The Application of Diffusing-Wave Spectroscopy to Monitor the Phase Behavior of Emulsion–Polysaccharide Systems

Journal of Colloid and Interface Science 227, 495–504 (2000) doi:10.1006/jcis.2000.6888, available online at http://www.idealibrary.com on

The Application of Diffusing-Wave Spectroscopy to Monitor the Phase Behavior of Emulsion–Polysaccharide Systems Erik ten Grotenhuis,†,1 Marcel Paques,∗ and George A. van Aken∗, † ∗ Wageningen Centre for Food Sciences, P.O. Box 557, 6700 AN Wageningen, The Netherlands; and †NIZO Food Research, P.O. Box 20, 6710 BA Ede, The Netherlands Received December 6, 1999; accepted April 3, 2000

Droplet aggregation is an important cause of instability in emulsions because it may, on one hand, lead to an increased creaming rate, resulting in fast separation of a concentrated emulsion phase (creamed layer). On the other hand, it may also lead to the formation of a stabilizing, droplet-based network. Early detection of instability is often difficult due to the high turbidity and viscosity of more concentrated food emulsions. The applicability of diffusingwave spectroscopy (DWS) for monitoring droplet aggregation and creaming was studied using a model system consisting of a proteinstabilized emulsion, to which a soluble polymer (“thickener ) was added. This addition leads to an increased solvent viscosity and may induce droplet aggregation. In addition, the redistribution process of emulsion droplets in aggregating concentrated emulsions was directly observed by confocal scanning laser microscopy (CSLM). By DWS the decrease of the droplet mobility caused by the viscosity increase of the continuous phase could be separated from the effect of droplet aggregation. Moreover, a distinction could be made between aggregation, leading to increased creaming rates and that leading to the formation of a stabilizing droplet network. The potential of DWS for in situ measurement of the stability of concentrated emulsions is discussed. °C 2000 Academic Press Key Words: diffusing-wave spectroscopy; light scattering; colloidal interaction; polysaccharides; emulsion stability; CSLM.

INTRODUCTION

Aggregation is an important process in dispersed systems because it strongly influences both the rheological properties of the system and the stability against sedimentation or creaming. The tendency for aggregation is determined by the colloidal interaction between the dispersed particles. Our interest in this matter lies in understanding and predicting creaming stability in foodtype emulsion systems, in which oils and fats are usually finely dispersed as emulsion droplets. Creaming is the gravity-driven vertical movement of emulsion droplets in an emulsion, caused by the difference in density between the emulsion droplets and the continuous phase. It may considerably reduce the storage time of emulsion-type products.

1

To whom correspondence should be addressed. E-mail: [email protected].

Creaming is accelerated when droplet aggregation leads to the formation of separate and relatively compact flocs of droplets (flocculation). However, droplet aggregation may also impede the creaming process when an extended network of emulsion droplets is formed, able to resist gravitational forces. Practical examples of such systems are various salad dressings in which the interaction is induced by the addition of a polymer that does not adsorb to the droplets, as explained by Parker et al. (1). Mostly, creaming does not become macroscopically visible within the first few hours, but shows up upon prolonged storage for several days or even months, and then leads to decreased performance or even failure and product loss. For this reason, a great demand exists for predictive stability tests that can be applied directly after the preparation of the emulsion-type product. At present, many techniques are available for the characterization of emulsion systems. Macroscopic detection of creaming can in principle be done by visual observation; however, in turbid systems substantial gradients of the droplet concentration may already exist long before they become apparent to the eye. The detection can be improved by using acoustic measurement (2). The velocity of ultrasound is sensitive to the droplet concentration, and therefore the transmission of sound waves through a sample as a function of the height in the sample can be used to detect creaming (3, 4). Similar information is obtained by scanning turbidity and reflectivity of light as a function of the height in the sample (5). Structural changes at colloidal scale will precede an actual phase separation, and monitoring these changes may therefore be useful for predicting stability. Methods that require dilution of the emulsion are not applicable for this purpose because dilution will inevitably change the structure and interaction between the droplets. Structural changes can be observed directly by microscopic imaging techniques (6). However, these usually require sample preparation in some form, leading to artefacts. These artefacts can be prevented by using advanced freezing methods as preparation for electron microscopic observation at ambient or low temperature (7). Mechanical deformation can be avoided by using confocal scanning laser microscopy (CSLM) (8); however, usually fluorescent probes have to be added. Rheological measurements give information about the interaction between the droplets (6, 9); for example, the formation of weak

495

0021-9797/00 $35.00

C 2000 by Academic Press Copyright ° All rights of reproduction in any form reserved.

496

GROTENHUIS, PAQUES, AND VAN AKEN

and strong droplet networks can be studied by using rheological measurements. However, accurate rheological measurements are often difficult to perform due to the formation of slipping layers between the emulsion and the wall of the measuring cell and due to artefacts caused by the transfer of the sample into the measuring cell. Furthermore, direct information on particle interaction at colloidal scale can only be obtained from rheological measurements by the application of a theoretical model and by variation of the measuring conditions. An important limitation of microscopy and rheological techniques is that in-line measurements are usually impossible. An emerging optical technique that enables the characterization of intact, concentrated systems is diffusing-wave spectroscopy (DWS) (10). It is well suited for strongly scattering systems, such as concentrated emulsions, and in-line measurements are possible. The method is based on the measurement of temporal fluctuations of multiple scattered light (10). The fluctuations are caused by the motions of the light-scattering particles, e.g., droplets in the case of emulsions and casein micelles in skimmed milk. DWS provides direct quantitative information about the relative displacement of particles as a function of time, averaged over the measured volume. The displacement is driven by convection or Brownian motion and depends on the mobility of particles. Therefore, DWS is sensitive to changes in the mobility of particles, for example, due to an increase in the viscosity of the solvent or due to particle interactions. Examples of the possibilities of DWS are its application to study the aggregation of casein micelles during the formation of cheese curd (11), to study the viscoelastic properties of highly concentrated emulsions (12, 13), and to study aggregation in emulsions to which a nonadsorbing polymer has been added (14). This paper describes a study on the applicability of DWS as a tool to investigate aggregation phenomena in oil-in-water emulsions. The interaction between the droplets is controlled by the addition of varying amounts of an exocellular polysaccharide (EPS) (15). In this type of system the interactions between the droplets can be explained by the depletion mechanism (16). The DWS results will be compared to the macroscopic behavior of the emulsions and to CSLM observations.

86 nm. EPS was completely dissolved in a 0.10 M NaNO3 solution at a concentration of 6.09 g/L before addition to the emulsions. Rhodamine B (Aldrich Chemical Co., Milwaukee, WI, CAS 81-88-9) was dissolved in distilled water to a concentration of 0.05%. Methods A stock emulsion with a volume fraction of 0.50 was prepared by mixing equal volumes of sunflower oil (Reddy, Vandemoortele, Roosendaal, The Netherlands) and an aqueous solution of 1 wt% whey protein isolate and 0.10 M NaNO3 and subsequent homogenization with a laboratory homogenizer (8.30H, Rannie, APV, Wilmington, MA) operated at a pressure of 50 bar. A small amount of thiomersal (sodium ethylmercurithiosalicylate, Fluka Chemie AG, Buchs, Switzerland) was added to prevent microbial growth, and the pH was adjusted to 6.7 by the addition of small amounts of 0.1 M solutions of HCl or NaOH. The emulsion droplets had an average diameter (d3,2 ) of 1.3 µm, as measured with an optical particle sizer (Mastersizer-X, Malvern Instruments Ltd., Malvern, Worcester, England). The size distribution was relatively wide: 90% of the particle diameters ranged between 0.6 and 4 µm (Fig. 1). Emulsions with lower volume fractions were prepared from the stock emulsion by dilution with a 0.10 M NaNO3 solution. The phase diagram was determined by mixing the emulsion, the EPS solution, and the NaNO3 solution in varying ratios. The samples were placed in glass tubes with an inner diameter of 10 mm. The transmitted and back-scattered intensity of light along the vertical dimension of the tubes was measured using a vertical scan macroscopic analyzer (Turbiscan MA 1000, Formulaction, Ramonville-St-Agne Toulouse, France). The presence of a sharp boundary between an emulsion-rich upper phase and an emulsion-poor lower phase after 24 h was taken as the criterion for phase separation.

MATERIALS AND METHODS

Materials Whey protein isolate was obtained from Davisco International, Inc. (BiPro, Le Sueur, MN) and consisted of βlactoglobulin (71 wt%), α-lactalbumin (12 wt%), immunoglobulin (5 wt%), bovine serum albumin (5 wt%), salts (2 wt%), lactose (1 wt%), and water (4 wt%). The EPS was produced at the NIZO Food Research pilot plant by inoculation of a whey permeate medium with Lactococcus lactis subsp. cremoris NIZO B40 and has been described in detail elsewhere (15). The EPS had a molar mass (Mn ) of 1.47 × 106 g/mol and a number-averaged radius of gyration (Rg ) of

FIG. 1. Droplet-size distributions of the emulsion immediately after preparation.

DWS ON EMULSION–POLYSACCHARIDE SYSTEMS

CSLM and DWS measurements were carried out on 20% oilin-water emulsions without and with added EPS. DWS measurements and CSLM images were recorded every minute for samples to which EPS was added to monitor aggregation. DWS was performed in an optical arrangement similar to that described by Weitz and Pine (10), by measurement of the intensity fluctuation of light transmitted through the emulsion located in a rectangular cuvette with a wall-to-wall thickness of 2.5 mm. The width and the height of the cuvette were 40.0 mm, which were sufficient to avoid boundary effects. A HeNe laser (wavelength λ0 = 632.8 nm) was used as a light source. The scattered light was focused by a lens into a single-mode fiber connected to a photomultiplier tube (ALV SO-SIPD, Langen/Hessen, Germany). The intensity fluctuations were recorded and transferred into intensity autocorrelation functions by a correlator board (ALV 5000/E, ALV GMBH, Langen/Hessen, Germany). CSLM imaging was carried out using CSLM equipment from a BioRad (MRC 1024 BioRad, Heml Hempstead Herts, U.K.) configured with an inverted microscope (Axiovert-100, Zeiss, Oberkochen, Germany). The CSLM was equipped with an air-cooled mixedgas Ar/Kr laser, which produces lines at 476, 488, 568, and 647 nm. Before CSLM observation a few droplets of an aqueous solution of 0.05% Rhodamine B were mixed through the solution with a spatula. The 488-nm line was applied to excite the Rhodamine B, which results in the emission of 550-nm light by fluorescence. Rhodamine B selectively stains the protein in the system, which then becomes visible in the image. For observation with the transmission electron microscope (TEM) small aliquots of the emulsions were physically stabilized by high-pressure freezing (HPF (17)). Subsequently, the frozen emulsions were fractured and etched, and the fresh fracture face was replicated by Pt shadowing. After the sample was removed from the replica by thorough washing with HClO3 and distilled water, the replica was placed on a 700-mesh Cu TEM grid and transferred to the TEM (CM12, Philips, Eindhoven, The Netherlands) for observation at ambient temperature. RESULTS AND DISCUSSION

Phase Diagram Figure 2 shows the phase diagram for emulsions with volume fractions of oil droplets between 0.05 and 0.50 and EPS concentrations up to 3.0 g/L. It resembles closely the phase diagram reported by Tuinier and de Kruif (16). In the emulsions with EPS concentrations below the boundary of phase separation, the sample turbidity showed a smooth gradient as a function of height due to normal creaming of the emulsion droplets. At EPS concentrations exceeding the phase boundary a sharp interface between the emulsion droplet-rich upper phase and the emulsion droplet-depleted lower phase was observed. It was observed that the initial rate by which the emulsion-rich phase separated from the emulsion-poor phase increases with an increasing amount of EPS. This is in agreement with observations by Tuinier and de Kruif (16), who explained this increase by the larger size of the

497

FIG. 2. Phase diagram for the addition of EPS to an oil-in-water emulsion stabilized by whey protein. The solid curve (spinodal demixing line) and dashed curve (gel line) are calculated according to the theoretical treatment given in the Appendix. Dotted lines are drawn by hand.

droplet aggregates formed at higher EPS concentrations, caused by a higher (depletion) force acting on the emulsion droplets. As long as the droplet aggregates remain separate from each other, the larger size of these aggregates leads to faster creaming. However, at higher EPS concentrations, the rate at which the emulsion phase separated was seen to decrease. This may have been caused by the increased viscosity of the continuous phase caused by the higher EPS concentration. Above approximately 0.6 g/L, the polysaccharide coils of the EPS molecules overlap, after which the viscosity increases more rapidly with the EPS concentration due to entanglements (15). Furthermore, the emulsion droplets may have formed extended aggregates that interconnect through the whole system, retarding the creaming process. Addition of higher concentrations of EPS gradually led to almost complete arrest of the phase separation. These systems appeared to be homogeneous on the macroscopic scale and had a gel-like consistency. For similar systems it has been suggested that the structure of the gelled emulsion is formed by a weakly aggregated network of emulsion droplets (1). A recent study on a model emulsion to which a nonadsorbing polymer (poly(ethylene oxide)) was added (φoil = 0.35, cp = 4 g/L, Mw,p = 900,000 g/mol) showed that in the gel region the emulsion droplets form clusters that are connected by a relatively small number of bonds, resulting in the formation of a continuous network (14). The positions of the phase boundaries (homogeneous/phase separated and phase separated/gelled) have been discussed by Tuinier and de Kruif (16). The phase boundary homogeneous/phase separated could be reasonably well described by the depletion interaction theory of Vrij (18), and the position of the gel region for this system was predicted fairly well

498

GROTENHUIS, PAQUES, AND VAN AKEN

by calculations analogous to those by Chiew and Glandt (19). The theoretical derivations of the position of the corresponding phase boundaries are given in the Appendix and the resulting positions of the corresponding phase boundaries are drawn in Fig. 2.

CSLM Measurements Figure 3A shows a CSLM image of the emulsion (20% oil in water) without EPS. Because the protein was present at a relatively high concentration at the surface of the emulsion droplets,

FIG. 3. CSLM image of a 20% oil-in-water emulsion: (A) without EPS added; (B) with 0.1 g/L EPS added; (C) with 0.3 g/L EPS added; (D) with 1.5 g/L EPS added. Length of bar = 5 µm.

499

DWS ON EMULSION–POLYSACCHARIDE SYSTEMS

additional techniques would be required, which is beyond the scope of this work. The addition of 1.5 g/L EPS (close to the gel region according to Fig. 2) led to the structure shown in Fig. 3D. It is clear that the emulsion droplets have aggregated, forming a space-filling network. The formation of the network proceeded in several minutes. The network appears to be strong enough to withstand gravitational forces because the structure is stationary with respect to the focal plane of the CSLM. Rearrangement of the structure was observed after it was disrupted by stirring (not shown). DWS Measurements, as a Function of EPS Concentration

FIG. 4. TEM image of a 20% oil-in-water emulsion with 0.3 g/L EPS. Length of bar = 0.9 µm.

the image shows the surfaces of the droplets. The distribution of emulsion droplets was homogeneous. The emulsion droplets were seen to move individually through the sample, showing no sign of long-lasting aggregates. A CSLM image of the emulsion after addition of 0.1 g/L EPS, still in the “stable” region of the phase diagram (Fig. 2), is shown in Fig. 3B. The distribution of the emulsion droplets has not changed compared to that in Fig. 3A and the droplets still moved individually. The addition of EPS to a concentration of 0.3 g/L (eventually leading to phase separation according to Fig. 2) immediately induced aggregation of emulsion droplets on a microscopic scale. The droplets were seen to be irreversibly captured in the aggregates. Fast aggregation occurred during the first few minutes, but a slow increase or reorganization continued during the next hour. After 20 min aggregates of emulsion droplets had been formed together with some regions depleted of emulsion droplets (Fig. 3C). The aggregates remained relatively small (<20 µm) and were not visibly interconnected. The aggregates slowly moved out of the focal plane of the CSLM due to creaming, and a macroscopically visible phase separation became apparent after several hours. A TEM image of this sample (Fig. 4) shows an aggregate of droplets. The appearance of the aggregate is in accordance with depletion interaction between the droplets caused by the added EPS: smooth droplets are in contact with each other, embedded by a continuous phase that is densely and homogeneously filled with polymeric structures. The observed structure gives no indication that other aggregation mechanisms, such as a flocculated protein layer binding the droplets together, were acting. The structure visible in the continuous phase is probably due to dissolved EPS, but the applied preparation and imaging techniques do not allow further interpretation of its threadlike structure. To obtain more insight into this structure,

DWS measurements were performed on emulsions with an oil volume fraction of 0.20. Increasing small amounts of EPS were added to the emulsion, and after each addition the intensity autocorrelation functions were recorded for 30 min at a rate of 1/min. Autocorrelation functions measured 30 min after addition of EPS are given in Fig. 5 for five different EPS concentrations. The amounts of EPS added resulted in macroscopic behavior of the emulsions ranging from stable to gelled (Fig. 2). The correlation function of the emulsion without EPS shows the expected decay (10). The addition of EPS causes a shift of the curves toward longer correlation times, reflecting a decrease in mobility of the emulsion droplets. The mobility of the emulsion droplets is usually expressed by their mean square displacement h1r 2 (t)i, which can be obtained by numerically inverting the correlation functions and using Eq. [1]: q 2 L/l ∗ k02 h1r 2 (t)i  q g (2) (t) − 1 = β  £ ¤ . sinh L/l ∗ k02 h1r 2 (t)i 

[1]

FIG. 5. Autocorrelation functions g (2) (t) − 1 as a function of correlation time measured by DWS 30 min after addition of EPS to an 20% oil-in-water emulsion, for various EPS concentrations.

500

GROTENHUIS, PAQUES, AND VAN AKEN

increases less than proportional with increasing correlation time. This shows that the droplets are captured in a network of emulsion droplets, in which case h1r 2 (t)i is expected to level off to a plateau value at long correlation times. The√maximum of the root mean square displacement (maximum h1r 2 (t)i) in the network for the highest EPS concentration was of the order of 10 nm. It could not be determined exactly because the large values of h1r 2 (t)i fall into the noise level of the autocorrelation functions. However, we may compare the deviation from linearity observed in our gelled emulsion (φ = 0.20) to measurements of the droplet mobility √ in highly concentrated emulsions, for was found at which a maximum h1r 2 (t)i of about 3 nm (12)√ a droplet volume fraction φ = 0.65. A maximum h1r 2 (t)i of about 6 nm was found by Meller et al. for a gelled emulsion with a volume fraction of 0.54 by using DWS (14). Despite the much lower volume fraction (φ = 0.20) of our systems, the deviation from linearity due to the restricted droplet mobility is apparent, and probably of the same order of magnitude as that for the concentrated systems. FIG. 6. Same as Fig. 5, but now (L/l ∗ )2 k02 h1r 2 (t)i is plotted as a function of the correlation time.

In this equation g (2) (t) is the intensity autocorrelation function, β is an instrumental factor, L is the width of the sample cuvette, l ∗ is the optical mean free path, and k0 is the length of the wave vector 2π/λ, where λ is the wavelength of light in the medium. This expression has been derived from the more general expression for g (2) (t) given by Weitz and Pine (10) by assuming that L À l ∗ and k02 h1r 2 (t)i ¿ 1. The value of l ∗ was estimated to be 20 µm from measurements of the transmitted intensity. This value is in the same order of magnitude as that found before by Ladd et al. for highly monodisperse latex spheres (20). The values for (L/l ∗ )2 k02 h1r 2 (t)i are plotted as a function of the correlation time in Fig. 6. For the emulsion without added EPS the logarithm of h1r 2 (t)i is seen to depend almost linearly on the logarithm of the correlation time. A best fit according to h1r 2 (t)i ∝ t γ yields γ = 0.95. This is very close to the expected value γ = 1 for diffusion of particles in a purely viscous medium. After addition of a small amount of EPS to the emulsion (remaining below the phase boundary, however), no significant change in the position and the shape of the curve is found. At intermediate EPS concentrations, where addition of EPS induces a phase separation, the curve is shifted to higher correlation times without a change in the shape or the slope of the curve. This means that the mobility of the emulsion droplets has decreased, but that there are no spatial limitations for the particles. This may be caused by the increase in viscosity of the continuous phase of the emulsion due to the addition of EPS. Another explanation is that reversible aggregates of particles were formed, causing a restriction in the mobility of the particles. If EPS is added at concentrations where a gel is formed, the curves are not only shifted to higher correlation times, but they also deviate from the linear behavior that is observed for lower EPS concentrations. At high correlation times (typically >0.1 ms), h1r 2 (t)i

Monitoring of the Aggregation Process After addition of EPS to the emulsions and mixing, it was found that it requires some time until the emulsion droplets have reorganized into their new configuration. This is reflected by a change in the correlation functions measured by DWS (Fig. 7). Each correlation curve was calculated from the intensity fluctuations measured for 1 min, and the relaxation process was monitored for 30 min. In accordance with Horne (21) we define a half-time, τ1/2 , of the correlation functions as the correlation time for which the correlation function has decayed to half of

FIG. 7. Autocorrelation functions g (2) (t) − 1 as a function of correlation time measured 1 and 30 min after the addition of 3 g/L EPS to a 20% oil-inwater emulsion.

501

DWS ON EMULSION–POLYSACCHARIDE SYSTEMS

FIG. 8. τ1/2 as a function of correlation time measured for a number of EPS concentrations added to a 20% oil-in-water emulsion. Recording of τ1/2 was started directly after EPS was mixed through the sample.

its initial value. The relaxation of τ1/2 toward a final value is shown in Fig. 8. The relaxation curves shift to higher τ1/2 values when more EPS is added. The fastest relaxation is observed during the first few minutes after EPS addition and stirring. CSLM observations confirmed that the relaxation process observed in Fig. 8 is indeed due to reorganization of the emulsion droplets after being mixed in the EPS (Fig. 9). Figure 10 shows the data points of Fig. 8, but now as a function of the EPS concentration for different times after EPS addition. The τ1/2 values for 10 and 30 min are averages of five data points. The τ1/2 values of the autocorrelation functions measured during the first minute after addition of EPS are seen to increase linearly with the EPS concentration. This is probably due to the viscosity increase of the continuous phase due to the addition of EPS. The slow increase of τ1/2 toward its final value is seen to be non linear with the EPS concentration. This effect is most evident for the EPS concentration of 3 g/L, where the emulsion had the appearance of a soft gel. So besides the immediate effect due to the viscosity change of the continuous phase, a slower process occurs, which is probably related to the interactions between the emulsion droplets. This process becomes even more evident from a plot of the mean square displacement of the emulsion droplets as a function of waiting times (Fig. 11). Here, (L/l ∗ )2 k02 h1r 2 (t)i is given for several times after addition of EPS at a concentration of 1.5 g/L. When the curve measured after 1 min is compared with the curve of the emulsion without EPS, it is obvious that the viscosity increase leads to a parallel shift of the curve along the horizontal axis toward longer correlation times. The curve remains linear with the same slope, which indicates that the droplets are still in unrestricted Brownian motion. At longer times after the addition of EPS the droplets become more and more trapped as a result of the net attractive interactions between the emulsion droplets, which is reflected in a deviation from linearity.

The present work has shown that DWS can be used to monitor droplet aggregation and the development of texture by the formation of a network of aggregated droplets. In on-going research we will further elaborate on this new opportunity. DWS can also be used to study mechanical properties of concentrated emulsions as has been shown by H´ebraud et al. (22). They studied highly concentrated (φ = 0.85) emulsions subjected to periodic shear strain. By determining the shape and height of the correlation functions at correlation times corresponding to the period of the strain, they were able to determine the fraction of droplets that was stationary and the fraction of droplets that repeatedly rearranged. This type of information is very useful for determining when an emulsion gel yields as a function of the strain applied.

SUMMARY

In this paper the use of diffusing-wave spectroscopy as a method to characterize aggregation phenomena in emulsions has been investigated. Measurements were carried out on a model system composed of a protein-stabilized oil-in-water emulsion to which varying amounts of a polysaccharide were added. The polysaccharide concentration was used to control the interaction between the droplets, and in this way the emulsion could be adjusted among stable, phase-separating, and gelling. When time-resolved DWS is applied to an oil-in-water emulsion, the effect of polysaccharide addition on the viscosity of the continuous phase and on droplet aggregation could be detected and distinguished by stirring the emulsion. Shortly after stirring is stopped, the droplet mobility is only influenced by the viscosity of the continuous phase. At longer times, the droplet mobility decreases further due to droplet aggregation.

502

GROTENHUIS, PAQUES, AND VAN AKEN

FIG. 9. CSLM images collected 1, 2, 5, and 10 min after EPS addition to a 20% oil-in-water emulsion, demonstrating slow droplet reorganization. Length of bar = 5 µm.

503

DWS ON EMULSION–POLYSACCHARIDE SYSTEMS

separating system, such a maximum displacement is not found, probably because the droplet aggregates are not stationary (e.g., due to creaming). We therefore conclude that DWS is a useful technique for studying the aggregation behavior of concentrated emulsions. It gives new perspective to the investigation of texture development in emulsions and has the potential to predict creaming stability. APPENDIX

Calculation of the Positions of the Phase Boundaries Corresponding to Phase Separation and Gelation Caused by Depletion of Polysaccharide Close to the Droplet Surface

FIG. 10. Same data points as those in Fig. 8. Now, τ1/2 was plotted as a function of the EPS concentrations for different times after EPS addition. Symbols: s, 1 min; 4, 2 min; e, 5 min; h, 10 min; 5, 30 min.

The macroscopically distinct phenomena phase separation and gel formation are both due to droplet aggregation, as could be confirmed by CSLM observations. Distinction between these phenomena could also be made by DWS. In a gelled system the droplets are bound to a stationary network of droplets, restricting the maximum displacement of the droplets. In a phase-

The position of the phase boundary homogeneous/phase separated is assumed to lie close to the spinodal demixing line, which can be calculated as the volume fraction φoil where the osmotic compressibility ∂5c /∂φoil of the emulsion becomes zero. The osmotic pressure was obtained from a virial expansion of the osmotic pressure (23) 5c Vc 2 3 + B3 φoil + ···, = φoil + B2 φoil kB T

[A1]

where Vc is the droplet volume and B2 and B3 are the second and third virial coefficients of the osmotic pressure. With neglect of the third- and higher-order terms of Eq. [A1], the spinodal demixing line is represented by sp

φoil = −

1 sp . 2B2

[A2]

Statistical thermodynamics leads to an expression of the second virial coefficient (24),

B2 =

2π Vc

¶¸ µ Z∞ · U (r ) r 2 1 − exp − dr, kB T

[A3]

0

where r is the distance between the centers of the emulsion droplets and U(r) is the depletion interaction potential given by Vrij (18): ¯ ¯ +∞ ¯ ¯ U (r ) = ¯ −5p Voverlap ¯ ¯0 FIG. 11. Measured (L/l ∗ )2 k02 h1r 2 (t)i as a function of the correlation time, measured 1, 2, 10, and 30 min after the addition of 1.5 g/L EPS to a 20% oilin-water emulsion. For comparison, results from a measurement without added EPS are also shown.

0 < r < σc , σc ≤ r ≤ σc + σp ,

[A4]

r > σc + σp ,

where σc and σp are are the diameters of the droplet and of the polysaccharide molecules, respectively, Voverlap is the overlap volume of the layers depleted of polysaccharides around the droplets, and 5p is the osmotic pressure of the polysaccharide

504

GROTENHUIS, PAQUES, AND VAN AKEN

solution. The overlap volume is given by · ¸ r3 1 3r 3 + , Voverlap (r ) = π (σc + σp ) 1 − 6 2(σc + σp ) 2(σc + σp )3 [A5] and for the osmotic pressure of the polymer solution the limiting Van’t Hoff’s law is taken 5p = cp RT /M,

[A6]

where M is the molecular mass of the polysaccharide. To calculate the spinodal demixing line in Fig. 2, we further assumed σc = d3,2 and σp is equal to twice the radius of gyration of the polysaccharide in solution, which is 86 nm (16). The gel line was calculated as the percolation transition for aggregating droplets, for which Chiew and Glandt (19) derived τB =

2 19φoil − 2φoil + 1 , 12(1 − φoil )2

[A7]

where τB is the Baxter parameter, for which Tuinier and de Kruif (16) found an exponential dependence with cp , τB = c2 exp(−cp /c1 ),

[A8]

where c1 and c2 are fitting constants. In Fig. 2, we used c1 = 1.9 g/L and c2 = 0.642. ACKNOWLEDGMENTS The authors would like to thank Dave Weitz for useful discussions on diffusing-wave spectroscopy. Franklin Zoet is acknowledged for his assistance in performing many experiments. Jean-Pierre Munch and his co-workers are gratefully thanked for the fruitful discussions about these and future experiments. Unilever Research Vlaardingen is thanked for providing the access to their microscopy facilities. Wim Agterof is greatly acknowledged for providing the financial support for the microscopical imaging. Ruud van den Adel is thanked for the highly skilled execution of the microscopical work. Ton van Vliet is acknowledged for critically reading the manuscript.

REFERENCES 1. Parker, A., Gunning, P. A., Ng, K., and Robins, M. M., Food Hydrocolloids 9, 333 (1995). 2. Howe, A. M., Mackie, A. R., and Robins, M. M., J. Dispersion Sci. Technol. 7, 231 (1986). 3. Gunning, P. A., Hibberd, D. J., Howe, A. M., and Robins, M. M., Food Hydrocolloids 2, 119 (1988). 4. Cao, Y., Dickinson, E., and Wedlock, D. J., Food Hydrocolloids 5, 443 (1991). 5. Chantrapornchai, W., Clydesdale, F., and McClements, D. J., J. Agric. Food Chem. 46, 2914 (1998). 6. Dickinson, E., and Golding, M., Food Hydrocolloids 11, 13 (1997). 7. Heertje, I., and Paques, M., in “New Physico-chemical Techniques for the Characterization of Complex Food Systems” (E. Dickinson, Ed.), p. 1. Blackie, London, 1995. 8. Blonk, J. C. G., and van Aalst, H., Food Res. Int. 26, 297 (1993). 9. Pettitt, D. J., Wayne, J. B, Renner-Nantz, J. J., and Shoemaker, C. F., J. Food Sci. 60, 528 (1995). 10. Weitz, D. A., and Pine, D. J., in “Dynamic Light Scattering” (W. Brown, Ed.), p. 652. Clarendon Press, Oxford, 1993. 11. Horne, D. S., and Davidson, C. H., Milchwissenschaft 45, 712 (1990). 12. Liu, A. J., Ramaswamy, S., Mason, T. G., Gang, H., and Weitz, D. A., Phys. Rev. Lett. 76, 3017 (1996). 13. Mason, T. G., Gang, H., and Weitz, D. A., J. Opt. Soc. Am. A 14, 139 (1997). 14. Meller, A., Gisler, T., Weitz, D. A., and Stavans, J., Langmuir 15, 1918 (1999). 15. Tuinier, R., Zoon, P., Cohen Stuart, M. A., Fleer, G. J., and de Kruif, C. G., Biopolymers 50, 641 (1999). 16. Tuinier, R., and de Kruif, C. G., J. Colloid Interface Sci. 218, 201 (1999). 17. Studer, D., Michel, M., Wohlwend, M., Hunziker, E. B., and Buschmann, M. D., J. Microsc. 179, 321 (1995). 18. Vrij, A., Pure Appl. Chem. 48, 471 (1976). 19. Chiew, Y. C., and Glandt, E. D., J. Phys. A: Math. Gen. 16, 2599 (1983). 20. Ladd, A. J. C., Gang, H., Zhu, J. X., and Weitz, D. A., Phys. Rev. E 52, 6550 (1995). 21. Horne, D. S., in “Laser Light Scattering in Biochemisty” (S. E. Harding, D. B. Satelle, and V. A. Bloomfield, Eds.), p. 225. The Royal Society of Chemistry, Cambridge, U.K. 1992. 22. H´ebraud, P., Lequeux, F., Munch, J. P., and Pine, D. J., Phys. Rev. Lett. 78, 4657 (1997). 23. Lyklema, J., “Fundamentals of Colloid and Interface Science,” Vol. 1, Chap. 2. Academic Press, San Diego, 1991. 24. McQuarrie, D. A., “Statistical Mechanics.” Harper & Row, New York, 1976.