Journal of Food Engineering 84 (2008) 420–429
www.elsevier.com/locate/jfoodeng
Interfacial rheology study of espresso coffee
foam structure and properties
L. Piazza *, J. Gigli, A. Bulbarello
Department of Food Science and Microbiology (DISTAM), University of Milan, via Celoria 2, 20133 Milan, Italy
Received 5 April 2007; received in revised form 30 May 2007; accepted 12 June 2007
Available online 21 June 2007
Abstract
The espresso coffee beverage is a polyphasic colloidal system, in which the liquid phase is topped by a wet foam of tiny sphere-shaped
gas bubbles. Each sphere is surrounded by a liquid film (lamellae) that isolates it from its neighbours and that hosts biopolymers and
natural surfactants. Foaming biopolymers of coffee (total fraction and its sub-fractions: proteins/melanoidins fraction and polysaccharides fraction) were extracted from defatted and raw, commercially roasted ground coffee. In order to study the viscoelastic behaviour of
the surface-adsorbed layer, all the extracted fractions were analyzed using a commercial interfacial rheometer CIR 100 operating in time
sweep mode. The growth of the interfacial elasticity of the lamella implicitly contains all the information about the molecular interaction
at the foam air/liquid interface. These interactions are described to be responsible for the foam stabilization. Results indicate that the
kinetics of the film formation is mediated by the polysaccharide component and that the protein/melanoidin component of the coffee
foaming fraction exhibits the highest viscoelastic interfacial properties. Lipids play a major role in the interfacial film formation due
to their interaction with protein-like macromolecules, the melanoidins. A correlation was established between air/water interface properties of the foaming systems and the respective foam volumes evaluated by means of the image analysis. A new mathematical description
of surface viscoelastic phenomena, covering the terms of transport of surfactant biopolymers to the interface and describing the coagulation of particles here taking place, is proposed. The suggested equation overcomes the Warburton model, taking into account the
complexity of real food systems as in the case of the espresso coffee beverage.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Interfacial rheology; Foam; Espresso coffee; Image analysis
1. Introduction
The espresso coffee beverage is a polyphasic colloidal
system, in which the liquid phase is topped by a thick layer
of dense, reddish-brown foam of tiny gas bubbles. The gas
phase of the foam consists of the water vapour from the
percolation process and the carbon dioxide formed from
the Maillard reaction during coffee beans roasting (Nicoli
& Savonitti, 2005). The texture and the persistence of the
foam layer are of utmost importance for the quality of
the espresso coffee brew, but the physical–chemical factors
*
Corresponding author. Fax: +39 02 50319222.
E-mail address: laura.piazza@unimi.it (L. Piazza).
0260-8774/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jfoodeng.2007.06.001
which influence foam formation and its stability are, up to
now, not completely clear.
Foams are inherently difficult to study because they are
transient and, hence, the study is essentially restricted to
the observation of a dynamic system. The gas–liquid
phases of foams are described as a liquid continuous phase
that surrounds a dispersed phase of gas bubbles. Each bubble within the foam takes a shape that gives minimal surface area and, due to thermodynamic reasons, must also
be consistent with the constraining presence of its neighbours. The prevailing liquid phase solubilizes biopolymers
and natural surfactants, which will participate in the formation of the liquid films (lamellae), framing the gas phase
and stabilising the bubbles against coalescence (Dickinson,
1999; Dickinson & Izgi, 1996; Rodriguez Patino, Naranjo
L. Piazza et al. / Journal of Food Engineering 84 (2008) 420–429
421
Nomenclature
a0
characteristic time of the transient phenomena
(s)
a
4pDRn0 (s1)
b
mathematical constant
D
in plane diffusivity (m s1)
FFA NL foaming fraction A without lipids
FFA foaming fraction A with lipids
FFB NL foaming fraction B without lipids
FFB
foaming fraction B with lipids
G0s
interfacial elastic modulus (lN m1)
H
height of foam (pixel)
n
number of particle at the surface (m2)
R
particle coagulation radius (m)
time at which H(t) = H0/2
t1/2
TFF NL total foaming fraction without lipids
Delgado, & Linares Fernandez, 1995). Two main classes of
surface active molecules stabilise the interfacial layer in
foam and emulsion systems: low molecular weight surfactants, i.e., lipids and emulsifiers that give high mobility to
the interface, and proteins that develop a surface physical
network. Therefore, the main difference lies in the viscoelasticity of the interface and the stability and drainage
can depend on this structural property.
Espresso coffee is the result of the extraction of gas and
active components in the roasted and ground coffee by
heated water, typically at a temperature between 88 and
94 °C, under a pressure up to 9 atm (Petracco, 2001,
2005): water percolates through a compact bed of ground
coffee particles that can be described as a micro-porous
structure in which the compressed particles adhere to one
another due to a thin coating of oil and give a packed layer.
The outcome hydraulic resistance of this bed causes the solvent to flow through at a rate of around a millilitre per second. The percolation process washes out the components
that are responsible for foam properties and that have been
identified by Petracco (Petracco et al., 1999) as the ‘‘total
foaming fraction” including polysaccharides, melanoidins
from Maillard’s reaction and oil, independently from coffee
species. The high pressure generated by the espresso
machine emulsifies part of the oils, which are responsible
for a special creamy sensation of the topping foam. Under
certain circumstances, surfactants molecules bind to protein and polysaccharides and the resulting surfactant–biopolymer complexes may have very different functional
characteristics than either of the individual components
(Chen & Dickinson, 1995; Dickinson & Euston, 1991; Golding & Sein, 2004; McClements, 2005; Miller, Fainerman,
Grigoriev, Wide, & Kragel, 1999). The surfactant–biopolymer interactions can occur through a variety of different
mechanism, with the two most important being electrostatic and hydrophobic interactions. These interactions
can have a large influence on the bulk physicochemical
TFF
total foaming fraction with lipids
Greek symbols
d
density (g cm3)
g
dynamic viscosity (mPa s)
g0s
viscous component of the complex interfacial
viscosity (lN s m1)
k
decay constant (s1)
t
kinematic viscosity (cSt)
Subscripts
1
at
0
at
(t)
at
i
at
infinite
time 0
any time t
inflection point
properties of biopolymer solutions which, in the case of
espresso coffee, are strictly linked to mouthfeel and taste
and, last but not least, to the physical attributes of the topping foam.
Correlation have been shown between espresso coffee
foamability and protein content and between foam stability
and the fraction with high molecular weigh polysaccharides
(D’Agostina, Boschin, Bacchini, & Arnoldi, 2004; Nunes &
Coimbra, 1998).
It has also been evaluated that the surface active agents
present in espresso coffee are responsible for a decrease in
the surface tension with respect to water–air interface
(46.2 mN m1 at 20 °C for pure Arabica blend espresso
with 1.34 refractive index) (Navarrini, Ferrari, Suggi Liverani, Liggeri, & Ravera, 2004). Finally, it is well known
that coffee bean roasting gives rise to pyrolysis of proteins
and de-polymerization of carbohydrate polymers plus formation of condensation complexes with proteins, along
with the browning reactions giving melanoidins. (Nunes
& Coimbra, 1998; Nunes, Coimbra, Duarte, & Delgadillo,
1997). If the chemistry of espresso foam is therefore well
studied, unfortunately a very feeble attention has been paid
to the foaming mechanisms.
In this work, surfactants and proteins role in forming a
two-dimensional viscoelastic gel at the gas/liquid interface
of the espresso coffee foam are studied by means of the
dynamic oscillatory interfacial rheological measurements.
The structure and the rheological properties of the interface can affect many aspects of the physical properties of
foam systems (Dickinson, 1999; Ispen & Otte, 2004; Ispen
et al., 2001; Langevin, 2000; Murray, 2002; Wilde, 2000).
This is the principle reason why interfacial characteristics,
such as tensiometry and interfacial rheology, are receiving
a growing interest when dealing with foam systems. If the
flow properties, texture and even sensory properties of a
foam or emulsion could be controlled by simply manipulating the interfacial rheological properties of the solution,
422
L. Piazza et al. / Journal of Food Engineering 84 (2008) 420–429
this would provide manufacturers with a powerful processing tool.
lated independent of the instrumental factors (Coffman &
Naumann, 2002).
2. Materials and methods
2.3. Viscosity
2.1. Extraction and isolation of roasted coffee foaming
fractions
Foaming fractions of biopolymers with or without lipids
were extracted from ground dark roasted coffee blend (70%
Coffea robusta and 30% Coffea arabica).
In order to get the defatted foaming fractions, ground
coffee was heated under reflux with hexane and extracted
with hot MilliQ water. The solution was filtered and
ammonium sulphate was added until saturation. Fractionation of total foaming fractions was performed according
to Petracco (Petracco et al., 1999) in order to obtain: the
total foaming fraction (TFF), the foaming fraction A
(FFA) with a prevailing carbohydrate-like character and
the foaming fraction B (FFB) with a prevailing melanoidin-like character. Material loss in the fractionation steps
can be neglected as it resulted from mass balance calculations on the extraction process.
Finally, to get the foaming fraction in presence of lipids,
the previous procedure was followed except for the Soxhlet
fat extraction step.
For all the aqueous solutions prepared from the foaming fractions, the kinematic viscosity (t) (cSt) was measured
using ASTM D445-97 (ASTM, 1997) procedure and a
Cannon Fenske viscometer (Poulten Selfe and Lee Ltd.,
UK). The density (d, g cm3) was measured by means of
a hydrostatic balance (GF-300, A&D Ltd., USA). Data
were finally expressed as dynamic viscosity g = t/d (mPa s).
2.4. Image analysis measurements
Water solutions (40 ml) of the foaming fractions, similar
to those prepared for the rheological tests, were stirred in a
Plexiglas vessel of rectangular section (30 30 90 mm)
in standard conditions to get foams. Images of the foams
were acquired by means of a scanner (19200 Trust, USA)
at different times ranging from 40 to 1860 s after foam
formation.
Images were processed using Image Pro Plus version 5.0
(Media Cybernetics, Inc.) and the frontal foam height (Ht)
was expressed in pixel. Three replicates were carried out for
each measurements.
2.5. Correlation matrix
2.2. Interfacial rheology measurements
Aqueous solutions (0.5% w/w) were prepared for all the
foaming fractions previously described and were analyzed
by means of the CIR-100 interfacial shear rheometer
(FTA, Portsmouth Virginia, USA) fitted with a Pt/Ir De
Noüy ring geometry (13 mm diameter). Solutions were
tested into the glass measuring dish (46 mm diameter).
The CIR-100 measures the interfacial properties by placing
the De Noüy ring at the interface and submitting it to small
angle oscillatory shear. Bi-dimensional dynamic storage
modulus ðG0s , lN m1) and interfacial shear viscosity (g0s ,
lN m1 s) were recorded vs. time (s) during a time sweep
test up to 18,000 s at an oscillation frequency of 3 Hz
and an amplitude of 5000 lrad. All the time sweep tests
were performed at 20 ± 0.2 °C. Each data point was averaged over three cycles. An air/water interface was used as a
reference for all the experiments. The rheometer uses an
oscillating De Noüy ring attached to a virtually frictionless
suspension wire. The system’s drive unit is controlled by
the drive unit coil, which operates similarly to a taut band
galvanometer. The movement of the ring is detected by a
sensor that reflects light off a target that rests on the saddle
of the ring. Working in normalized resonance mode
(>2 Hz), the feedback control system forces the system into
phase resonance. In this case, the experiments are conducted under the condition that the input stress leads the
output strain by 90°. Thus, the storage modulus ðG0s Þ and
the interfacial shear viscosity ðg0s Þ modulus can be calcu-
The correlation matrix of the image analysis variables
and interfacial rheological ones were calculated by means
of the SCAN Release 1.1 software (Minitab Inc., USA).
3. Results and discussion
3.1. Macroscopic foam parameters
The surface active molecules were isolated from the coffee powder. According to Petracco and D’Agostina
(D’Agostina et al., 2004; Petracco et al., 1999), foaming
fraction A (FFA, or FFA NL if no lipids are present), that
was obtained by sub-fractioning of the total foaming fraction (TFF or TFF NL), accounts for about 60% of the
total foaming fraction and shows a prevailing carbohydrate-like character (arabinogalactans, galactomannans).
To the foaming fraction B (FFB, FFB NL) that was
obtained by sub-fractioning of the total foaming fraction
and accounts for about 40% of TFF, the authors attributed, on the other hand, a prevailing melanoidin-like character (carbohydrates, proteins, melanoidins).
A macroscopic evaluation of the foaming performance
of these coffee biopolymers was obtained by means of the
image analysis technique. Aqueous dispersions (0.5%
w/w) of the freeze-dried extracted foaming fractions were
used. Foaming fraction dispersions were stirred at 23 °C
and atmospheric pressure to get foams. Foam lifetime
was followed for 30 min and the decreasing volume of
L. Piazza et al. / Journal of Food Engineering 84 (2008) 420–429
the foams was monitored with respect to the observation
time.
Fig. 1 shows a stereo-microscope picture (enlargement
of 200) of the foam surface that was created by the foaming fraction FFB with lipids.
Foams are transient systems and, of course, the observation of a dynamic system require adequate time-scales.
During percolation process the wet foams drains and, at
our staring observation time, espresso coffee foam appears
as a dry foam with a predominance of the gas phase on the
liquid phase. Since the walls between adjoining bubbles are
very thin, bubbles disappear fast because of successive wall
ruptures, according to a probability proportional to the
physical properties of interface between two cells.
This dispersed system can be classified as a short life
foam, whose decay occurs in a time scale less than an hour:
a foam system can show smooth decay or catastrophic collapse. As it was suggested in the previous literature (Hackbarth, 2006), two indices were considered in order to
quantify the foam behaviour: the foamability, as an index
of the ease and of the extent of foam formation, and the
foam stability, as an index of the rate of loss of foam structure once formed.
A first order kinetic equation was used to model
espresso coffee foam decay
H ðtÞ ¼ H 0 ekt :
423
Fig. 2. Fitting of the experimental data for the foaming fraction FFB
according to a first order decay kinetic.
Eqs. (1) and (2). Fig. 2 gives an example of the fitting of the
experimental data for the foaming fraction FFB. The fitting of the model (R2), in respect to the experimental data,
was higher than 0.97 in all cases.
In Fig. 3a and b, the parameters for all the kinetics are
summarized. The protein-rich solutions (FFB fractions)
give higher volumes of foam, generated by a standard stirring procedure, both if lipids are present or not. The carbohydrate-rich FFA fractions, with or without lipids,
exhibited the worst performance, while an intermediate
ð1Þ
Consequently, the mean life time (half decay) referred to
first order decay kinetic is the follow
ln 2
:
ð2Þ
k
The H0 parameter was assumed as numerical index of
foamability, while the t1/2 value represented the numerical
index of foam stability.
Each of the six extracted foaming fractions (three of
them with lipids: TFF, FFA, FFB and three without lipids:
TFF NL, FFA NL; FFB NL) were processed according to
t1=2 ¼
Fig. 1. Stereo-microscope picture (enlargement: 200) of the foam surface
that was created by the foaming fraction FFB with lipids by stirring in
standard conditions.
Fig. 3. Characteristic foam parameters: foam stability (t1/2) (a) and
foamability (H0) (b) from the decay kinetics for all the samples (raw
foaming fractions TFF, FFA, FFB and defatted foaming fractions TFF
NL, FFA NL, FFB NL).
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L. Piazza et al. / Journal of Food Engineering 84 (2008) 420–429
behaviour can be observed for the total foaming fraction
TFF: it seems that the presence of polysaccharides brings
down the attitude to foam of the coexisting protein-like
compounds. Moreover, data indicate that the foamability
is more consistent if lipids are not separated from the
FFB fraction. This is true for the TFF and FFA fractions,
too. Furthermore, lipids are needed to improve foam stability, as it can be observed on the basis of the higher values
of the half decay time, t1/2, for all the no-lipids (NL)
samples.
The values of the thickness of the foam layer can be replotted according to the first order decay law in a dimensionless form, as ln (H(t)/H0) vs. (t/t1/2) (Fig. 4), i.e., by
using the characteristic H0 and t1/2 foam parameters only
for the FFB (with and without lipids) and FFA (with
and without lipids).
It can be observed that not all the samples are represented by the same dimensionless line: a deviation from
the master curve of the foaming sub-fractions with lipids
FFA and FFB is evident. For these samples the trends
change their slope when the half time is reached due to a
slower decay rate, probably a hint that another mechanism
of foam formation is taking over. It is however interesting
to note that the new decay rate also follows a straight line
variation on the dimensionless plot.
Proteins, polysaccharides and lipids are the main types
of components involved in coffee foaming mechanism
(Nunes & Coimbra, 1998, 2001; D’Agostina et al., 2004).
There are two main ways how protein and polysaccharide species may become strongly coupled together in bulk
solution or at a fluid interface: the attractive electrostatic
interaction or covalent bonding to form a permanent protein–polysaccharide hybrid. Covalent complexes can be
produced from reactions of lysine groups on protein with
carbohydrate ester groups or reducing sugars: the complexes produced during coffee beans roasting by the Maillard reaction are exactly of the covalent type. The nature
and properties of protein–polysaccharide complexes, obviously, widely vary due to the wide variation in food protein
structure. In particular, the flexibility of the polymer chain
guarantees ready change in conformation at the interface
(Ispen & Otte, 2004).
Moreover, from the previous results it can be observed
that the foamability is more consistent if lipids are not separated from the foaming biopolymers (proteins and polysaccharides), while foam stability increases in defatted
systems. Triglycerides (with a small amount of free fatty
acids, phosphatides, mono and diglycerides) and diterpens
alcohol esters are the major lipid classes in coffee brewed
from ground coffee beans and range from 86.6% to
92.9% and 6.5% to 12.5% of total lipids, respectively (Ratnayake, Hollywood, O’Grady, & Stavric, 1993). When
present in the protein–polysaccharide dispersions, the
emulsified lipids can act as additional surfactants. It has
been shown that in mixed protein–surfactant interfaces,
the weak protein interactions and restricted diffusion of
surfactants result in reduced stability and, probably, foam
rupture (Coke, Wide, Russel, & Clark, 1995; Heertje, Roijers, & Henrickx, 1998). But an extension in the foam volume would not be expected (Fig. 4). On the basis of the
previous results, different mechanism of lipid functionality
have therefore to be taken into account.
It has been reported that the lowering of surface tension
in the case of emulsion of triglycerides applied to an air/
water interface is mainly caused by spreading of oil (Schokker, Bos, Kuijpers, Wijnen, & Walstra, 2002). Moreover, a
carrier role of surface active compounds towards the air/
water interface charged to micro-emulsified oil droplets
might be hypothesized.
A direct insight was therefore provided by surface rheology experiments that allows an evaluation of the mechanisms responsible for foaming performance.
First, a relationship was evaluated between the foams
and the liquid phases properties, in particular between
the foam amount at t = t0 and the dynamic bulk viscosity
(g). Fig. 5 shows that a straight dependence exists between
H0 and g: the higher the relative amount of polysaccharide
in the foaming fractions (or the less the relative amount of
Fig. 4. Characterization of the foaming behaviour: master curve in the
dimensionless space: log (H/H0) vs. t/t1/2. FFB NL (empty triangle), FFB
(filled triangle), FFA NL (empty circle), FFA (filled circle).
Fig. 5. Relationship existing among foamability (H0 index) and liquid
phase bulk viscosity.
L. Piazza et al. / Journal of Food Engineering 84 (2008) 420–429
425
protein-like components), the higher the viscosity. For each
of the three classes of fractions (TFF, FFA, FFB) the
higher the lipid content, the lower the viscosity.
A difference in viscosity implies different diffusion of
surface active molecules from the liquid bulk to the surface.
This is the main reasons for considering diffusion phenomena in describing the foaming mechanisms. An inverse
dependence of diffusion on viscosity has been described
and modelled for solutions of pure proteins (Tanford,
1961). In all practical applications of diffusion to macromolecular solutions, the macromolecules are assumed to act as
if they were solute particles in a two component system, so
that the Fick’s law applies. Moreover, these studies are carried out at very low solute concentrations. In actual food
systems, containing several diffusing components, only
apparent diffusion coefficients could be calculated but the
risk of unnatural average D values could be high because
the problem of interacting flows could not be ignored.
As previously mentioned, several surface active soluble
compounds in coffee participate in foam stabilization and
therefore are active in the expected diffusion mechanisms.
Lacking a quantitative estimation of coefficients of diffusion, an indirect approach was then followed to link diffusion processes to foaming mechanisms. The interfacial
viscoelastic properties of the gas/liquid interface were
therefore studied by means of interfacial shear rheological
measurements.
3.2. Viscoelastic properties of the interface
Fig. 6. Development of the interfacial elasticity (G0s , bold line) and of the
interfacial shear viscosity (g0s , normal line) plotted vs. time for the defatted
foaming fractions FFB NL (a) and for the foaming fractions FFB (b).
When proteins, carbohydrates and lipids move from the
liquid continuous phase that surrounds gas bubbles to the
surface, thin interface films that coat the bubbles form.
These interfaces are complex nano-structured systems
whose deformation and flow are responsible for the bubbles stability. The results of dynamic interfacial experiments are illustrated in Fig. 6a and b. The developments
of the interfacial elasticity ðG0s Þ and the interfacial shear viscosity ðg0s Þ plotted vs. time are shown for the foaming fractions named FFB NL and FFB, i.e., the foaming fractions
with melanoidins as surface active component without or
with lipids, respectively.
The trends of the interfacial dynamic moduli differ for
FFB NL and FFB both in the shape, both in the absolute
values. In Fig. 6a, up to about one hour of curing the surface film, a very feeble growth of G0s can be clearly recognized. A rapid increase in the interfacial elastic modulus
G0s then follows: an inflection point splits this viscoelastic
region in two sub-regions. Finally, a forth zone shows an
arrangement of the curve towards asymptotic values. Due
to the presence of lipids (sample FFB) the starting step
(up to 1800 s) is shorter than the previous one, the rate
of the tailoring phenomena at the surface is higher and
the viscoelastic properties are higher in value up to a point
where the G0s is no more instrumentally detectable (about
10,000 s) (Fig. 6b).
Taking into account the viscous contribution ðg0s Þ to the
complex shear interfacial modulus, some interesting considerations arise.
An hypothesis is that the viscous contributions ðg0s Þ to
the surface complex modulus Gs is mainly due to the lipids,
which do not develop any elastic properties. In the absence
of lipids (Fig. 6a), the shape of g0s t vs. time is quite similar to
that one of G0s . In Fig. 6b, (FFB with lipids), a local maximum of g0s followed by a local minimum is clearly evident
after 8000 s of curing. A similar trend is not recorded in the
G0s vs. time curve, which increases monotonically. The viscosity peak was found to be consistent with all the three
test replicates. The rheological behaviour supports the
hypothesis that the surface properties of surfactants are
to be explained not only in flow-time dependent terms,
but also by important molecular mechanism that affect surface film structure and film formation capacity as partially
described in the literature. The most interesting suggested
mechanisms deal with the protein–lipids relationships: (1)
the hydrophobic effect that is eventually the main factor
to the interaction of lipids and proteins at the interface
(Zhang, An, & Cui, 2003) or (2) the conformational
changes of high molecular weight substances as proteins.
It would be due to the competitive presence of lipids that
could influence the formation of 2D gel (Rodriguez Patino
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L. Piazza et al. / Journal of Food Engineering 84 (2008) 420–429
& Rodriguez Niño, 1995) or to the noticeable rearrangements of lipids physical conformation, from monolayer
of lipids to micelles, when the surface concentration of lipids exceed a certain critical value (CMC). This value is
function of the nature of lipids and of the temperature,
and accounts for a phase inversion with the formation of
inverse protein/lipids micelles (McClements, 2005). Ionic
surfactants (as free fatty acid) actually only form micelles
when their hydrocarbon chains are sufficiently fluid at temperatures above their chain melting temperature. Below a
specific temperature for a given surfactant, the Krafft temperature, the surfactant becomes insoluble rather than to
self-assemble in micelle-like structure.
3.3. Modelling kinetics of interfacial elasticity
The surface viscoelastic properties of multi-component
systems, like the dispersion under study, is scarcely
described in mathematical terms (Warburton, 1998).
In order to model the kinetics of interfacial elasticity, the
Warburton equation is typically used when simple biopolymer systems at very low concentration are studied for the
adsorption behaviour at the interface (Roberts, Kellaway,
Taylor, Warburton, & Peters, 2005). The Warburton
kinetic equation describes the rate of formation of an interfacial gel network using a combination of theories on coagulation and on classical rubber elasticity
1
1
1
:
¼
þ
G0sðtÞ G0s1 G0s1 at
ð3Þ
In the absence of interaction (very low concentration),
particles take up any position in, and diffuse through the
suspension without interference from other particles. In
the case of real food system, as in the case of the espresso
beverage, this model fails due to the complex picture of
biopolymers involved in the formation of the interfacial
layer. For high biopolymers concentration, or in the case
of non-homogeneity of solutes, interaction potentials affect
their relative instantaneous positions, resulting in a compromised diffusion to the surface and in a more complex
interface structuring.
In Fig. 7a, the increase of the surface elastic property vs.
time is presented for a diluted solution (0.1%) of soy protein in water (unpublished data).
A monotone increase of the interfacial elastic modulus
ðG0s Þ is clear. The Warburton kinetic equation successfully
fits the experimental data (Fig. 7b): the theory proposed
by Warburton therefore states that a plot of 1=G0s against
1/t should give a straight line of slope ð1=G01 aÞ and intercept ð1=G01 Þ on the ordinate.
The typical G0s f(t) curve obtained for the protein-like
biopolymers which are responsible for the espresso coffee
foam (FFB NL sample), is otherwise shown in Fig. 8.
The dynamic elastic modulus increases with time in a
sigmoid-like mode that makes not possible the physical
description of the phenomena according to Warburton.
Fig. 7. Development of the interfacial elasticity ðG0s Þ plotted vs. time for a
diluted solution (0.1%) of soy protein in water (unpublished data) (a) and
fitting (dotted line) (b) according to the Warburton kinetic equation on the
plane 1=G0s against 1/t.
Fig. 8. Modelling of G0s vs. time according to the descriptive Eq. (4) (see
text) for the defatted protein-rich foaming fraction (sample FFB NL).
Bold line: raw data; normal line: fitted data. Inflection point at t = 7200 s.
The curves contain the particle coagulation kinetic governed by Smoluchowski equation and the migration of
particles from the bulk phase to the interface. More precisely, four different subsequent steps expected events, that
account for the interfacial networking of surface active
compounds, are evidenced by the interface rheology analysis in terms of increasing viscoelastic character of the
L. Piazza et al. / Journal of Food Engineering 84 (2008) 420–429
427
interface film. These events could be summarized as follow:
diffusion of surface active compounds from the bulk (starting plateau), their link at the interface (growth of G0s before
the curve’s inflection point), structural rearrangements that
take place due to steric hindrance at the surface (growth of
G0s after the curve’s inflection point) and final entangling in
the new tailored coating (ending plateau).
The inflexion point of the G0s ðtÞ function separates the
transient phase of acceleration from saturation to equilibrium phase. This kind of elasticity growth makes a
mathematical pattern necessary, encompassing the particle coagulation kinetic governed by Smoluchowski equation and the migration of particles from the bulk phase
to the interface. The following system of two coupled
non-linear equations, which are based on a zero order
kinetic equation, seems to provide a more appropriate
mathematical description. It successfully fits the experimental data
( 0
b
Gs0 þ G0s1 at0 ; 0 6 t 6 ti ; b P 1;
0
Gs ðtÞ ¼
ð4Þ
b
G0si þ G0s1 at0
t P ti ; b P 1:
The coupled phenomenological equations combine the
previously described interactive processes.
The domain of validity of the equations is governed by
the inflection point of the curve ðG0s i ; ti Þ, which was calculated numerically, or by the corresponding ti, that is the
time at the inflection point.
Further mathematical investigations are under work to
verify the type of discontinuity at the inflection point.
The domain-size varies with the composition of the fractionated foaming mixtures (Fig. 9a and b): the time of transient phenomena (a0 values in the equations) is higher in
presence of polysaccharides in TFF and TFF NL samples
(6000 s of time cure). This is due to the thickening role of
polysaccharides which results in an increase in the bulk viscosity and hence in a lower diffusion of surface active compounds to the air/water interface. The elastic character of
the surface film ðG0s1 values in the equations) is higher
for protein-rich fractions while the polysaccharides rich
fractions FFA (with or without lipids), that are free from
the surface active proteins, do not develop any elasticity
(data not presented in the graphs).
As for the total foaming fractions systems with or without lipids (TFF and TFF NL), the G0s vs. time curves are
quite similar and indicate an analogous response of physical networks to the applied stress. From the kinetics of the
surface elasticity of total foaming fractions (TFF), an
hypothesis on the polysaccharides role in weakening the
protein layer can be advanced. This phenomenon is more
evident if lipids do not protect, according to the micelle
organization, the protein-like macromolecules. In fact after
18,000 s the absolute value of G0s is still low.
Finally, a correlation is shown between the outcomes of
interfacial rheology analysis and the macroscopic foaming
parameters taken from the previous image analysis of
espresso coffee ‘‘crema”. In Table 1, the original data are
Fig. 9. Development of the interfacial elasticity ðG0s Þ plotted vs. time for:
(a) defatted foaming fractions FFB NL (bold line), TFF NL (normal line)
and (b) for foaming fractions with lipids FFB (bold line) and TFF (normal
line).
therefore summarized and Table 2 shows the correlation
matrix.
The correlation matrix computes the correlation coefficients of the columns of a matrix. That is, row i and column j of the correlation matrix is the correlation between
column i and column j of the original matrix. The diagonal
elements of the correlation matrix will be 1 since they are
the correlation of a column with itself. The correlation
matrix is also symmetric since the correlation of column i
with column j is the same as the correlation of column j
with column i.
The correlation matrix shows that the best (positive or
negative) correlations are found between the variable a0
from Eq. (4), the characteristic time of the transient phenomena, and the variables H0 and t1/2 from Eqs. (1) and
(2), which were selected as the numerical quantification
of the foamability and foam stability of espresso coffee,
respectively.
The faster the transient phenomena are (low value of
variable a0 ) the lower are the values of t1/2, i.e., the foam
is more stable and the higher the foamability.
These considerations allow us, in principle, to suppose
that a detailed knowledge of the transient phenomena (diffusion from bulk to interface and linking at the surface)
should improve our capability of manipulating the technological properties of espresso coffee foam.
428
L. Piazza et al. / Journal of Food Engineering 84 (2008) 420–429
Table 1
Original data for the behaviour of the foams and for the viscoelastic properties of the surfaces that were used to build the correlation matrix
Variables
Foaming fraction
t1/2 (s)
H0 (pixel)
g (mPa s)
G01 (lN m1)
a0 (s)
b (–)
FFB
FFB NL
TFF
TFF NL
570.074
877.288
736.162
1562.918
57148.0
43765.5
33254.5
25389.5
1.028
1.075
1.129
1.098
16604.3
19664.9
6886.0
6277.3
10254.7
13295.6
18971.7
31350.6
1.655
2.742
1.854
2.880
Table 2
Correlation matrix for the indices describing the behaviour of the foams
and for the viscoelastic properties of the surfaces
H0
g
G0s1
a0
b
t1/2
H0
g
G0s1
a0
0.796
0.374
0.529
0.926
0.82
0.857
0.807
0.916
0.583
0.736
0.598
0.252
0.81
0.047
0.594
4. Conclusions
This study provides phenomenological observations of
changing interactions between neighbouring polymer molecules in protein/polysaccharides/lipids foaming systems
that were isolated from the roasted ground coffee.
The lack of detailed information on espresso coffee
foams could be filled from further studies on the interface
networking: surface rheology provides information on the
ability of adsorbing species to stabilize espresso coffee
foam. The results of this study suggest that the relative
strength of the two-dimensional physical network at the
air/water interface is mainly dependent on the interaction
between protein-like macromolecules and lipids.
The kinetic of the growth of the interfacial elasticity
implicitly contains all the information about the molecular
interaction at the foam air/liquid interface responsible for
the foam stabilization. In the case of real food system, like
in the case of the espresso coffee beverage, due to the complexity of the system, the foaming mechanisms can be
described by appropriate mathematical descriptions of
the surface viscoelastic phenomena, containing the terms
of transport of surfactant biopolymers to the interface
and describing the coagulation of particles taking place
here.
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