with thin glass walls (1 mm) to mink& ultrasound reflections within the wall, and the width of the cuvette is sufficiently large to eliminate side-wall reflections for all echoes of interest. The cuvettes are manufactured to the authors’ specifications by Chandos Intercontinental Ltd, Cheshire, England. For measurements of ultrasound velocity in solids, ordinary metals testing probes may be used, depending on the impedance of the test material. It is possible to excite flexural modes in the barium titanate disc transducers normally used, and these modes can have frequencies as low as 25 kHz in transducers with a resonant frequency of 500 kHz. These modes can be advantageous if a range of frequencies is required from a single transducer but may be a problem in materials whose attenuation is highly frequency dependent. If unaware of the possibility of receiving a range of frequencies, the user may be deceived into thinking that observed results were obtained at the nominal frequency of the probe, whereas, in fact, the effects resulted from waves of much lower frequencies. Ceramic disc transducers are restricted to frequencies below about 30 MHz; above this, quartz or lithium niobate crystals are required. Pulse echo overlap

By varying the pulse repetition frequency of the ultrasound, the detected pulses resulting from two successive transmitted pulses can be made to overlap. By superimposing the images of the two pulses on an oscilloscope screen an interference pattern can be made to appear which is sensitive to small changes in velocity. This technique will not improve the overall accuracy of the pulse echo technique but will improve its resolution. Errors can also arise from pulse timing errors between subsequent pulses. Pulse interferometer

By lengthening the transmitted pulse, its trailing edge can be made to coincide with a subsequent echo. An interference pattern will be formed, in a similar manner to pulse echo overlap, but because the pattern is formed from interference between echoes in a single pulse train, errors arising from timing between successive pulses will be absent.

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M. J. W. Povey. D. J. McClements

Buffer rod techniques

The use of a buffer rod between the probe and the sample makes it possible (a) to make ultrasonic measurements in hostile environments and (b) to make velocity and attenuation measurements in very small and/or highly attenuating materials. Interference between the pulse reflected at the rod-sample interface and that which has travelled from the further face of the sample provides the equivalent in the buffer rod of the pulse interferometry technique described above. This provides a means of making accurate measurements in very small or highly attenuating materials. Alternatively, by shortening the pulse, ordinary pulse echo measurements can be made. Beam spreading and phase cancellation can be a problem with long buffer rods, phenomena described later in this review. Continuous wave inteiferometry

A standing ultrasonic wave can be set up within a cell containing the sample. This is done by matching an integral number of wavelengths to the cell length. The distance between probe and reflector is varied, at fixed ultrasonic frequency, and the distance corresponding to successive maxima in the standing wave pattern is the wavelength. If the input frequency is known then the phase velocity v=fA can be obtained. Careful experimental design can produce very accurate measurements. It is possible to use a fixed path length sample and investigate the resonances as a function of frequency, although in the authors’ experience it is very difficult to prepare solid food samples to the degree of parallelism and smoothness needed to observe resonances. Rejlectance techniques (1) Shear reflectance. The shear reflectance

technique was described by McSkimin ( 1964) for investigation of the rigidity of liquids and involves either normal or oblique reflection of a shear wave at the interface between a solid and the liquid. Measurement of the reflection coefficient (eqn (4)) allows the determination of the impedance of the liquid, and the oblique reflection method also permits the determination of a phase shift from which both the real and imaginary parts of the rigidity may be obtained. (2) Compressional rej7ectance. The same technique can also be used with compressional waves. It is useful in cases where the sample attenuation is very high, but suffers from the disadvantage of measuring only the boundary layer properties at the solid-liquid interface, rather than a bulk property. A simple application of the technique (Fig. 7) permits the

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detection of the presence of liquid in pipes, drops of liquid trickling down an overflow and foams. A buffer rod can also be used, protruding into a liquid sample. The amplitude of the echo reflected from the far end of the rod can then be measured. It is often not clear what is being measured, however, owing to uncertainties about the penetration depth of the reflected signal and reflection from the rod walls.

Process fluid

t

Fig. 7. Shear-wave probe monitoring of the signal within a pipe wall. The presence or absence of fluid on the inside of the wall will cause a change in signal amplitude.

Attenuation measurements The pulse echo technique By fitting a decaying exponential curve to the peaks of the echoes in Fig. 1, the exponent will give the attenuation in Nepers m- ‘. Nepers are dimensionless units whose magnitude is the distance in meters required for the amplitude of the ultrasonic signal to diminish by a factor of l/e. Care must be taken to eliminate, reduce or account for all the errors described below.

Substitution technique Many of the error sources described in the section on errors can be considerably reduced by immersing the sample in a liquid in which the ultrasound velocity and acoustic impedance are similar to those of the sample. As long as care is taken to ensure that the linear approximation is adhered to, then any change in the amplitude of the ultrasonic signal observed must be a result of absorption or scattering in the sample. This technique is particularly easy to use in the case of liquid samples, as the sample liquid can completely replace the reference liquid and the attenuation coefficient may be calculated by subtracting the signal amplitude in the reference liquid from that measured in the sample liquid. Variations on this technique may lend themselves well to in-line applications. Otherwise, it is likely to be very difficult to make accurate attenuation measurements. The accuracies of various techniques for

M. .I. W. Povey, D. J. McClements

238

TABLE 2 Accuracies of Techniques for Measuring Ultrasonic Velocity and Attenuation Technique

Velocity

Pulse echo Pulse echo with liquid calibrant Pulse echo overlap

1:lO”

Pulse ‘sing around’ Pulse cycle-forcycle matching Buffer rod Pulse interferometer

Attenuation

Breazeale et al. ( 198 I

1:104 l:lOJ-1:lO’

McSkimin & Andreatch (1967) Forgacs ( 1960)

l:lOj-1:lO’ l:lOj-1:4x 1:lOJ l:loJ-l:lox

Reference

lo4

Continuous wave interferometer

1:10X

measuring

velocity

SOURCES

l:lO?-1:lOJ

Papadakis (1964) McSkimin (1964) Williamson & Eden (1970) Del Gross0 & Mader (1972) Inoue et al. (1986) Pierce (1925)

and

attenuation

OF ERROR

Time and distance measurement Obvious sources of error are the measurements of time and distance required to determine velocity. As such measurements are not unique to ultrasonics no further consideration will be given to them in this review. Phase cancellation Detection by piezo-electric probes involves a device having a finite aperture which converts the strain resulting from the pressure wave to a voltage. If the phase of the pressure wave varies across the aperture then different parts of the signal can cancel each other out and the apparent amplitude will be less than the true value. For time of flight measurements this involves a small error but in amplitude measurements the effect can be very severe, increasing at higher frequency. Diffraction A finite source will have an associated diffraction field. This effect can be separated into a near zone and a far zone (Fig. 8). Assuming the trans-

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X

Fig. 8. Ultrasonic pressure intensity plotted against distance away from a disc-shaped transducer radius a. In the near zone, from x = 0 to x = a/A, intensity varies greatly with distance, a, away from the transducer face.

ducer to be a circular piston source of radius a, the near zone extends over a distance of approximately a/L and within this distance the beam is parallel but its amplitude fluctuates widely. Outside the near-field the amplitude falls inversely with distance from the transducer, the wavefront becoming spherical and hence spreading out. The beam spreading angle is sin- ‘(d/4A ). This can have severe consequences for propagation down rods. The spreading beam is reflected at the sides of the rod, eventually returning to the source without ever reaching the end! For attenuation measurements the decay of the signal amplitude with distance must be corrected for this effect. Seki et al. (1956) gave the required correction, and quoted a value of 1 dB per unit of a/L travelled by the beam as a useful estimate of the attenuation owing to diffraction. Diffraction can also occur where multiple reflections are deliberately encouraged; for example, in pulse echo experiments where a series of echoes is produced, thereby eliminating probe and bond delays. However, if the reflecting faces are not parallel, a wedge effect can introduce diffraction because of phase cancellation and beam spreading. Temperature and density fluctuation As I(, G and p. in eqn (1) are all temperature dependent, u1 can be expected to depend on temperature. Consequently, temperature fluctuations in a flowing liquid can introduce scattering effects and apparent velocity fluctuations. For water, for example, the temperature coefficient of velocity is 3 m s- ’ T-l, so control to within f O*l”c will produce a velocity fluctuation of f 0.3 m s - ‘.

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M. J. W. Povey. D. J. McClements

Dispersion Measurement of velocity involves measurement of either a time of flight over a known or measured distance or of wavelength and frequency, In the first case, the group velocity is obtained; in the second, the phase velocity. In many cases, the velocity is dependent on frequency and then a difference appears between group and phase velocities. This dispersion can be especially severe within a transducer and its bond to the sample and at higher frequencies. The interface between the transducer and the sample Variable delays, pulse broadening, dispersion and change in the transducer resonant frequency are all phenomena associated with the bonding of the transducer to a sample. This bond is necessary for efficient transmission of the ultrasound generated in the transducer to the sample. Care has always to be taken to minimise and account for these errors, as described by McSkimin (1961) and Papadakis (1967). Their effect is more severe and difficult to account for in attenuation measurements than in velocity measurements. Refraction In the case of oblique incidence, changes in the path length of the sound beam due to refraction must be accounted for.

TRANSDUCERS Choice of the appropriate transducer is central to any successful application of ultrasonics. The main transducer materials and some of their properties are summarised in Table 3. TABLE 3

Transducer

Quartz crystal Barium titanate Lead zirconate titanate (PZT ) Polyvinylidene fluoride (PVDF )

Materials and Their Properties PO (kg m-.7

1’1 (kms-‘)

2650 5400 7500 1800

5.74 5.1 4.0 2.2

I%*, (MPasm-‘)

15.2 27 30 4.0

*\ (km s- ‘)

3.8 2.8 2,3 1.04

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For high frequencies, above about 20 MHz, quartz or lithium niobate crystal plates are used and resonated in thickness mode for longitudinal generation. In this mode, the transducer’s faces remain parahel whilst its thickness increases and decreases. The higher frequencies are obtained by operating on overtones. Most transducers in the frequency range 50 kHz to 10 MHz are discs of piezoelectric ceramic, of which lead zirconium titanate is the most popular. For frequencies in the megahertz range, a thin plate is used which resonates in the half-wavelength thickness mode. At lower frequencies a hollow cylinder may be used depending on the directionality required of the transducer. The plate source is normally required to produce ‘short pulses’ of ultrasound so that echoes from objects close together in distance can be resolved. This is particularly important when making velocity measurements using the pulse echo technique. To prevent undue ‘ringing’ of the plate it is normally backed by a solid material which is highly attenuated and acoustically matched to the plate, and thereby absorbs any vibration of the rear face and directs the ultrasonic power forward. Tungstenloaded epoxy resin is a common choice. The ringing of a transducer is analogous to the ringing of a bell as it continues to vibrate for some time after it has been struck. In the case of a transducer the ‘blow’ is struck electrically and the consequent ringing of the transducer can extend the pulse length considerably beyond that desired. The plate source can be matched to the sample in a number of ways: (a) A tungsten-loaded epoxy resin is coated on to the front face of the transducer and the tungsten loading is varied from the front to the back of the coating. This is done in such a way that the impedance varies continuously from that of the transducer crystal to that of the material to be examined. (b) A ‘quarter-wave plate’ - a slab of material whose thickness is exactly one-quarter of a wavelength of ultrasound - may be used to provide an acoustical match between the front and back surfaces. (c) Choice of an appropriate transducer material; polyvinylidene fluoride is a common choice for this purpose where a good impedance match to water is required. The film is easily shaped for focused or wide-angle applications but has poor sensitivity when compared with other transducer materials, thus reducing considerably the generated and detected signal amplitude. Probe design and construction is complicated, and a number of manufacturers (Schlumberger-Sonatest, Mateval, Diagnostic-Sonar, Wells-Krautkramer) provide a range of off-the-shelf probes and some offer a design service.

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CONCLUSIONS The foregoing analysis leads to a number of conclusions regarding properties of interest to the food engineer which may be measurable ultrasonically: ( 1) Bulk modulus, K, and rigidity modulus, G, may be determined by measurements of the compressional and shear wave velocities (eqns ( 1) and (3)) and of the density po. (2) The complex shear viscosity of viscoelastic media may be found by the shear reflectance technique. This reflectance technique can also be used with compressional waves but in that case it is often not clear what is being measured. (3) Scattering experiments can provide information on shear viscosity and thermal diffusivity. (4) Particles suspended in a dispersion may be sized (a) if the density of the two phases is significantly different, (b) if the thermal diffusivity of the two phases is significantly different, and (c) if the dispersion is dilute (volume fraction of the dispersed phase, 9, Q O-4). Particle size determination may be possible in more concentrated systems using empirical methods (see e.g. Ballaro et al., 1980). (5) Reflection at boundaries can provide a means of gauging thickness and depth of acoustically dissimilar layers. Boundary reflections contribute to the images produced in ultrasonic imaging. (6) The temperature dependence of the quantities in eqn ( 1) provides a means by which the velocity of sound measurements can be used to measure temperature. (7) Fluid flow velocity and velocity profile can be determined ultrasonically. Combined with a density measurement, mass flow rates can be determined. (8) Measurement of ultrasound velocity in two-phase systems can provide information about the volume ratio of the phases and compressibility of the dispersed phase.

ACKNOWLEDGEMENTS The authors wish to thank the Ministry of Agriculture, Food and U&ever Research, Colworth Laboratory, support for one of us (D.J.M.).

Fisheries and for financial

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