International Dairy Journal 18 (2008) 1222

Determination of water droplet size distribution in butter: Pulsed eld

gradient NMR in comparison with confocal scanning laser microscopy
Katrien Van lent
a
, Brecht Vanlerberghe
b
, Patrick Van Oostveldt
c
,
Olivier Thas
d
, Paul Van der Meeren
a,
a
Particle and Interfacial Technology Group, Faculty of Bioscience Engineering, Ghent University, Coupure Links 653, B-9000 Ghent, Belgium
b
Campina Milk Fat Products NV, Klerkenstraat 92-94, B-8650 Klerken (Houthulst), Belgium
c
Department of Molecular Biotechnology, Faculty of Bioscience Engineering, Ghent University, Coupure Links 653, B-9000 Ghent, Belgium
d
Department of Applied Mathematics, Biometrics and Process Control, Faculty of Bioscience Engineering, Ghent University,
Coupure Links 653, B-9000 Ghent, Belgium
Received 7 December 2006; accepted 3 July 2007
Abstract
The size of the water droplets in butter determines its microbial stability and sensorial properties. In this work, two techniques to
determine the water droplet size distribution in butter were compared, namely confocal scanning laser microscopy (CSLM) and pulsed
eld gradient nuclear magnetic resonance (pfg-NMR). Six commercial butters from different manufacturers were studied. CSLM proved
to be a good method to obtain visual information on the microstructure of the butter, but its limited resolution makes it less suitable for
the accurate determination of droplet size distributions containing an important fraction of submicron particles. pfg-NMR gives no
visual information, but sample preparation, measurement and data analysis are less time consuming. This method yields reproducible
quantitative information. However, the accuracy depends on the correctness of the assumptions made. For all samples, except the one
containing the biggest droplets, signicantly different results were obtained by both techniques.
r 2007 Elsevier Ltd. All rights reserved.
Keywords: Butter; Water droplet size distribution; pfg-NMR; CSLM
1. Introduction
According to the EC Council regulation No. 2991/94,
butter is a water-in-oil emulsion that consists of minimum
80% of milk fat, maximum 16% of water and a maximum
dry non-fat milk material content of 2%. As the water
droplet size distribution determines the microbial stability
(Gould, 1995) as well as the avour release (Dickinson &
Stainsby, 1982), its experimental determination is of
technological importance. A fast and efcient method to
determine the water droplet size distribution would there-
fore be very valuable.
Some conventional techniques, such as laser diffraction,
are unsuitable for the determination of the water droplet
size distribution in butter, since part of the continuous fat
phase of butter is in a solid state. Though time consuming,
microscopy offers some possibilities. Analysis of light
microscopic images is possible, but the required thin
sample slices limit the detectable droplet size (Fourel,
Guillement, & Lebotlan, 1995). Confocal scanning laser
microscopy (CSLM) offers the possibility to image a very
thin sample section, without having to cut the butter in
thin slices. This technique has been used in the food
research on water-in-oil emulsions (Blonk & Vanaalst,
1993; Van Dalen, 2002; van Duynhoven et al., 2002;
Vodovotz, Vittadini, Coupland, McClements, & China-
choti, 1996). Blonk and Vanaalst (1993) have described the
use of CSLM to visualise the microstructure of food
products, including butter. Van Dalen (2002) evaluated
the reliability of CSLM as a method to determine the
water droplet size distributions of margarines with a fat
content ranging from 40% to 80%. Only for high fat
contents were the CSLM results in good agreement with
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doi:10.1016/j.idairyj.2007.07.002

Corresponding author. Tel.: +32 9 264 60 03; fax: +32 9 264 62 42.
E-mail address: Paul.VanderMeeren@UGent.be (P. Van der Meeren).
the results obtained by nuclear magnetic resonance (NMR)
spectroscopy.
Pulsed eld gradient (pfg)-NMR systems to measure
water droplet size distributions typically operate at low
magnetic elds. The method was rst described by
Packer and Rees (1972). It is based on the restricted
diffusion of the liquid inside a droplet and generally
assumes a log-normal droplet size distribution. During the
last decades, other researchers have improved the method
of Packer and Rees for margarines and low-calorie spreads
(Balinov, Soderman, & Warnheim, 1994; Vandenenden,
Waddington, Vanaalst, Vankralingen, & Packer, 1990).
The main advantage of pfg-NMR is the simple and non-
perturbing sample preparation. However, the lack of
reference techniques to validate this method slows
down its application as a standard tool in research and
industry (Vodovotz et al., 1996). Van Duynhoven et al.
(2002) also compared pfg-NMR results for the water
droplet size distributions with the distributions obtained by
CSLM for margarine with a fat content ranging from 40%
to 80%. In contrast to the ndings of van Dalen (2002),
they concluded that both methods produced equivalent
results.
For butter, no comparison between pfg-NMR and other
techniques to determine the water droplet size has been
found in literature. The physical composition of butter and
margarine differs, since the different production methods
used will lead to different microstructures. Moreover,
butter is less homogeneous and has a more complex
chemical composition than to margarines (Dickinson &
Stainsby, 1982). Therefore, techniques that have
been validated for margarines, like pfg-NMR, are not
necessarily suitable for butter, as they depend on the
chemical characteristics of the sample. Since the water
droplet size distribution determines the microbial stability
of butter, a fast method to determine it would be very
welcome in the milk fat industry. Therefore pfg-NMR
and CSLM were compared in this work for their ability
to determine the droplet size distribution of different
commercial butters.
2. Materials and methods
2.1. Butter, milk fat, fat spread and serum samples
Six different non-salted commercial butters with a fat
content of 82% were bought in a supermarket. For ve of
these butters, the production process is not specied
(and therefore presumably continuous), whereas for one
butter, butter B, packaging indicates a batch churning
production process. A commercial fat spread (fat content
38%, pure vegetable) was also bought in a supermarket.
Butter and fat spread serum was obtained by melting the
butter or fat spread (4550 1C) and centrifuging it at 2800 g
during 20 min, after which the serum is the lower phase.
Anhydrous milk fat (AMF) and its low (melting point
13 1C) and high (melting point 42 1C) melting fractions as
well as skim milk were obtained from Campina Milk Fat
Products NV, Klerken, Belgium.
2.2. Confocal scanning laser microscopy
2.2.1. Staining procedure
For the staining of the butter samples, 5 mL plastic
syringes were used, of which the top was cut off. This
syringe was pushed in the cooled (57 1C) butter sample,
and carefully taken out again with the plunger immobi-
lized. Then, the butter sample was partly pushed out of the
syringe and was cut at the syringe opening with a
polyamide sewing thread to have a at butter surface.
Subsequently, the syringes with butter were left to hang in
a staining solution for at least 24 h at 6 1C. The different
staining solutions used were (a) 0.01% Nile Red
(Sigma-Aldrich Inc., St. Louis, MO, USA) in Hozol
(High Oleic Sunower Oil, Contined B.V., Bennekom,
the Netherlands), (b) 0.01% Nile Red (Sigma-Aldrich) in
the olein fraction of butterfat, (c) 0.05% Rhodamine 6G
(Janssen Chimica, Beerse, Belgium) in demineralized
water and (d) 0.03% Acridine Orange (George T. Gurr
Ltd., London, UK) in demineralized water. After 24 h,
the sample was taken out of the staining solution, the
excess solution at the butter surface was removed by
holding an absorbing paper at the edges of the surface
and a cover glass was put on the butter surface. Finally,
the butter sample with cover glass was carefully pushed
out of the syringe. During sample preparation, the
temperature should not exceed 20 1C, since the butter
structure will be altered if a signicant part of the milk
fat melts.
2.2.2. Imaging procedure
Visualization of the stained butter was carried out with a
Nikon Eclipse TE300 (Analis, Belgium) epiuorescence
microscope connected to a Biorad Radiance 2000 (Bio-Rad
Laboratories, Belgium) confocal system. A plan corrected
40 oil microscopic objective (NA 1.3) was used. Digital
images were acquired with Lasersharp 2000 software
under Windows 2000. Nile Red was excited by a 543 nm
green heliumneon laser and its uorescence was
detected with a photomultiplier tube through a 570LP
lter. Acridine Orange was excited by a 488 nm argon-ion
laser and detected through a 515/30 lter, while reection
of the 543 nm green He/Ne laser was detected through a
528/50 lter. The confocal microscopy imaging was
performed in an air-conditioned room (1820 1C). For
every commercial butter, three samples were prepared and
for each sample ve images were taken on different
positions at the sample surface. These positions were
chosen at random, after which the depth of imaging
was selected. This was typically 512 mm from the cover
glass, deep enough to avoid the artefacts at the sample
surface, but not too deep so that a sufcient contrast
between the black droplets and the uorescing fat matrix
was obtained. Unless stated otherwise, the resulting images
ARTICLE IN PRESS
K. Van lent et al. / International Dairy Journal 18 (2008) 1222 13
were the mean of three scans and the dimensions of
these images were 99 mm124 mm (pixel size 0.10 mm, real
pinhole diameter 3 mm).
2.2.3. Image analysis
The processing and analysis of the CSLM Nile Red
uorescence images to determine the distribution of the
water droplets was carried out with ImageJ 1.34i Freeware
(Abramoff, Magelhaes, & Ram, 2004). When necessary, a
pseudo ateld lter (mean lter kernel size 150) was used
to correct the images for non-uniform illumination.
Subsequently, white spots in the black droplet sections
were lled with the command ll holes. For calculations,
the section thickness was assumed to be innitely small.
2.3. Pulsed eld gradient NMR
The pulsed eld gradient nuclear magnetic resonance
(pfg-NMR) experiments were performed on a Bruker
Minispec mq (Ettlingen, Germany), operating at 20 MHz
equipped with a PH20-10-25-RVGX probe at 5 1C. The
glass sample tubes with an inner diameter of 8.8 mm were
lled up with 1 cm of sample. The Diffusio Application
was used for the measurement of the diffusion coefcients,
whereas the Water Droplet Size Application V1.1 rev 2
provided data to determine the water droplet size distribu-
tion in butter. A constant gradient strength g of 2 Tm
1
was used at a gradient pulse width d varied automatically
between 0.1 and 5 ms. For each butter, three samples were
measured with eight gradient pulse widths d, which were
determined automatically by the system so that the eight
measured signals M
g
/M
0
had a value of minimum 15% and
maximum 96%.
2.4. Statistical comparison between NMR and CSLM
results
The particle size distributions of the water droplets in the
different types of butter were assumed to be log-normal.
Eq. (1) describes a volume-weighted log-normal distribu-
tion F as a function of particle diameter d. F(d) is
characterized by the volume-weighted geometric mean
diameter

D
3;3
(nomenclature of Alderliesten, 1991) and
the geometric standard deviation s
g
. The number-weighted
geometric mean diameter

D
0;0
can be calculated with
Eq. (2) (Alderliesten, 1990):
Fd
1
d ln s
g

2p
p exp
ln d ln

D
3;3

2
2 ln
2
s
g

, (1)
ln

D
0;0
ln

D
3;3
3ln
2
s
g
. (2)
To statistically compare the resulting volume-weighted
log-normal distributions for both methods on the same
butter, the covariance matrices have to be taken into
account, which were estimated as 2 [Hessian matrix]
1
.
The Hessian matrices were computed by the nonlinear
optimization algorithm used. Let y and C be matrices as
dened in Eqs. (3) and (4):
y

D
3;3 cslm
s
g cslm

D
3;3 nmr
s
g nmr

, (3)
C
1 0
0 1
1 0
0 1

. (4)
The null hypothesis of equality of the two log-normal
distributions can then be expressed as
C y

D
3;3 cslm

D
3;3 nmr
s
g cslm
s
g nmr

0
0

. (5)
This is a general linear null hypothesis that can be tested
by means of a Wald test (see e.g., Johnson & Wichern,
1998). For this test, we need the covariance matrix S of
^
y
(the least squares estimator of y), which is a 4 4 matrix
VAR
^
y S
VAR
^

D
3;3 cslm
; ^ s
g cslm

0 0
0 0
0 0
0 0
VAR
^

D
3;3 nmr
; ^ s
g nmr

.
(6)
The covariance matrix S
C
of C
^
y (the least squares
estimator of Cy) is then expressed in
VARC
^
y S
C
C S C
t
. (7)
The test statistic T (Eq. (8)) then has a w
2
2
null distribution.
The hypothesis will be rejected when T45.99, on a 5%
signicance level,
T C
^
y
t
S
1
C
C
^
y. (8)
3. Results and discussion
3.1. Determination of water droplet size distribution in
butter with CSLM
3.1.1. Optimization of the staining procedure of butter for
CSLM
Different uorescent dyes were used to stain the butter.
The selection of these dyes was based both on there ability
to interact with specic components in the butter and on
their ability to be excited by the laser wavelengths of the
confocal system.
Rhodamine 6G (absorption maximum at 525 nm) and
Acridine Orange (absorption maximum at 490 nm) were
tested to stain the water droplets in butter. Fig. 1 shows that
both dyes are able to diffuse through the continuous fat
phase and accumulate inside the water droplets. However,
the uorescence of Rhodamine was not evenly distributed
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K. Van lent et al. / International Dairy Journal 18 (2008) 1222 14
inside the droplets nor between droplets. This is probably
due to an uneven distribution of proteins inside the water
phase. Acridine Orange showed a similar behaviour, though
to a much lesser extent. The uneven distribution of the
uorescence of the water-soluble dyes in the droplets makes
it difcult to perform image analysis on these images.
Nile Red (absorption maximum at 520 nm) is an
excellent dye to stain the liquid fraction of the fat phase
in butter, which leaves the water droplets as non-
uorescing regions (Fig. 2a). First, the low melting fraction
of butterfat was evaluated as solvent for Nile Red, but the
resulting staining solution partly crystallized at the staining
temperature of 6 1C. Therefore, high oleic sunower oil was
used as a substitute, which was easier to handle and did not
show an inuence on the butter microstructure.
In order to discriminate between water droplets and air
bubbles in butter, a double staining procedure was
developed. Different methods were tested to stain the
butter sample, with both the water-soluble Acridine
Orange and the water-insoluble Nile Red. A staining of
24 h with Nile Red, followed by a 24 h contact of the
sample with the Acridine Orange solution, did not provide
a good contact of the sample surface with the cover glass.
When the staining with Acridine Orange was done prior to
the staining with Nile Red, the contact of the sample with
the cover glass was excellent, because of the oil present in
the Nile Red staining solution. The high concentration of
Nile Red in the lm of oil between the sample and the cover
glass did not cause problems during confocal microscopy.
By sequential detection of their uorescence (Fig. 2a
and b), it is possible to obtain an image in which the
uorescence of both dyes can be visualized (Fig. 2d).
Deeper in the sample, only the uorescence of Nile Red
was seen, since it diffuses deeper in the sample than
Acridine Orange (images not shown). Although fresh
butter can contain up to 5% of air, mostly visible
microscopically as air cells (Dickinson & Stainsby, 1982),
no air bubbles could be observed in the studied CSLM
images of butter. Most particles in the images had a
spherical shape, and no water channels connecting water
droplets could be detected.
Since fat in butter is partly crystallized at the tempera-
ture prevailing during the imaging procedure (1820 1C),
reection was also evaluated to see if it could provide
extra information on the fat crystal microstructure of
butter. This extra information turned out to be
minimal. A continuous crystal network in the fat phase
could not be seen (Fig. 2c), which might be due to
the relatively high temperature (i.e., 1820 1C) at which the
butter was examined. The strongest reection in the
samples was seen at the water droplet surfaces (arrows
in Fig. 2).
3.1.2. Optimization of CSLM image analysis
Confocal microscopy offers the possibility to look at
different levels inside the sample, which gives three-
dimensional information on the microstructure of the
sample. Hereby, sections of water droplets are seen in these
images, because the optical section is thinner than the
droplet sizes. The diameters of these droplet sections are
equal to or smaller than the actual droplet diameter. From
the CSLM images, a distribution of section diameters can
be obtained, which in turn contains information on the
actual droplet size distribution.
As explained before, uorescence of water-soluble
dyes was not suitable for image analysis. Images
taken deeper in the butter samples show a lot of shading
effects as demonstrated by van Dalen (2002), which hinder
the threshold of the images. Therefore, two-dimensional
Nile Red uorescence images were used to determine
the distribution of section diameters of water droplets
in the butter. The uorescence of Nile Red from outside
the focal plane might cause an underestimation of the
section diameters, in particular for the smaller droplet
ARTICLE IN PRESS
Acridin
10 m
Acridine Orange 10 m Rhodamine 6G
Fig. 1. CSLM images of butter stained with different water-soluble dyes.
10 m
a b
d
c
10 m
10 m 10 m
Fig. 2. CSLM images of butter showing (a) uorescence of Nile Red in the
fat phase, (b) uorescence of Acridine Orange in the water droplets, (c)
reection and (d) the combined image of images a, b and c in red, green
and blue, respectively (the arrows show droplet surfaces with strong
reection).
K. Van lent et al. / International Dairy Journal 18 (2008) 1222 15
sections, but according to van Dalen (2002), the effect
on the resulting volume-weighted mean diameter is
limited.
In accordance to the EC Council regulation mentioned
before, these butters should contain approximately 16%
water. This water fraction was tested as a criterion to set
the threshold level (16% black). However, in most images
smearing occurred for an important fraction of the
particles (image B in Fig. 3, threshold image at the left),
whereas an underestimation of the smaller section dia-
meters was observed in other images (image A in Fig. 3,
threshold image at the left). Therefore, the threshold level
was set manually to obtain maximal information without
smearing of particles occurring (Fig. 3, threshold images at
the right).
Image analysis was carried out, in which edge particles
and particles with a surface area smaller than 36 pixels were
excluded (Fig. 4ac). The latter corresponds to the area of
a circle with a diameter of 0.65 mm, i.e. about three times
the lateral resolution of the microscope. From the area of
the particle sections, the corresponding section diameters
were calculated, assuming that they were perfect circles.
The ve images that were analysed for each butter sample
provided together 13005000 particles. The resulting
section diameters of each sample were put in a histogram
with a class width of 0.1 mm (Figs. 4d and 5). The
normalized section diameter distributions resulting from
all these histograms show very little differences between
different butters (inset in Fig. 5). Due to the limited
resolution of the microscope, the rst class that contained
data was 0.650.75 mm, which also contained the highest
number of section diameters for all samples. Unfortu-
nately, since no information on section diameters below
0.65 mm can be obtained by CSLM, this implies that the
modal value for the observed section diameter distributions
was not known.
3.1.3. CSLM data analysis
From an initial log-normal droplet diameter distribution,
it is possible to calculate the corresponding section diameter
distribution. The relationship between a true particle size
distribution and an apparent section diameter distribution
was rst described by Wicksell (1925). An overview on this
stereological problem is given by Weibel (1980).
For the calculation of the section diameter distribution,
the number-weighted log-normal distribution F

D
0;0
; s
g

was divided into 500 classes (class interval, Dd 0.1 mm,

class mean diameter, D
j
and relative class frequency of
particle diameters, N
P,j
). The relative frequency of sections
diameters N
S,i
between d
i
and d
i
Dd resulting from the
particle distribution can then be calculated with Eq. (9)
(Weibel, 1980):
N
S;i

500
j1
N
P;j

D
2
j
d
i
Dd
2

D
2
j
d
2
i

D
j
! d
i
. 9
This theoretical section diameter distribution, correspond-
ing to a log-normal particle size distribution, was
calculated in order to compare it with the observed section
diameter distribution. Since edge particles were excluded in
the latter, every frequency in the theoretical histogram was
multiplied with a correction factor (Eq. (10)) for the
excluded edge particles:
correction factor
H diW di
HW

. (10)
In this correction factor, d(i), H and W are the class mean
section diameter, the height and width of the images,
respectively. The numerator represents the image surface
area in which the particles in this class are not excluded,
whereas the denominator represents the total image
surface area.
ARTICLE IN PRESS
16% black
Image A
Image B
16% black
20% black
8% black
10 m
10 m
Fig. 3. Two CSLM images of butter F, and their threshold images (left: threshold set to obtain 16% of black pixels in accordance with the water content;
right: threshold set manually after visual inspection).
K. Van lent et al. / International Dairy Journal 18 (2008) 1222 16
For an initial log-normal particle size distribution, the
corresponding number-weighted section diameter distribu-
tion was calculated and through iterations, the parameters

D
3;3
and s
g
of the log-normal distribution were varied so
that the corresponding section diameter distribution
(Fig. 6) tted the experimentally determined section
diameter distribution as good as possible (nonlinear
optimization of the least squares criterion). Because of
the lacking data in classes below 0.65 mm of the observed
distribution, the t is done on the upper tail of the
distribution, not knowing the contribution of this part to
the total area under the distribution curve.
This procedure was executed for all the observed section
diameter distributions of Fig. 5, i.e., three repetitions for
each commercial butter. Of the resulting log-normal
droplet size distributions, the means of

D
0;0
,

D
3;3
and s
g
were calculated (Table 1). The geometric mean diameter
ARTICLE IN PRESS
10 m
Section diameter (m)
0
N
u
m
b
e
r

o
f

s
e
c
t
i
o
n

d
i
a
m
e
t
e
r
s
0
50
100
150
200
250
300
10 m
b a
c
2 4 6 8
d
Fig. 4. Example of CSLM image analysis: (a) the uorescence of Nile Red in the fat phase in a CSLM image of butter D, (b) the threshold image,
(c) the image of particles that were selected for size analysis and (d) the resulting histogram of section diameters (based on ve of these images in the same
butter sample).
0
900
800
700
600
500
400
300
200
100
0 2 3 4 5
BButter A
Butter B
Butter C
Butter D
Butter E
Butter F
N
u
m
b
e
r

o
f

s
e
c
t
i
o
n

d
i
a
m
e
t
e
r
s

Section diameter (m)
1
Fig. 5. Differential distributions of section diameters of droplets in butters
AF, obtained by image analysis of ve CSLM images (99 mm124 mm),
repeated three times for each butter; the insert shows the normalized
distributions.
Diameter (m)
0 1 2 3 4
F
r
e
q
u
e
n
c
y
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
X
X
X
X
XX
X
XXX
X
X
X
XX
XXXX
X
XXXXXXXXXX
X
X
X
observed section
diameter distribution
X
best fitting section
diameter distribution
best fitting number based
lognormal diameter distribution
best fitting volume based
lognormal diameter distribution
Fig. 6. CSLM data t for the histogram in Fig. 4d, including the observed
section diameter distribution (no data o0.65 mm), the best tting
calculated section diameter distribution, and the corresponding number
and volume based particle size distributions.
K. Van lent et al. / International Dairy Journal 18 (2008) 1222 17
and standard deviation of a log-normal distribution are not
independent. Because of this correlation between the two
factors, the covariance matrices for

D
0;0
and s
g
, as well as
for

D
3;3
and s
g
, are added in Table 1.
Distributions with a slightly higher

D
0;0
and lower s
g
or
vice versa gave similar ts to the number based CSLM
data, resulting in a negative covariance of these parameters
(Table 1). This negative covariance is probably due to the
lacking information on section diameters below 0.65 mm
(see above). When converted to

D
3;3
and s
g
, this effect is
inverted, and therefore the covariances of

D
3;3
and s
g
in
Table 1 are all positive.
Table 1 reveals that the resulting geometric number-
weighted mean diameters

D
0;0
are lower than or close to
0.65 mm, the detection limit of this technique. Furthermore,
errors on the measured section diameters occur during
threshold and image analysis. These errors are relatively
higher for smaller particles. Hence, the estimated para-
meters resulting from CSLM should be examined with
precaution.
3.2. Determination of water droplet size distribution in
butter with pfg-NMR
3.2.1. Optimization of pfg-NMR measurements
Before pfg-NMR measurements can be executed, the
diffusion time D has to be chosen at which measurements
take place. Furthermore, the oil suppression delay t
0
needs
to be known, which is necessary to suppress the signal of
protons in the fat phase so that only the water proton
signal is picked up. Measurements were done at 5 1C, to
assure a maximal microstructural stability of the samples.
The parameter t
0
was determined by varying it so that
there was no signal measured with the water droplets
application on a sample of anhydrous milk fat. The
standard t
0
for margarine at 5 1C was 85 ms (Manual
Bruker Optik, 2001), for the butters tested it turned out to
be approximately 70 ms (Fig. 7).
For measurements at 5 1C, the variation of the diffusion
time D in a range of 100210 ms did not have a signicant
effect on the results (results not shown). Therefore, the
default diffusion time of 210 ms was used for further
experiments. Since the upper limit of particle diameters
that still can be detected with pfg-NMR (d
max
) is
determined (Fourel et al., 1995) by the diffusion time D
and the free diffusion coefcient D
S
of the water in the
aqueous phase (Eq. (11)), it follows that for a diffusion
time of 210 ms at 5 1C, this corresponds to a d
max
of 41 mm.
Particles with a diameter lower than approximately 1 mm
cannot be detected either (Fourel, Guillement, & Lebotlan,
1994):
d
max

6D
S
D

. (11)
The diffusion coefcient D
S
of water in the aqueous phase
of the butters at the temperature of measurement was
ARTICLE IN PRESS
Table 1
Parameters

D
3;3
(volume-weighted mean droplet diameter),

D
0;0
(number-weighted mean droplet diameter) and s
g
(geometric standard deviation) of the
most probable log-normal water droplet size distributions in commercial butters AF, acquired by means of a t of a calculated section diameter
distribution to the observed section diameter distribution of CSLM images (n 3)

D
3;3
(mm) s
g Covariance matrix of

D
3;3
and s
g

D
0;0
(mm) Covariance matrix of

D
0;0
and s
g
Butter A 1.85 1.89 6.51E04 5.20E04 0.55 3.47E04 4.16E04
5.20E04 5.11E04 4.16E04 5.15E04
Butter B 6.46 2.86 3.42E01 5.95E02 0.24 1.17E03 3.60E03
5.95E02 1.06E02 3.60E03 1.12E02
Butter C 2.46 1.92 1.63E03 6.35E04 0.67 1.73E04 2.14E04
6.35E04 2.80E04 2.14E04 2.80E04
Butter D 6.72 3.21 6.69E01 1.22E01 0.14 1.21E03 8.22E03
1.22E01 2.31E02 8.22E03 7.27E02
Butter E 3.17 2.38 1.18E02 4.93E03 0.35 5.08E04 1.05E03
4.93E03 2.18E03 1.05E03 2.31E03
Butter F 3.42 2.22 5.32E03 1.70E03 0.51 2.56E04 3.80E04
1.70E03 5.85E04 3.80E04 5.88E04
0
10
20
30
40
50
60
0 50 100 150 200 250 300
Oil suppression delay
0
(ms)
M
g
/
M
0

(
%
)
anhydrous milk fat
low melting fraction
high melting fraction
Fig. 7. Determination of the pfg-NMR signal M
g
/M
0
in the water droplet
size application for anhydrous milk fat and its low and high melting
fractions at 5 1C.
K. Van lent et al. / International Dairy Journal 18 (2008) 1222 18
compared to the diffusion coefcient of water in the
aqueous phase of a commercial fat spread (38% fat
content) and of free water at 5 1C, in order to examine
whether the latter could be used as a good approximation
in the calculations (Fig. 8). The diffusion coefcients of the
water in the aqueous phase of the fat spread and of free
water were comparable, whereas the results for water in the
butter serums were signicantly lower and comparable to
the diffusion coefcient of water in skim milk. Among
butters too, signicant differences could be observed.
Therefore, the calculations were carried out with the
specic diffusion coefcients of each butter, and not with
the diffusion coefcient of water, which is used as a
standard setting for margarine measurements (Manual
Bruker Optik, 2001).
For the three samples of each commercial butter, the
measured pfg-NMR signal with different gradient pulse
widths are shown in Fig. 9. The different butters are clearly
distinguishable.
3.2.2. NMR data analysis
For the data analysis of the pfg-NMR measurements, it
was also assumed that butter contains spherical water
droplets with a log-normal diameter distribution. Non-
spherical water droplets might cause an articial broad-
ening of the size distribution found (Balinov et al., 1994),
but since the CSLM images conrmed the assumption of
spherical water droplets, this was not taken into account in
this study.
For a given distribution, the corresponding NMR signal
was calculated, and by altering the parameters

D
3;3
and s
g
that dene this distribution, the best t to the experimental
data was searched for (nonlinear optimization of the least
squares criterion). To do the comparison of the experi-
mental and the calculated distributions, they were divided
into classes of diameters with a class width of 0.1 mm.
For each class, all particles were assumed to have the
class mean diameter d
i
, and its theoretical pfg-NMR signal
M
g
/M
0
(d
i
) was calculated with Eq. (12) (Murday & Cotts,
1968). For some diameters, the theoretical signal is shown
in Fig. 10:
with M
g
being the peak echo amplitude for measurement
with gradient; M
0
being the peak echo amplitude for
measurement without gradient; a
m
being the mth root of
Eq. (13):
1
ad
i
=2
J
3=2
a
d
i
2

J
5=2
a
d
i
2

. (13)
g being the gyromagnetic ratio for protons
(267,522,128 s
1
T
1
); g being the gradient strength
(2.0 Tm
1
); d being the gradient pulse width (s); D being
the diffusion time (s); D
S
being the free diffusion coefcient
of the water in de aqueous phase (m
2
s
1
).
The theoretical pfg-NMR signal for the total distribution
was then calculated by summing the theoretical signal for
each class multiplied with the frequency of the class in the
volume-weighted distribution. An extra term was added in
the theoretical signal, for the free water in the sample, which
results in a pfg-NMR signal M
g
/M
0
(free water) correspond-
ing to Eq. (14) (Murday & Cotts, 1968):
M
g
M
0
free water exp g
2
D
S
d
2
D
d
3

g
2

. (14)
The fraction of free water was also varied during the t to
the experimental data.
ARTICLE IN PRESS
1.310
1.285
1.029
0.900
1.031
0.889
0.864
1.027
0.850
w
a
t
e
r
f
a
t

s
p
r
e
a
d
s
e
r
u
m
s
k
i
m

m
i
l
k
b
u
t
t
e
r
s
e
r
u
m

A
b
u
t
t
e
r
s
e
r
u
m

B
b
u
t
t
e
r
s
e
r
u
m

C
b
u
t
t
e
r
s
e
r
u
m

D
b
u
t
t
e
r
s
e
r
u
m

E
b
u
t
t
e
r
s
e
r
u
m

F
D
s

(
1
0
-
9

m
2

s
-
1
)
Fig. 8. Diffusion coefcients (D
S
) for water in the serum of commercial
butters AF, compared with free water and to water in skim milk and in
the serum of a commercial fat spread (n 6, condence interval
71.96S.D.).
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 5
(ms)
M
g
/
M
0

(
%
)
Butter A Butter B
Butter C Butter D
Butter E Butter F
4
Fig. 9. Observed NMR signal M
g
/M
0
at different gradient pulse widths
(d) for three samples of each commercial butter.
ln
M
g
M
0
d
i

2g
2
g
2

1
m1
2d=a
2
m
D
S
2 expa
2
m
D
S
D d 2 expa
2
m
D
S
D 2 expa
2
m
D
S
d expa
2
m
D
S
D d=a
2
m
D
S

2
a
2
m
a
2
m
d
i
=2
2
2

,
(12)
K. Van lent et al. / International Dairy Journal 18 (2008) 1222 19
For an initial log-normal distribution and free water
fraction, the theoretical pfg-NMR signal was calculated
and through iterations, the parameters

D
3;3
and s
g
of the
log-normal distribution as well as the percentage of free
water were varied to obtain the best t of the calculated to
the observed signal. An example of a typical t is shown in
Fig. 10. This procedure was executed for each of the three
samples of each commercial butter. Of the resulting log-
normal distributions, the means of

D
0;0
,

D
3;3
and s
g
were
calculated (Table 2). The fractions of free water ranged
from 1.1% to 3.7%. Notice that butter B, the butter with
the highest geometric volume-weighted mean diameter

D
3;3
also has the smallest geometric number-weighted mean
diameter

D
0;0
, due to a high geometric standard deviation
s
g
. This

D
0;0
is a lot smaller than the CSLM detection limit
of 0.65 mm.
The pfg-NMR experiments, that yield volume-based
information, give similar ts with a slightly higher

D
3;3
and lower s
g
or vice versa, for four out of the six
butter samples. For butters B and D, the two parameters
were also correlated, but the covariance was positive.
Because of the correlation between the two factors,
the covariance matrices for

D
3;3
and s
g
are added in
Table 2.
The inuence of D
S
on the results was also evaluated.
For butter F,

D
3;3
was 2.33, 2.47 and 2.64 mm and s
g
was
1.68, 1.64 and 1.61 for a D
S
of 0.85 10
9
m
2
s
1
(experimentally determined value for butter F),
1.03 10
9
m
2
s
1
(experimentally determined value for
butter B) and 1.31 10
9
m
2
s
1
(value for pure water),
respectively. When these calculations for butter F (lowest
D
S
of water in butter serum) were done with the water
diffusion coefcient of butter B (highest D
S
of water in
butter serum), the log-normal distribution obtained
differed signicantly (po0.0001) from the original result.
Calculations for butter B, done with D
S
of butter F,
did not give a signicant difference with the original
result (T 3.3). Nevertheless, the result for butter F
indicates that it is advisable to use the specic D
S
for
every butter.
3.3. Comparison between NMR and CSLM results
Results for both methods were statistically compared as
described in Section 2. Since the largest water droplets have
the biggest inuence on the microbial stability, the volume-
weighted droplet size distributions were chosen for this
comparison. Only one commercial butter, butter B, showed
no signicant difference between the droplet size distribu-
tions obtained with the two methods (T 1.47). For all
other butters, the results for the CSLM method and the
pfg-NMR method were signicantly different (po0.0001).
These results are supported by the graphical illustration of
the comparison of the two methods (Fig. 11). The precision
for the determination of

D
3;3
was better with pfg-NMR
(relative standard deviation R.S.D. 14%) than with
CSLM (R.S.D. 112%). For s
g
, however, the precision
of pfg-NMR (R.S.D. 48%) was worse than that of
CSLM (R.S.D. 15%). This is in agreement with the
conclusions of the comparison of these two methods for the
water droplet size distribution in non-dairy fat spreads
(Van Dalen, 2002).
Butter B, the only butter that was labelled as batch
churned, had the largest droplet sizes. Butter D also
contained large droplets, but the reproducibility of the
CSLM method was very low. This might be due to an
heterogeneous butter product, which affects the CSLM
method most because it is number based on a small sample
volume of three times 0.60 10
8
mL for each butter
(cf. three times 0.61 mL for pfg-NMR). Furthermore,
ARTICLE IN PRESS
0
20
40
60
80
100
0 1 2 3 4 5
(ms)
M
g
/
M
0

(
%
)
1.5 m
2.5 m
3.5 m
4.5 m 9.5 m 6.5 m
1.5 m
2.5 m
3.5 m
4.5 m 9.5 m 6.5 m
Fig. 10. Theoretical NMR signals M
g
/M
0
( ) at different gradient
pulse widths d for water in droplets with different diameters (Eq. (12)) and
for free water (Eq. (14)) (), the pfg-NMR signal measured for one of the
three samples of butter D ( ), and the corresponding best tting
calculated pfg-NMR signal for a log-normal distribution of water
droplets ( ).
Table 2
Parameters

D
3;3
(volume-weighted mean droplet diameter),

D
0;0
(number-
weighted mean droplet diameter) and s
g
(geometric standard deviation) of
the most probable log-normal distributions of water droplet sizes in
commercial butters AF, acquired by means of a t of a calculated
theoretical pfg-NMR signal to the experimental data (n 3)

D
3;3
(mm) s
g
Covariance matrix of

D
3;3
and s
g

D
0;0
(mm)
Butter A 2.60 1.85 6.05E04 3.75E04 0.84
3.75E04 6.02E03
Butter B 6.36 2.76 5.60E02 2.51E02 0.29
2.51E02 1.71E02
Butter C 2.23 1.32 7.91E03 9.22E03 1.77
9.22E03 1.10E02
Butter D 3.70 2.24 5.04E03 5.42E03 0.53
5.42E03 9.26E03
Butter E 2.70 1.91 5.57E04 3.11E04 0.77
3.11E04 6.47E03
Butter F 2.33 1.68 1.01E03 2.11E03 1.04
2.11E03 6.59E03
K. Van lent et al. / International Dairy Journal 18 (2008) 1222 20
Masuda and Gotoh (1999) demonstrated that more
particles are needed to determine a good estimate of the
mean diameter of wide distributions, such as butter D. The
other butters had such small droplets, that a signicant
part of the smallest section diameters could not be
observed during imaging with CSLM. This might be the
reason for the signicant differences observed between the
two methods.
4. Conclusion
During this study, confocal scanning laser microscopy
has proven to provide valuable qualitative information on
the microstructure in the butter (shape of water droplets,
multiple emulsions, outliers, etc.) and can be used to check
the assumptions made in the data analysis, e.g. a
monomodal log-normal distribution. The staining proce-
dure where the butter sample is successively stained with
Acridine Orange and Nile Red, offers the possibility to
distinguish between water droplets and air bubbles. In the
studied butter images, no air bubbles were seen. When
using CSLM for the determination of a droplet size
distribution, some drawbacks have to be taken into
account. Firstly, the image analysis is number based and
therefore reliable information on small section diameters is
a necessity for an effective estimation of the size distribu-
tion. Especially for butters with small droplet sizes, the
limited resolution of confocal microscopy causes a lack of
necessary information on these small section diameters.
Secondly, the images represent a very small fraction of a
sample, and this might cause a low reproducibility of the
determination of the droplet size distribution if the butter is
not perfectly homogeneous. Finally, the CSLM method is
labour intensive and time consuming.
Pulsed eld gradient NMR on the other hand, is a fast
method that yields very reproducible quantitative informa-
tion, when used for the determination of the water
droplet size distribution in butter. In contrast with CSLM,
the pfg-NMR analysis is volume based on a much bigger
sample volume. Therefore, it can yield very reliable results,
provided that the assumptions are correct and that the
diffusion coefcient of the butter serum is determined for
every butter sample.
Acknowledgements
This research was carried out with the nancial support
of the Institute for the Promotion of Innovation by Science
and Technology in Flanders (IWT). The authors would like
to thank ir. Winnok De Vos for his help on CSLM and ir.
Pieter Saveyn for the valuable discussions on pfg-NMR.
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