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). 424 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 426 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. 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