rheology of milk foams produced by steam injection

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Rheology of Milk Foams Produced by SteamInjectionCarlos A. Jimenez-Junca, Jean C. Gumy, Alexander Sher, and Keshavan Niranjan

Abstract: Rheology of milk foams generated by steam injection was studied during the transient destabilization processusing steady flow and dynamic oscillatory techniques: yield stress (τ y) values were obtained from a stress ramp (0.2 to25 Pa) and from strain amplitude sweep (0.001 to 3 at 1 Hz of frequency); elastic (G′) and viscous (G′′) moduli weremeasured by frequency sweep (0.1 to 10 Hz at 0.05 of strain); and the apparent viscosity (ηa) was obtained from the flowcurves generated from the stress ramp. The effect of plate roughness and the sweep time on τ y was also assessed. Yieldstress was found to increase with plate roughness whereas it decreased with the sweep time. The values of yield stressand moduli—G′ and G′′—increased during foam destabilization as a consequence of the changes in foam properties,especially the gas volume fraction, φ, and bubble size, R32 (Sauter mean bubble radius). Thus, a relationship between τ y,φ, R32, and σ (surface tension) was established. The changes in the apparent viscosity, η, showed that the foams behavedlike a shear thinning fluid beyond the yield point, fitting the modified Cross model with the relaxation time parameter (λ)also depending on the gas volume fraction. Overall, it was concluded that the viscoelastic behavior of the foam below theyield point and liquid-like behavior thereafter both vary during destabilization due to changes in the foam characteristics.

Keywords: cappuccino, milk foams, rheology, steam injection, yield stress

Practical Application: Studying the transient rheology of milk foams during destabilization contributes to our knowledgeof the relationships between the changes in foam properties: texture and mouth feel during the consumption of hotfoamed beverages.

IntroductionFoams are gas–liquid systems which have applications in differ-

ent fields: cosmetics, drugs, oil extraction, chemical industry, andfood (Herzhaft 1999). The incorporation of bubbles into foodshelps to improve the texture, appearance, and taste while decreas-ing the caloric content (Campbell and Mougeot 1999). Thereare several methods employed to incorporate bubbles within foodstructures: mechanical whipping, air injection, chemical decom-position, fermentation, and so on (Campbell and Mougeot 1999).A less understood method is steam injection to froth the milkwhich is used in the preparation of coffee beverage such as cap-puccino, latte, and mochaccino (Silva and others 2008). This isa nonisothermal method, which employs steam flow to draw airand simultaneously heat up the milk (Silva and others 2008). Likeany other foam, milk foams produced by steam injection begin todestabilize soon after the steam flow is switched off causing theircharacteristics to change continuously with time. This process isalso accompanied by a drop in temperature which influences foamproperties further (Silva and others 2008). Foams have been tradi-tionally characterized in terms of overrun and stability, but other

MS 20110606 Submitted 5/13/2011, Accepted 7/27/2011. Authors Jimenez-Junca and Niranjan are with Dept. of Food and Nutritional Sciences, Univ. of Reading,Whiteknights, P.O. Box 226, Reading, RG6 6AP, U.K. Author Gumy is with NestlePTC Orbe, Rte de Chavornay 3, Orbe, CH-1350, Switzerland. Author Sher is withNestle R&D Marysville, 809 Collins Avenue, Marysville, OH 43040, U.S.A.Direct inquiries to author Niranjan (E-mail: [email protected]).

properties like bubble size distribution and rheology can also beused to gain insights into their complex structure and texture(Magrabi and others 1999; Luck and others 2001). Foams are es-sentially composite structures formed by liquids and gases whichdemonstrate different rheological behaviors depending on thestress levels applied. Most foams show yield behavior and behavelike an elastic solid at stresses below the yield stress; at higher valuesof the yield stress the foam exhibits pseudoplastic flow (Hohler andCohen-Addad 2005). The yield point marks the transition fromsolid-like to liquid-like behavior. This parameter has been in-vestigated in emulsions, foams, and soft pastes (Princen and Kiss1989; Mason and others 1996; Pernell and others 2000). In foams,it depends mainly on the gas volume fraction, bubble size, andliquid surface tension (Rouyer and others 2005), although someauthors have suggested that it also depends on the experimentaltime scale and technique used (Cheng 1986; Mason and oth-ers 1996). Yield stress vanishes at a critical gas volume fractionwhich depends on the size distribution of the bubbles and theway the bubbles are packed in the foam (Saint-Jalmes and Durian1999).

In addition, there are other parameters characterizing the rhe-ological behavior of foams: elastic G′- and loss G′′-moduli todescribe the viscoelastic behavior and the flow curves to studythe liquid-like performance (Khan and others 1988; Hohler andCohen-Addad 2005; Weaire 2008).

Earlier work on the rheology of milk foams have beenundertaken with model solutions of individual milk proteins(Gunasekaran and Ak 2000; Luck and others 2001; Yang and

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Rheology of milk foams produced by . . .

others 2009). Further, these works only focused on yield stress asthe main rheological property and measured this parameter at aspecific time during destabilization (Pernell and others 2000; Luckand others 2001; Yang and others 2009).

Since there is no information available on the transient varia-tions in the rheological properties of real systems like milk foamsproduced by steam injection, which is valuable for understandingfoam texture and mouth feel, the aim of this work is to undertakean in-depth study into the rheological behavior of such foamsover a wide range of shear conditions, and correlate the transientvariation of these properties with other characteristics of the foams,such as gas volume fraction and bubble size.

Materials and Methods

Foam preparation and characterizationHomogenized pasteurized semiskimmed milk (Freshways,

London, U.K.) was bought in a local shop; this was stored ina fridge (5 ± 1 ◦C) and used within 3 d of the purchase.

Commercial red food coloring (Supercook, Leeds, U.K.) wasadded to the milk in the proportion 10 drops/L, in order toenhance the visibility of the liquid/foam interface for measuringthe air volume fraction of the foam. It was shown that the additionof dye at this concentration did not influence milk surface tensionand other foaming properties (Silva and others 2008).

The experimental setup used has also been described in the samestudy (Silva and others 2008). The setup allowed foam formationby steam injection under controlled and reproducible conditions.A steam injection valve connected to a supply of steam operatingat 280 kPa, fixed the steam flow rate at 1 g/s. The sparging unitwas adapted from a commercial espresso machine (Krupps Vivo,Solingen, Germany); 2 stainless steel tubes were connected to arubber sparger (Figure 1). Steam was sourced from a central boilerand introduced in a controlled manner through one of the tubes,

Figure 1–Schematic representation of the venturi nozzle device used toproduce milk foams by steam injection.

while air was drawn through the other (7 cm length) by the Venturieffect. A mixture of the wet steam and air left the nozzle througha 1 mm orifice at the tip of the rubber unit.

A fixed volume of milk, 200 mL, was taken in a 1 L graduatedcylinder (reading error of ±10 mL), and the sparging unit wasplaced in such a way that the orifice on the rubber unit waslocated 10 mm below the surface of the milk. The steam wasinjected at a constant flow rate for 30 s, which is the durationnecessary for the milk to reach a maximum temperature of 70 ◦C(Silva and others 2008).

The foam was then allowed to destabilize in the same graduatedcylinder. The total volume of the dispersion (VT ) and clear liq-uid volume (VL) in the cylinder were monitored over time asthe foam was left to stand in a controlled temperature room. Thetemperatures were measured continuously at 2 positions usingK-type thermocouples connected to a data acquisition system(Grant Systems, Cambridge, U.K.); one of the thermocouples waspositioned in the foam, approximately 2 cm above the foam–liquidinterface, and the other was placed in the clear milk, approximately2 cm below the interface.

The cylinder and contents were weighed before and after steaminjection, in order to determine the mass of condensate in themilk. The air volume fraction in the foam, at any time, was basedon the foam volume, and it was calculated by dividing the volumeof gas in the foam by the foam volume.

The surface tension of milk at different temperatures was es-timated by using the empirical equation developed by Bertsch(1983) for different kinds of milk valid in the temperature range18 to 135 ◦C:

σ= 1.8 × 10−4T2 − 0.1638T + 55.6, (1)

where σ is the surface tension in mN/m and T is the temper-ature in ◦C.

Bubble size distributionAn optical system with a CCD camera was used to measure

the bubble size distribution. The system consisted of an invertedmonofocal lens of 25 mm focal length (Pentax-Cosmicar, Slough,U.K.) attached to the CCD camera with an extension tube of20 mm length; this system allowed visualizing a minimum size of20 μm and capturing digital images for storage and further analysison a computer.

The foam was cautiously sampled at 1, 3, 5, 7, and 9 minafter steam injection ceased, using a flat transparent polycarbonatespoon which also served as a clear sample container for takingimages. The foam was left in the spoon for a minute to stabilizeprior to taking images in 4 different areas.

The images were edited and processed using the software ImageJ 1.42 and Bubbles Edit 1.1.

Foam rheologyA high-resolution CVO rheometer (Bohlin Instruments,

Worcestershire, U.K.) was run in viscometry and oscillatorymodes, using a 40-mm parallel plate as a measuring system witha gap of 2000 μm. As the foams show slippage at the walls, 3levels of roughness in the parallel plates were assessed: smooth sur-face, plates covered with sandpaper (Norton, Stafford, U.K.) gradeP600, and grade P120.

Foam samples were gently removed from the plastic cylinderwith a tea spoon at 1, 3, 5, 7, and 9 min and transferred to the flat

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base plate on the rheometer. The upper parallel plate was slowlylowered down to make contact with the sample with minimumstructural damage, and any excess foam was cautiously removed.The foam was then left to stabilize between the plates for 1 minbefore running any test.

The yield point and flow curves were obtained from steadyflow experiments by running the rheometer in the viscometrymode; the stress was ramped linearly (0.2 to 25 Pa) over 60,120, or 180 s at controlled room temperature (19 ◦C). The yieldstress was determined using the “yield stress analysis” functionprovided by the Bohlin software. The software monitors the de-formation produced by the applied stress and calculates the “in-stantaneous” viscosity, which increases until it reaches the stress atwhich the material begins to flow; this stress is defined as the yieldstress.

Dynamic oscillatory experiments were performed using thesame plate geometry. A logarithmic amplitude sweep (strain con-trolled between 0.001 and 3) at frequency of 1 Hz was appliedto find the linear viscoelastic region (LVR) and the yield pointfor the foams. Storage (G′) and loss moduli (G′′) were recordedrunning a logarithmic frequency sweep (0.1 to 10 Hz) at a strainof 0.05. No precondition (stirring or heating) was applied to thesamples.

Statistical analysisAll statistical analyses were completed using the SPSS 17.0

system software. Analysis of variance was conducted to deter-mine differences between treatments. Significant differences wereestablished with a Tukey’s test at a significance level of 0.05. Exper-iments were carried out in triplicate using freshly prepared sampleseach time, and the results were reported as the mean and standarderror of these measurements.

Results and Discussion

Effect of surface roughness on yield pointDifferent studies have suggested avoiding slip effect to obtain

real rheological properties of foams, especially when parallel plateor cone and plate systems are used (Khan and others 1988; Pernelland others 2000; Kealy and others 2008). However, there are noclearly defined criteria available to select the appropriate level ofroughness. Thus, some authors do not use antislip surfaces (Lau andDickinson 2004), while others utilize serrated plates (Kealy andothers 2008) or sandpaper having different roughness to cover theplates. Allen and others (2006) used sandpaper grade P600 whileKhan and others (1988) used grade P120 to study the rheologyof foams; as a consequence, the rheological properties can dependon the level of roughness used.

Figure 2 shows the yield stress and strain values for foams, whensandpaper grades P600 and P120 were used and compared withsmooth plates.

The 3 sets of plates gave significantly different values of yieldstress and strain (P = 0.001). Although the yield stress values werepractically equal in the case of smooth plates and plates coveredwith sandpaper P600, the value increased by 56% when sandpaperP120 was used. Yield strain was different for each roughness usedbut the extreme values only differed by 38%. According to Khanand others (1988), the bubbles adjacent to smooth plates are ableto slip over a thin liquid film formed on the plate; this distortsthe rheological properties. On the other hand, the slip is reduced

by covering the plates with rough surfaces since the liquid film isnow able to reside in the depressions between the particles.

The similarity of yield stress values for smooth plates and platescovered with sand paper grade 600 (Figure 2) also suggests thathaving low roughness does not eliminate slip completely. Khanand others (1988) stated that the particle size of the sandpaperhad to be commensurate with the bubble size for the rheologicalmeasurements to remain uninfluenced by slip. The mean particlesize of sandpaper Grade 600 was 25.8 μm and significantly smallerthan most mean bubble sizes. Therefore, sandpaper Grade 120(average particle size of 125 μm) was used for all the experiments,since the mean bubble size was never bigger than 280 μm in thisstudy.

Effect of sweep time on yield stressAs the yield stress is a time-dependant property (Cheng 1986),

the effect of the sweep time was studied by changing the timeduration over which the stress was linearly ramped from 0.2to 25 Pa. Figure 3 shows that the highest value of yield stress(10.22 Pa) was observed when the sweep time was 60 s, and itfell to 7.48 and 7.86 Pa when the sweep time increased to 120and 180 s, respectively. This behavior partially agrees with Cheng(1986) who states that the yield stress does not assume a uniquevalue, but it depends on the sweep time, with longer sweep timesresulting in lower values. In this study, the yield stress fell from10.22 to 7.48 Pa when the sweep time increased from 60 to 120s, but it marginally increased to 7.86 Pa when the sweep timeextended to 180 s. The values of yield strain, on the other hand,changed from 0.37 at 60 s to 0.45 at 180 s, which represents a 9%increase in elasticity.

The above observations can be explained by extending thehypothesis of Mason and others (1996) about the structure ofconcentrated emulsions. The bubbles in the foams are groupedinto irregularly shaped clusters, each having a definite orientationin the plane. When the sweep time is low, the stress is rampedup quickly, and the clusters do not have enough time to reorient

Figure 2–Effect of the roughness of the rheometer plates used on yieldstress and yield strain for milk foams obtained by steam injection, and sam-pled 3 min after switching off the steam flow. The stress ramp was appliedfor 60 s. The error bars represent standard error (n = 3) and differentletters on the bars represent significantly different values. The rectanglesmarked “smooth” represent data obtained using the original rheometerplates; the rectangles marked grades P600 and P120 represent the dataobtained when both the rheometer plates are covered with sandpaperhaving average particle sizes of 25.8 and 125 μm, respectively.

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themselves in the direction of the applied stress. This raises thethreshold stress required to make the foam flow.

On the other hand, if the sweep time is longer (120 or 180 s),the clusters are able to reorient themselves in the direction of theapplied stress thereby lowering the yield.

Changes in yield stress and strain during foamdestabilization

Milk foams are very unstable systems whose properties vary withtime. Table 1 and Figure 4 show the changes in foam propertiesand yield stress and strain, respectively, during the destabilization.

As in the case of most foams, the gas volume fraction (φ) in-creased with time. The highest changes in φ were in the first 4min of destabilization, but it was less pronounced after 6 min.These small changes are due to the progressively lower rate ofliquid drainage from the foam caused by the liquid viscosity in-creasing with a drop in temperature and less available liquid in thefoam.

As mentioned before, the destabilization of milk foams producedby steam injection is a nonisothermal process (Table 1) with foamtemperature dropping from 65 ◦C when it is first prepared to45.1 ◦C after 10 min. This results in the surface tension changingas shown in Table 1. At the same time, the Sauter mean radius (R32)

Figure 3–Effect of sweep time (that is the time duration over which thestress was ramped up from 0.2 to 25 Pa) on yield stress and yield strainfor milk foams obtained by steam injection and allowed to destabilize for 3min after switching off the steam flow. The rheometer plates were coveredwith sandpaper P120; error bars represent standard error (n = 3) anddifferent letters significantly different values.

Table 1– Transient changes in milk foam properties during thedestabilization (the foam was generated by injecting steam with aventuri nozzle for 30 s in 200 mL of semiskimmed milk).

Destabilizationtime (min) φ(a T (◦Cn)a σ (mN/m) R32 (μm)b

2 0.78 ± 0.01 59.2 ± 0.6 46.6 ± 0.1 1324 0.81 ± 0.01 53.1 ± 0.7 47.5 ± 0.1 1356 0.84 ± 0.01 49.3 ± 0.7 48.0 ± 0.1 1378 0.86 ± 0.01 46.9 ± 0.7 48.4 ± 0.1 13710 0.86 ± 0.01 45.1 ± 0.9 48.6 ± 0.2 138a Values correspond at the mean of 3 values ± the standard error.bSauter mean radius was calculated over the total number of bubbles (minimum 100bubbles were measured for each time).

of bubbles varied marginally from 132 to 138 μm, and remainedpractically constant after 6 min.

These transient values of gas volume fraction, bubble size, andsurface tension influence the yield stress and strain of the foams(Figure 4). The yield stress increased progressively from 4.98 Paat 2 min to 11.00 Pa at 10 min, although the rate of increasedropped after 6 min. It is also interesting to note that the gasvolume fraction and the Sauter mean bubble radius values did notchange much after 6 min.

Although it is not possible to draw an absolute comparisonbetween the yield stress values for milk foams produced by steaminjection, and other foams reported in the literature (because ofthe differences in protein concentration, method of preparation,rheological technique employed, gas volume fraction, and bubblesize distribution), the values suggest that milk foams obtained bysteam injection are weaker. For instance, Yang and others (2009)found yield stress values greater than 30 Pa for foams producedfrom 10% (w/v) solutions of whey protein isolates, egg whiteprotein, and their combinations.

The milk foams tested in this study were found to become moreelastic as they destabilized (Figure 4), since the yield strain changedfrom 27% at 2 min to 37% at 10 min. This behavior can also beexplained using the model of Mason and others (1996) describedearlier; as the gas volume fraction increases and the liquid drains,a lower volume of liquid tends to distribute itself between theclusters of bubbles, which tends to produce bigger clusters, fewerdislocations, and the requirement of a greater yield stress to induceflow.

If the yield stress normalized by the Laplace pressure (σ/R32)is plotted as a function of the gas volume fraction (Figure 5), astatistically significant linear relationship (P = 0.0005) is observed:

τy = 0.14σ

R32(ϕ − 0.64). (2)

It is clear from Eq. 2 that the yield stress vanishes at gasvolume fraction of 0.64 which is consistent with earlier studies(Saint-Jalmes and Durian 1999; Rouyer and others 2005). This

Figure 4–Changes in yield stress and yield strain during the destabilizationof milk foams obtained by steam injection. The experimental data weredetermined by employing a linear stress ramp (0.2 to 25 Pa) over a sweeptime of 120 s, after covering the rheometer plates with sandpaper P120 tolimit slip. The values correspond to the mean of 3 measures and error barsrepresent the standard error.


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value corresponds to the gas volume fraction at which the bubbleshave a spherical shape for a random closed packing system anddo not lend themselves to further compression. Some oscillatorystudies have found a quadratic relation between the yield stress andthe gas volume fraction instead of Eq. 2 (Mason and others 1996;Saint-Jalmes and Durian 1999) following an empirical equationtype:

τy = βσ

R32(ϕ − 0.64)2, (3)

where β is a dimensionless factor. This discrepancy is probably dueto the limited range of gas volume fractions used to determine Eq.1 (0.78 to 0.86), in comparison with values of 0.5 to 1 used byMason and others (1996) and Saint-Jalmes and Durian (1999).

Viscoelastic response during foam destabilizationDynamic oscillatory experiments were undertaken to character-

ize the viscoelastic behavior of the foams during destabilization.The LVR and the oscillatory yield point (γ y

o, τ yo) were found by

applying an amplitude sweep, whereas the elastic (G′) and viscous(G′′) moduli were obtained employing frequency sweep.

Figure 6 shows the amplitude sweep plot for different foams.The LVR for foams of all ages is clearly between strain valuesof 0.004 and 0.11, although the exact interval depends on thefoam age: the range is narrower for younger foams but it widenswith foam age. As mentioned earlier, the foams turn more elasticwith aging because of the increase in the gas volume fraction. Asa result, the G′ values increase with aging. This change is moreevident between the foam ages of 2 and 4 min when G′ increasesfrom 36 to 51 Pa, while attaining a maximum value of 64 Pa afterdestabilizing for 10 min.

The transition from linear to nonlinear viscoelastic region(NLVR) is called oscillatory yield strain (γ y

o) and yield stress (τ yo)

(Hohler and Cohen-Addad 2005).As the behavior of G′ against γ in the LVR and NLVR can

be described by power laws that correspond to straight lines on alog–log plot, their intersection was used to define the oscillatoryyield strain (Rouyer and others 2005) and yield stress (Table 2).It is important to note that the oscillatory yield stress and strainare empirical values which depend on the frequency employed,

Figure 5–Yield stress of milk foams produced by steam injection, τ , normal-ized against the Laplace pressure, σ/R32, as a function of the gas volumefraction. The solid line represents Eq. 2 with R2 = 0.98 and P = 0.0005.

so the values reported in Table 2 are only valid at 1 Hz. Further,Table 2 shows that there are no significant differences betweenthe yield stress obtained by steady flow and dynamic oscillatoryexperiments, except when foam age is 2 min, where the oscillatoryvalue is lower. On the other hand, the oscillatory yield strainvalues are significantly greater than the yield strain values deducedfrom steady flow, again, the foam age of 2 min proving to be anexception where the oscillatory value is lower. Rouyer and others(2005) report that the values of yield stress and strain obtainedby oscillatory and steady shear experiments can differ by a factorof 3 at gas volume fractions greater than 0.7 attributable to shearbanding and/or strain history.

The frequency sweep plots (Figure 7) show the changes in G′and G′′ during the foam destabilization. Values of G′ increaseslightly with the frequency for a given foam age, reflecting theviscoelastic response of the material. This observation is consistentwith the work of Cohen-Addad and others (1998) for dry foams.In the case of G′′, this was between 3 and 5 times lower than G′,and it remained practically constant at frequencies in the range0.3 to 6 Hz. Since the foam structure changes continuously dueto destabilization, one can expect changes to occur even duringthe course of a rheological experiment. However, we found thatthe measured data on G′ and G′′ were very stable and reproducible.It appears that the foam history prior the rheological test is thedetermining factor accounting for the values observed in Figure 7.

If G′ and G′′, for a given frequency (1 Hz in the present case),are plotted against foam age (Figure 8), the 2 moduli can be

Figure 6–Viscoelastic moduli (G′—filled symbols, G′′—open symbols) asfunction of the strain (fixed frequency of 1 Hz) during the destabilizationof milk foams generated by steam injection (the data correspond to themean of 3 values, the error bars were omitted to improve clarity).

Table 2–Oscillatory yield strain and yield stress, at a frequency of 1Hz, of milk foams during destabilization.

Destabilization time (min) γ yoa(%) γ y

b (%) τ yo (Pa)a τ y (Pa)b

2 14 ± 0 −13∗ 3.2 ± 0.3 −1.8∗

4 42 ± 3 11∗ 9.3 ± 0.6 0.56 45 ± 1 9∗ 10.9 ± 1.1 0.48 47 ± 1 12∗ 11.5 ± 0.3 0.710 43 ± 1 6∗ 13.2 ± 1.3 2.2aValues correspond at the mean of three values ± the standard error.bThis is the difference between the dynamic oscillatory values and these obtained fromsteady flow experiments.∗ Indicates there are statistical significant differences by applying a t-test at a significancelevel of 0.05.




seen to increase with foam age, but the elastic modulus is alwaysbetween 3.7 and 4.7 times higher than the viscous modulus in-dicating a high elastic nature of these foams. It is interesting tocompare these results with data reported earlier by Cohen-Addadand others (1998). These authors observed that G′ and G′′ bothdecreased as the foam aged, which contradicts the trend foundin this work. Elastic module is related to bubble interfacial areawhich is proportional to φ/R32.Cohen-Addad and others (1998)investigated very dry foams whose gas volume fraction hardlychanged with age (φ varied between 0.926 and 0.936 over 8 h)but the bubble size increased due to coarsening. This caused theinterfacial area, and therefore the storage modulus, to decrease. Inthe present study, the hold-up increased from 0.78 to 0.86, but thebubble size almost remained unaltered. This resulted in the inter-facial area, and therefore the storage modulus, to increase with age.

Liquid-like response during the foam destabilizationWhen subjected to shear stress beyond the yield point, the

foams begin to flow showing interesting properties; the foam vis-cosity is some orders of magnitude greater than the viscosity of

Figure 7–Viscoelastic moduli (G′—filled symbols, G′′—open symbols) as afunction of the frequency (fixed strain of 0.05) during the destabilizationof milk foams generated by steam injection (the data correspond to themean of 3 values, the error bars were omitted to improve clarity).

Figure 8–Transient changes in elastic and viscous moduli for milk foamsobtained by steam injection. The data correspond to the mean of 3 repli-cates and the bars represent the standard error. Values were obtained fromFigure 7 at a frequency of 1 Hz.

the continuous phase and behaves like a shear thinning material.Figure 9 shows that milk foams produced by steam injection have,almost, half a million times greater viscosity than the milk justwhen it begins to flow, but the viscosity sharply decreases withshear rate. Similar values and trends were reported by Khan andothers (1988) working with a polymer-surfactant foam. The effectof the aging on apparent viscosity is more marked between 2 and4 min than for older foams (Figure 9), although these have slightdifferences at low shear rates. An interesting finding is that, at lowshear rate (γ < 0.02 s −1), viscosity of foams 8 min and older islower than at 4 and 6 min and it is almost the same at highershear rates. These results contradict to Khan and others (1988)who suggest that the viscosity is correlated with the yield stressand as the yield stress increases with foam aging, so should theviscosity.

The presence of a Newtonian plateau at shear rates lower than0.2 s−1 (Figure 9) suggests that the flow curves can be describedby the modified Cross model (Masalova and others 2003):

η = η0

1 + (λγ )n, (4)

where η is the apparent viscosity, η0 is the asymptotic value ofviscosity at very low shear rate, λ is the characteristic relaxationtime, and n is the dimensionless power index of the Cross model.The model parameters are stated in Table 3 for all foams. It isclear from Table 3 that the value of n does not change significantly(P = 0.331) as the milk foam ages.

Figure 9–Apparent viscosity as a function of the shear rate during destabi-lization of milk foams produced by steam injection. The data correspond tothe mean of 3 values; error bars were omitted to improve clarity. The solidlines represent the best fitting curves to the modified Cross model (Eq. 4).

Table 3–Modified Cross model constants: asymptotic value of viscos-ity at very low shear rate, η0, relaxation time, λ, and the dimensionlesspower index, n, as a function of foam age or destabilization time.

Destabilization time (min) η0 (Pa s)a λ (s)a na R2

2 331 ± 9e 16 ± 1b 1.4 ± 0.1A 0.994 900 ± 15f 27 ± 1c 1.4 ± 0.0A 0.996 1282 ± 27g 35 ± 1d 1.3 ± 0.0A 0.998 1174 ± 37g 37 ± 2d 1.2 ± 0.0A 0.9910 1322 ± 28g 36 ± 1d 1.3 ± 0.0A 0.99a Values correspond at the mean of three values ± the standard error.R2indicates fitting of data to the modified Cross model (Eq. 3). Different letters in thesame column represent significantly different values.


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Figure 10–Variation of relaxation time (λ) in the modified Cross model asa function of the gas volume fraction (φ) for milk foams produced by steaminjection. Values correspond to the mean of three replicates and the barsrepresent the standard error.

On the other hand, the characteristic relaxation time, λ, in-creased with foam age although it was only significantly different(P = 0.001) between 2 and 6 min. As a low relaxation time indi-cates a predominantly liquid-like material (Sai Manohar and others2011), the increase in this parameter with foam age is related tothe process of liquid drainage during destabilization. The plot ofgas volume fraction (a measure of the liquid content in the foam)and the relaxation time (Figure 10) confirms this fact.

The viscosity at very low shear rates (η0) also increased duringdestabilization (Table 3). The change was significant (P = 0.001)until 6 min and it changed marginally thereafter.

ConclusionViscoelastic behavior, yield thresholds, and liquid-like behavior

of milk foams produced by steam injection were characterizedduring the destabilization process. A direct dependence of theyield stress on the roughness of the rheometer plates was found,but an inverse relationship was observed between yield stress andsweep time. Yield stress values were independent of the techniqueused to measure it; however, the yield strain was dependent onthe methodology employed. The yield stress, elastic, and viscousmoduli and apparent viscosity changed with foam aging becauseof the variations in the foam properties. The yield stress varieswith dispersion properties according to the following equation:τy = 0.14 σ

R32(φ − 0.64). Elastic and viscous moduli increased with

foam age as a consequence of changes in the gas volume fraction.Liquid-like behavior was modeled using the modified Cross equa-tion; the dimensionless power index, n, did not change with foam

aging and the relaxation time, λ, was only different between 2 and6 min. Finally, a direct variation between the relaxation time andgas volume fraction was found.

AcknowledgmentsDr. Xenophon Zabulis from the Inst. of Computer Science,

Foundation for Research and Technology (Greece), is acknowl-edged for providing a copy of the software Bubbles Edit 1.1 toanalyze the bubble size. The financial support of Nestle and theEngineering and Physical Sciences Research Council (EPSRC),U.K., is also gratefully acknowledged.

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rheology of milk foams produced by steam injection

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