Ultrasound measurements to monitor the specific gravity of food batters

Journal of Food Engineering 65 (2004) 317–324

www.elsevier.com/locate/jfoodeng

Ultrasound measurements to monitor the specificgravity of food batters

Paul Fox a, Penny Probert Smith a,*, Sarab Sahi b

a Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UKb Campden and Chorleywood Food Research Association, Chipping Campden, Gloucestershire, GL55 6LD, UK

Received 6 August 2003; accepted 19 January 2004

Abstract

This paper describes the design and application of a low cost ultrasound system to monitor the specific gravity of batter as it is

mixed. The quantity of air is believed to be the main factor in determining the quality of the finished product and specific gravity

measurement is common for assessing the quality and progress of the mixing process. A probe is designed to allow measurements in

reflection and the relationship of ultrasound gain to specific gravity determined theoretically and justified experimentally. Operation

was conducted in pulsed mode using a nominally 2.25 MHz, 15 mm diameter transducer. The work may have application to

measurements on industrial sludges in which similar material properties are observed.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: Ultrasound; Bubbles; Aerated foams; Specific gravity

1. Introduction

In this paper we describe steps towards the develop-

ment of an in situ ultrasound system to monitor the

mixing process of food batters and similar thick liquids.

Ultrasound is non-invasive and therefore suitablepotentially to monitor progress in real time. An in situ

system would open a way to feedback control in mixing,

and hence improve quality control of the finished

cooked product. This paper describes early experiments

to determine whether ultrasound can provide suitable

information.

The factors which the industry would like to measure

are user related, for example taste and texture. Unfor-tunately these cannot be quantified easily. In fact it is

unusual at present to make any measurements on the

batter formation. However it is known that the quantity

and distribution of air, especially just the bulk air con-

tent, is one of the most significant factors in determining

quality. Air bubbles affect many aspects of the batter

and of the finished product, including appearance, tex-

ture, consistency and size per unit weight. The presenceof a well-defined volume of gas cells is essential for the

*Corresponding author.

E-mail address: [email protected] (P.P. Smith).

0260-8774/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jfoodeng.2004.01.028

characteristic properties of that particular food (Carlin,

1944; Hodge, Woodward, & Wade, 1972; Mansvelt,

1975).

Bulk air content is assessed most easily through

measuring specific gravity. Rheology is used too to

estimate quality. Rheology again is sensitive to airquantity, as well as to mechanical properties such as

viscosity and elasticity. Whereas specific gravity is a bulk

measurement of air content rheology is sensitive to

bubble size and distribution (Sahi, 1999). However since

the overriding factor for determining quality, given a

certain batter mix and mixing process, appears to be the

total air content, the progress of mixing is determined

most commonly simply through monitoring specificgravity (if indeed it is monitored at all).

Air filled batters can be considered as composed of

two phases: a visco-elastic liquid and air. The mechan-

ical properties of the liquid affect the acoustic properties,

such as velocity, loss and scattering characteristics.

Ultrasound is sensitive too to food composition. For

example velocity measurements have been used by a

number of workers to determine the composition ofemulsions and food products (McClements & Povey,

1992; Saggin & Coupland, 2001).

Ultrasound is particularly sensitive to air content.

Although this is partly because of the marked contrast

between the acoustic properties of air and liquids it is

mail to: [email protected]

Fig. 1. Variation of specific gravity with time as batter is mixed. For

the best results mixing should continue until around 6 min.

318 P. Fox et al. / Journal of Food Engineering 65 (2004) 317–324

especially significant because the air exists as bubbles,and these have an effect far out of proportion to their

volume fraction because of resonance. Air bubbles un-

dergo forced radial oscillations over a wide band of

frequencies around resonance and cause both harmonic

and subharmonic frequency generation. Leighton (1994)

provides a mathematical treatment of bubble resonance

and scattering. The composition of aerated foods may

be investigated using spectroscopy, to find informationon the bubble size distribution (Kulmyrzaev, Cancilliere,

& McClements, 2000).

In this paper we examine the relationship between

ultrasound measurements and specific gravity. One of

the difficulties of aeration is the high attenuation (Morse

& Ingard, 1968) and for this reason a probe was devel-

oped to make measurements in reflection, using as the

source standard low cost immersion transducers oper-ating at high frequency. The relationship between the

gain in reflection (effectively the reflection coefficient at

the batter) and the specific gravity is investigated to

determine the sensitivity and linearity over the region

encountered during the mixing process, both important

for a sensor used in process control.

2. The batter mix process

2.1. Batter recipe

The batter used in this work had the recipe given in

Table 1. A commercial emulsified shortening fat suitablefor a high ratio recipe was used, such as Hedlex (which

can be obtained from Anglia Oils Ltd (UK)). The flour

used was heat-treated, such as Kingfisher (which can be

obtained from ADM (UK)). Mixing was performed

using a laboratory scale Hobart Mixer (with 81 bowl)

fitted with a paddle beater.

2.2. Monitoring bubble formation

Air incorporation within the batter depends on beater

speed and design, batter viscosity and surface tension of

the batter. The efficiency of air retention however, will

Table 1

Recipe used for making high ratio cake batters

Ingredient Concentration (g)

High ratio cake flour 100.00

Castor sugar 115.00

Fat 60.00

Skimmed milk powder 7.00

Salt 2.50

Baking powder 4.00

Water 70.00

Liquid whole egg 80.00

Glycerine 8.00

depend on factors such as the film-forming capacity and

the speed at which air bubbles will rise out of a batter.

The type and amount of emulsifier used can affect

bubble structure and distribution, and these in turn

influence the structure of the final product (Sahi, 1999).

The standard method to monitor specific gravity re-

quires the mixing to be stopped at intervals, a portion ofthe batter to be removed in a measuring cup, and

weighed. Mixing stops when the specific gravity either

reaches a minimum or a particular value (depending on

the mix). Because the method requires intervention, it is

only used when changes in the mix or problems are

anticipated. It is a time consuming and labour intensive

process.

Fig. 1 shows a typical variation in specific gravitywith mixing time using a batter with the recipe above.

Prior to mixing, all ingredients were equilibrated to 21

�C and blended together at a low mixing speed for 90 s

to achieve homogeneity. Measurements were then taken

every 60 s. At each instance a portion of the batter was

removed and the specific gravity was measured using

standard techniques. The gain was then measured on

this portion using the probe. Temperature was moni-tored throughout the process.

The batter relative density was measured using a

calibrated plastic cup of known volume (100 g/cm3 wa-

ter at 21 �C) and a balance (precise to 2 decimal places).

Batter was poured into the cup and excess material re-

moved using a palette knife. Relative density was

accurate to 2 decimal places (1%).

3. Ultrasound measurement on visco-elastic materials

Batter, and many other food stuffs, are often mod-elled as visco-elastic fluids. The propagation of ultra-

sound waves relates to the mechanical properties of

these materials. We can describe the propagation of a

wave travelling at frequency x and wavelength k

P. Fox et al. / Journal of Food Engineering 65 (2004) 317–324 319

through a medium of density q and compressibility jthrough a complex propagation constant k as follows:

k ¼ k0 � jk00 ¼ xffiffiffiffiffiffiqj

p ð1Þ

Typically we might expect to be able to measure three

quantities: wave velocity c, attenuation coefficient a and

acoustic impedance Z. For a wave with low attenuation

these relate to material properties as follows:

c ¼ xk0; a ¼ k00; Z ¼

ffiffiffiqj

r¼ qc ð2Þ

3.1. Velocity and attenuation measurements

Transmission ultrasound can be used to measure

velocity and attenuation. However over the frequencyrange in which low cost immersion transducers are

available the air bubbles cause such high attenuation as

to make transmission impossible.

Tests between 300 kHz and 2.25 MHz confirmed the

difficulty of transmitting ultrasound through batters

over the normal range of low cost transducers. Trans-

mission was observed through the individual ingredients

of the batter, even through flour alone, but as soon asthey were mixed sound could not be propagated even

over a few millimetres. This is believed to be due to the

emulsifiers present which distribute the air uniformly as

small bubbles. This belief is reinforced by the observa-

tion that although the emulsified fat used in the cake

batter blocked ultrasound, when bubbles were removed

through heating the fat and allowing it to solidify,

ultrasound could be transmitted.

3.2. Measurements in reflection: reflection coefficient and

reflection gain

Alternatively measurements may be made in reflec-

tion. The reflection coefficient, C12, for a wave travelling

from medium 1 to 2 depends on the acoustic impedance

of the media and the angles of incidence and refraction

Fig. 2. The construction of the buffer rod. The dashed line sh

according to the following expression (Morse & Ingard,1968):

C12 ¼Z2 cos h1 � Z1 cos h2

Z2 cos h1 þ Z1 cos h2

ð3Þ

where Z1;2 are the acoustic impedances of the media and

h1;2 the angles of incidence and refraction.

The magnitude of the reflection coefficient may be

determined through measuring the ratio of the reflected

wave to the transmitted wave.

The difficulty with using reflection measurements isthe persistence in time of the transmission pulse, which

obscures a small pulse returning. The way to overcome

this is to insert a delay line, commonly called a buffer

rod, between the transducer and the batter, to guide the

pressure wave into the batter under test and ensure that

the transmitted pulse has time to die away before any

reflection returns.

4. Experimental technique to measure reflection coeffi-

cient

4.1. Probe construction

A probe incorporating a buffer rod was designed to

couple the sound from the transducer into the batter. It

used a short hollow buffer rod, made of perspex and

filled with water for low attenuation, as shown sche-

matically in Fig. 2. The end of the probe must be de-

signed to give a well-defined wave front at the batter

interface.

The transducer contacted the water chamber, which isseparated from the batter by means of the perspex

housing. The water transmits a wave with low attenua-

tion. The wave may be assumed to be compressive since

any shear component is small because of the liquid

nature of batter (Leighton, 1994). The housing is ter-

minated in the form of a 45� conical tip such that the

probe enters the batter cleanly without trapping external

ows the path of a typical ray emitted by the transducer.


air bubbles on the outer surface. The angle of 45� en-sures that all components of the sound wave go along

paths of equal length before being reflected back to the

receiver as shown in Fig. 2.

4.2. Transducer and data acquisition

A Cygnus Instruments 2.25 MHz standard immersion

transducer was chosen, since it was readily available and

of reasonable size (15 mm diameter). It was pulsed using

Panametrics 500 PR pulser-receiver.

Measurements were taken using a Hewlett Packard

Infinium 54820 A digital oscilloscope. Amplitude read-

ings were digitised at a sampling rate of 50 MHz, well

above the Nyquist frequency. Readings were taken usingjust the peak voltage of the pulse received and the energy

in the whole pulse. Amplitude was recorded to 1%

accuracy.

Fig. 3 shows how this arrangement separates out the

transmitted and reflected waves when the rod was in-

serted into a typical batter mix, allowing measurement

of the reflection coefficient.

4.3. The reflection gain: wave propagation in the buffer

rod

The measurements are made in terms of a quantity

defined as an acoustic gain in reflection of the system, G.To show how this depends on the batter, we use thestandard model for a plane wave passing between two

media.

Consider a narrow pressure wave of instantaneous

pressure p0. It travels down the water channel to the

water–perspex interface (point (b) in Fig. 2). For a

reflection coefficient Cwp at the water–perspex interface

and (complex) propagation coefficient in water of kwthen the signal received from the pressure wave reflectedat (a) is

u ¼ HCwpp0e�jkw2Lw ð4Þwhere H is the transfer function of the transducer (which

we assume to be matched to water) at the frequency of

interest and 2Lw the total path length in the water.

Fig. 3. Separation of input and reflected pulses.

The wave transmitted forwards at this interface, pbt,towards the perspex–batter interface (point (c)) has

pressure:

pbt ¼ ð1� CwpÞp0e�jkwLw ð5Þ

Following reflection at (c) with reflection coefficient Cpb,

the wave reflected through the perspex across to theother tip face (point (d)), has pressure:

pcr ¼ ð1� CwpÞCpbp0e�j½kwLwþkpLbc ð6Þ

where Lbc is the length from point (b) to point (c), and

kp the propagation coefficient in the perspex. At this

point the wave is reflected again, back to the transducer

with the same reflection coefficient so the pressure wave

incident at point (e) is

pei ¼ ð1� CwpÞC2pbp0e

�jðkwLwþkpLpÞ ð7Þ

where Lp is the total path length in the perspex.

Following further reflection at (e) with reflection

coefficient �Cwp the signal received at (f) is

y ¼ Hð1� C2wpÞC2

pbp0e�jð2kwLwþkpLpÞ ð8Þ

where Lp is the total path length of the wave in the

perspex. Hence defining the probe gain G2 as the ratio ofjyj to juj

G2 ¼ð1� C2

wpÞC2pbe

�k00pLp

Cwp

ð9Þ

where k00p is the imaginary part of kp.In this equation the only term depending on the

batter properties is Cpb. We define m0 to include all other

factors such that

m20 ¼Cwp

ð1� C2wpÞ

e�k00pLp ð10Þ

m0 is then independent of the batter properties. Hence we

can relate the gain to the reflection coefficient at the

boundary:

G2 ¼ Cpb

m0

� �2

ð11Þ

If we consider typical values of acoustic impedance of

liquids and solids (Onda Corporation, 2003), it is rea-

sonable to assume that the reflection coefficient Cpb is

negative. For convenience we take G positive, so that

G ¼ �Cpb

m0ð12Þ

4.4. Initial measurements

As the air content of the batter increases (specificgravity decreases), we expect the gain to increase since

the acoustic impedance of air is much lower than that of

liquids and solids. To investigate the variation with

Fig. 4. Variation of grain with time as batter is mixed on the left; variation with specific gravity on the right.


specific gravity, a batch of the standard cake batter was

used.

Fig. 4 shows the variation in ultrasound gain at dif-

ferent frequencies for a typical high fat batter mix, and

its relationship to specific gravity. We see the anticipated

increase in gain with time, and an inverse relationship

between gain and specific gravity.

4.5. Errors in the experiment

As described above, the specific gravity is measured

to approximately 1%, and the amplitude of the reflected

wave also to around 1%. However further error isintroduced by two factors. First it has been assumed in

the derivation above that only compression waves are

excited in the batter, whereas in fact there will be a small

amplitude shear wave as well. In addition too there will

be some spread in the path length within the buffer rod

because of imperfections in the construction, and

divergence of the acoustic source. However the cali-

bration procedure described in the next section shouldeliminate the systematic errors.

5. Relationship between gain and specific gravity

The results above show a mono-valued relationship

between gain and specific gravity, suggesting that gain

measurement is a possible method to estimate specific

gravity. In addition, over the early stage of mixing in

which specific gravity is changing fast, the region of

interest, Fig. 4 shows that the gain is sensitive to thechange in mixture. In this section we investigate the

relationship in more detail.

5.1. Reflection at the perspex–batter boundary

Consider the magnitude of the reflection coefficient atthe perspex–batter boundary. We can write the reflec-

tion coefficient Cpb, in terms of the properties of perspex

and batter (Morse & Ingard, 1968).

From Eq. (3):

Cpb ¼qbcb cos hp � qpcp cos hb

qbcb cos hp þ qpcp cos hb

ð13Þ

Rearranging the right hand side:

Cpb ¼cos hpqpcp

� cos hbqbcb

cos hpqpcp

þ cos hbqbcb

ð14Þ

We define new variables, db which depends only on the

propagation in the batter and mp which depends on

propagation in the perspex:

db ¼cos hb

cbð15Þ

mp ¼cos hp

qpcpð16Þ

Then we can rewrite Eq. (13):

Cpb ¼mp � db

qb

mp þ dbqb

ð17Þ

Rearranging this expression using the relationship

Cpb ¼ �m0G from Eq. (12):

qb ¼db

mp

1� m0G1þ m0G

ð18Þ

This equation relates the gain and the specific gravity, Sbthrough qw, the density of water.

Sb ¼db

mpqw

1� m0G1þ m0G

ð19Þ

where Sb ¼ qb=qw.

Unfortunately this expression does not allow us to

relate the specific gravity to the gain directly, since db

depends on specific gravity too. The next stage in the

analysis develops an expression for db through two

stages:

• relating the velocity of the batter to the volume frac-

tion of bubbles,

• relating the variable db to density and hence specific

gravity using this expression for velocity and Snell’s

law.


We assume throughout that only one type of wave isexcited in the batter (the compression wave) as discussed

in Section 4.

5.2. Velocity in the bubbly batter

First consider the velocity of sound in the mixture.

Studies on sound velocity in emulsions and in tissue

composition have used the mixture law (McClements &Povey, 1992; Sehgal, 1993). However in aerated foams

such as the batter, the air bubbles act as resonators and

have an effect much greater than the mixture law would

predict over about two decades of frequency.

The ultrasonic behaviour of bubbles of radius r in a

liquid depends on their adiabatic stiffness, jðrÞ, the

damping of the bubble motion bðrÞ, and the inertial

mass mðrÞ. In water at atmospheric pressure they reso-nate at a natural frequency (the Minnaert frequency)

approximately equal to 3r Hz (Leighton, 1994). We can

assume that in batter the frequency is of the same order,

since there is a significant water content.

Consider a liquid containing a population of bubbles

with radius described by the probability density func-

tion pðrÞ. Feuillade (1996) shows that, provided the

specific gravity of the liquid ql and the bubble filled li-quid are not too different, the velocity of ultrasound in

the bubble filled liquid, cb is related to the velocity in

the bubble free liquid, cl according to the following

expression:

1

c2b¼ 1� x

c2lþ sðrÞql ð20Þ

where

sðrÞ ¼Z 1

0

f ðrÞpðrÞdrjðrÞ � x2mðrÞ þ ixbðrÞ ð21Þ

In this equation f ðrÞ is the fractional volume of bubbles

with radius r and x is the fractional volume of all bub-bles.

Consider now the group of bubbles in the batter

over the batter development. Measurements show

that the radius of bubbles is between around 10 and

100 lm, corresponding to a range of resonant frequen-

cies from tens to hundreds of kHz. The excitation at

2.25 MHz is therefore a decade away from the natu-

ral frequency of the smaller bubbles. Although reso-nance effects are probably still significant, we would

expect properties not to change too fast with radius even

near resonance. Therefore we assume that the denomi-

nator in Eq. (21) remains constant over the batter for-

mation.

Therefore noting that

x ¼Z 1

0

f ðrÞpðrÞdr ð22Þ

we can rewrite Eq. (20):

1

c2b¼ 1� x

c2lþ xqls0 ð23Þ

where

s0 ¼1

j0 � x2m0 þ ixb0ð24Þ

where j0, m0, b0 represent typical average values. s0 is infact the compressibility of the bubble population (Feu-illade, 1996).

This equation establishes a linear relationship be-

tween sound velocity in the aerated batter, cb, and the

volumetric fraction of air bubbles. Note its similarity to

the mixture law referred to earlier.

To apply these results to the experiments, it is more

convenient to deal with the change in volumetric frac-

tions, Dx over the mixing process. Assuming that westart with volume fraction x01

c2b¼ 1� x0 � Dx

c2lþ ðx0 þ DxÞqls0 ð25Þ

Hence

1

c2b¼ 1

c2b0þ Dx qls0

�� 1

c2l

�ð26Þ

where the batter velocity before mixing is cb0.Fuller studies of the behaviour of bubbles in visco-

elastic liquids are presented by Allen and Roy (2000a,

2000b).

5.3. Relationship between db and specific gravity

Now return to Eq. (15) which defines db.

In Eq. (15):

db ¼cos hb

cbð27Þ

Using the trigonometric relation: cos2 hb þ sin2 hb ¼ 1:

d2b ¼

cos hb

cb

� �2

¼ 1

cb

� �2

� sin hb

cb

� �2

ð28Þ

Using Snell’s law at the perspex–batter interface the

unknown batter velocity is described in terms of the

(known) perspex velocity and angle of incidence:

sin hb

cb¼ sin hp

cpð29Þ

Hence substituting in Eq. (28):

d2b ¼

1

cb

� �2

� sin hp

cp

� �2

ð30Þ

We can now substitute from Eq. (26) for cb:

d2b ¼

1

c2b0þ Dx qls0

�� 1

c2l

�� sin hp

cp

� �2

ð31Þ

Fig. 5. Variation of db with time as batter is mixed.


Now define a constant A:

A ¼ qls0 �1

c2lð32Þ

and define db0 as the initial value of db at the start of

mixing. Then

db ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffid2b0 þ ADx

qð33Þ

¼ db0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ ADx

d2b0

!vuut ð34Þ

Because Dx is small, we assume that changes in db are

small so we can approximate the square root by the

binomial expansion:

db � db0 þ1

2

ADxdb0

ð35Þ

Therefore according to this simple model we expect db tovary linearly with the volumetric proportion of air, x,and hence the specific gravity.

Therefore overall, we expect a linear relationship

between db and density, since density varies linearly with

air quantity. We postulate that we can define constants

a, b such that

db ¼ ða þ bqwSbÞ ð36Þwhere the specific gravity, Sb ¼ qb=qw.

5.4. Final stage

Finally we use this expression in Eq. (19):

Sb ¼a

mpqw1þm0G1�m0G

� � b

ð37Þ

All the terms relating Sb and G now depend only on the

probe design and initial batter conditions. Therefore

provided these can be determined, and are stable be-

tween different instances of the batter, this equation can

be used to determine Sb from a measurement of G.A number of assumption have been made in deriving

this expression. In the next section we examine its

validity empirically.

Fig. 6. Variation of specific gravity with grain (calibrated). The squares

show measurements and the solid line the fitted data.

6. Experiments

6.1. Investigation of linearity relation

The expression above suggests that the specific

gravity can be determined from probe gain, provided a

calibration procedure can be determined. However a

number of assumptions have been made in the deriva-tion, especially in terms of linearity. To examine these

over the region of interest, the validity of Eq. (36) was

tested through experiment. A portion of batter was

mixed and the specific gravity measured at intervals. At

each interval the gain, G, was measured too and db

calculated from Eq. (19) using this value together with

the specific gravity measured.

Fig. 5 plots the measured values of the specific gravity

measured against db (squares), together with a least

squares linear fit. These experiments support the

assumption of linearity.

6.2. Calibration and repeatability

The values of the constants in Eq. (37) were deter-

mined through calibration. Those depending on the

probe can be determined through using the probe on a

known liquid (such as degassed water). Those depending

on the initial batter (a and b) were determined throughfitting calibration data to measurements of gain and

specific gravity using a least squares fit. Results are

shown in the top curve of Fig. 6.

The lower curve in this figure shows measurements on

a different batch of batter using the same recipe. The

solid curve is drawn using the values of the calibration

constants from the first batch. It can be seen that the


calibration is consistent between the two instances of thebatter. This suggests that it is indeed valid to use the

same calibration across different instances of batter mix

to the same recipe although a larger number of batches

is needed for full validation. A new set of calibration

constants would be required for each recipe.

It is also worth noting that the relationship between

gain and specific gravity (not just db and specific gravity)

is reasonably linear over the region of interest, a usefulfeature in terms of probe performance.

7. Discussion and conclusions

The buffer rod proved successful as a technique to

measure properties at the interface to a high viscosity,

air filled mixture which did not support significanttransmission. Early results suggest that specific gravity

may be estimated from the probe gain over the region of

interest for mixing, and that the relationship is close to

linear. This implies that the probe is well suited as a

feedback sensor in a control system. Digital filtering of

the measurements would be required to remove the ef-

fect of the mixer periodicity. Because the time scale of

mixing is long compared with the settling time ofacoustic waves, high order filters could be used, resulting

in high quality filtering.

A number of areas remain to be examined. The

foremost of these is the extent to which reflection coef-

ficient is useful to investigate bulk properties, since pri-

marily it measures effects at the interface. Certainly

longer buffer rods could be used to penetrate further

into the batter, and a range of materials studied. Theflow of batter over the rod needs to be examined to

ensure that a static layer does not build up. Repeat-

ability too is an issue and a larger sample is required to

assess the consistency and repeatability of the technique.

Work is continuing in these areas.

Acknowledgements

This work was funded by DEFRA Bridge Link Grant

FQS-21. The authors are grateful to Dave Cartwright

from Cygnus Instruments Ltd, Dorchester, UK for thesuggestion of a buffer rod and for the loan of the probe

transducer. Also to Paul Catterall and Dr Terry Sharp

at Campden and Chorleywood Food Research Associ-

ation for their assistance with experimental proce-

dures. Final data analysis was completed under grant

26-01-0178 from the Danish Science Foundation, Den-

mark.

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Ultrasound measurements to monitor the specific gravity of food batters

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