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Nondestructive Monitoring of Sucrose Diffusion in Oil-in-Water Emulsions by Ultrasonic Velocity Profiling
Journal of Colloid and Interface Science 220, 429 – 435 (1999) Article ID jcis.1999.6548, available online at http://www.idealibrary.com on
Nondestructive Monitoring of Sucrose Diffusion in Oil-in-Water Emulsions by Ultrasonic Velocity Profiling Taygun K. Basaran and D. Julian McClements 1 Biopolymers and Colloids Research Laboratory, Department of Food Science, University of Massachusetts, Amherst, Massachusetts 01003 Received June 10, 1999; accepted September 15, 1999
One of the major problems in studying the diffusion of molecules within colloidal dispersions is the fact that these systems are usually optically opaque. Consequently, it is not possible to use the techniques that have been developed for the analysis of optically transparent systems, such as measuring the absorbance vs height profile by UV-visible spectroscopy (5). Optically opaque systems can be studied by physically sectioning a sample and measuring the concentration of the diffusing molecules in each section (4). The major disadvantage of this technique is that it is destructive and it is not possible to obtain a detailed profile of the change in the concentration with distance. Techniques based on magnetic resonance imaging (MRI) have recently been developed to nondestructively monitor molecular diffusion in optically opaque systems (3). These techniques are extremely powerful; however, their application is limited because of their high cost and need for skilled operators. A number of workers have shown that ultrasonic profiling measurements can be used to monitor mass transport processes in optically opaque materials. Ultrasonic profiling has been used to monitor the creaming of oil droplets in emulsions (6 –10), the sedimentation of pulp in orange juices (11), and the diffusion of small molecules through gels (12–14). These techniques measure either the ultrasonic velocity or attenuation coefficient of a material as a function of its height and then use empirical or theoretical equations to convert the ultrasonic parameters into concentration profiles. In this study, we use an ultrasonic velocity profiling technique to examine the influence of droplet concentration on the diffusion of sucrose through oil-in-water emulsions.
The diffusion of sucrose through an optically opaque oil-inwater emulsion was monitored nondestructively by measuring the ultrasonic velocity as a function of height. Initially, a corn oil-inwater emulsion (0, 5, 10, 15, or 20 wt% oil) stabilized by Tween 20 (1 wt%) and xanthan (1 wt%) was placed in a measurement cell at 30°C. A 20 wt% sucrose solution containing the same concentration of Tween 20 and xanthan as the aqueous phase in the emulsion was placed on top of the emulsion. The ultrasonic velocity of this two-layer system was measured as a function of sample height and time and then converted into sucrose and oil concentration– distance profiles using empirical calibration curves. The translational diffusion coefficient of the sucrose in the upper and lower layers was determined by fitting the experimental data to a Fickian diffusion model. The measured diffusion coefficients of the sucrose molecules decreased as the droplet concentration in the emulsion increased, indicating retardation of the sugar molecule movement. Ultrasonic profiling was also used to monitor the compression of the emulsion due to movement of water molecules into the upper layer. © 1999 Academic Press Key Words: ultrasound; sucrose; emulsion; diffusion coefficient.
INTRODUCTION
The movement of small molecules through colloidal dispersions is important in a variety of scientific and technological applications. The separation and identification of substances using many chromatography and electrophoresis techniques relies on differences in the speeds that different molecules pass through a colloidal dispersion (1). Many types of pharmaceutical products utilize colloidal matrixes to control the rate at which drugs are released in the body (2). The diffusion of small molecules through biopolymer networks and colloidal dispersions is of great importance in the production of many types of foods. The diffusion of salts in cheese curd is an important stage in the manufacture of some cheeses (3). The diffusion of sugars from fruit purees into yogurts containing a network of aggregated milk proteins influences product quality (4). It is therefore of great technological and scientific interest to establish the factors that determine the rate at which small molecules diffuse through colloidal dispersions. 1
EXPERIMENTAL PROCEDURES
Materials
To whom correspondence should be addressed.
Sucrose, sodium azide, and Tween 20 were obtained from the Sigma Chemical Company (St. Louis, MO). The polysaccharide, xanthan, was obtained from Kelco International (London, UK). The corn oil was obtained from a local supermarket. All solutions were prepared with double-distilled and deionized water.
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0021-9797/99 $30.00 Copyright © 1999 by Academic Press All rights of reproduction in any form reserved.
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BASARAN AND MCCLEMENTS
Emulsion Preparation An aqueous surfactant solution containing 1 wt% Tween 20 and 0.02 wt% sodium azide (an antimicrobial agent) was prepared. Corn oil-in-water emulsions were prepared by homogenizing weighed amounts of oil (25 wt%) and surfactant solution (75 wt%). A coarse emulsion premix was prepared using a high-speed blender (Waring Model 33BL79, New Hartford, CT). This emulsion was further homogenized by passing it three times through a high-pressure valve homogenizer (APV-Gaulin, Model Mini-Lab 8.30H, Wilmington, MA) at a pressure of 5 3 10 7 Pa. This produced a final droplet mean diameter of ' 0.6 mm. Emulsions with different droplet concentrations were prepared by diluting the initial emulsion with an aqueous solution containing 1 wt% Tween 20 and 0.02 wt% sodium azide; 1 wt% xanthan was also incorporated into all of the emulsions to stabilize the droplets against creaming. Preparation of Two-Layer System A vertical two-layer system was used to study the molecular diffusion of sucrose through the emulsions (Fig. 1a). About 40 cm 3 of emulsion (0, 5, 10, 15, or 20 wt% oil) was carefully poured into the bottom of the measurement cell, avoiding the incorporation of any air bubbles that would interfere with the ultrasonic signal. About 40 cm 3 of aqueous solution consisting of 20 wt% sucrose, 1 wt% Tween 20, 1.0 wt% xanthan, and 0.02 wt% sodium azide was poured on top of the emulsion, being careful to keep the boundary between the upper and lower layers flat. All solutions were prepared at ; 30°C and kept covered at all times to prevent evaporation. Ultrasonic Velocity Profiling
FIG. 1. (a) Diagram of the ultrasonic profiling device used to monitor diffusion in the two-layer systems. The upper layer consisted of 20 wt% sucrose, 1 wt% xanthan, and 1 wt% Tween 20. The lower layer consisted of oil droplets (0, 5, 10, 15, or 20 wt%) dispersed in an aqueous phase that consisted of 1 wt% xanthan and 1 wt% Tween 20. (b) The ultrasonic velocity was determined by measuring the time-of-flight of an ultrasonic pulse across the sample.
The ultrasonic profiler used in this work consisted of (Fig. 1a) a custom-built measurement cell, a 5 MHz broadband ultrasonic transducer (Panametrics, Waltham, MA), a pulse generator (200 MHz computer-controlled ultrasonic pulser– receiver, Model 5900PR, Panametrics, Waltham, MA), a digital storage oscilloscope (Lecroy 9300, Lecroy Instruments, Chestnut Ridge, NY), and a stepper motor capable of moving the transducer in the vertical direction (Ultrapac II, Physical Acoustics Corporation, Princeton, NJ). The pulse generator produced an electrical pulse with an appropriate amplitude, duration, and frequency content, which was converted into an ultrasonic pulse by the transducer. The ultrasonic pulse propagated through the front wall of the measurement cell where it was partly reflected and partly transmitted at the wall-sample boundary. The reflected part traveled back to the transducer where it was converted back into an electrical pulse that was displayed on the oscilloscope. The transmitted part propagated through the sample, was reflected from the back wall of the measurement cell, and then traveled back to the transducer where it was also detected and displayed on the oscilloscope. The ultrasonic velocity was determined by measuring the time-
of-flight ( d t) of the pulse through the sample: c 5 2d/ d t, where d is the sample path length (Fig. 1b). This procedure was repeated over a range of vertical positions by moving the ultrasonic transducer from the bottom to the top of the measurement cell using the stepper motor. The ultrasonic velocity measurements were obtained by manually measuring the time difference between the echoes using the cursors on an oscilloscope. For this reason, a complete velocity profile of the sample took about 30 min to acquire. This time could be reduced to less than a minute if the measurement procedure was fully automated. The measurement cells used in this study were custom made. Each one consisted of a 10 mm thick plexiglass front wall (the “delay line”) and a 20 mm thick brass back wall (the “reflector plate”). The side walls were constructed of aluminum. Each measurement cell had a vertical height of 250 mm, a width of 30 mm, and a path length of approximately 16 mm. The path length was determined accurately at each height of the measurement cell by using distilled water, a liquid of known ultrasonic velocity, as a calibrant: d 5 c waterDt water/2 (15). The
MONITORING OF SUCROSE DIFFUSION IN EMULSIONS
431
decrease within the upper layer because of the downward movement of sucrose into the emulsion. Preparation of calibration curve. To convert the ultrasonic velocity profiles into sucrose and oil concentration profiles it was necessary to construct a calibration curve. Ultrasonic velocity measurements were made at 30°C on a series of emulsions with different oil (0, 5, 10, 15, and 20 wt%) and sucrose concentrations (0, 5, 10, 15, 20, and 22 wt%), but the same aqueous phase xanthan (1 wt%) and Tween 20 (1 wt%) concentrations (Fig. 3). The ultrasonic velocity increased with sucrose concentration and decreased with oil concentration. The relationship between the ultrasonic velocity and composition of the emulsions was described using the empirical relationship c 5 c 0 1 A f m 1 BS 1 CS 2 1 DS f m , FIG. 2. Time dependence of the ultrasonic velocity vs height for a twolayer system initially consisting of 20 wt% sucrose in the top layer and 20 wt% oil in the lower layer.
measurement cells containing the samples were stored in a temperature controlled water bath (30.0 6 0.5°C) throughout the duration of the experiment. The precision of the ultrasonic velocity measurements was 60.3 m s 21, while the accuracy was about 61.5 m s 21. The vertical resolution of the ultrasonic velocity profile was determined by the distance moved by the transducer between each measurement step. In our experiments we used fairly fine intervals (;1 mm) close to the initial boundary position between the upper and lower layers (where the concentration profile was steep) and fairly coarse intervals (;2.5 mm) away from the initial boundary position. Ultrasonic velocity profiles were acquired as a function of time after the upper layer was placed on top of the lower layer.
[1]
where c is the ultrasonic velocity (in m s 21) of the emulsion containing sucrose, c 0 (5 1516.02 m s 21) is the ultrasonic velocity in the absence of sucrose and oil, S is the sucrose concentration (in wt%) and f m is the oil concentration (in wt%). The constants A (5 21.357), B (5 2.922), C (5 0.0177), and D (5 20.0357) were determined by finding the values that gave the best least-squares fit between the experimental measurements and Equation 1 (MathCad 7 Professional, MathSoft, Inc). The agreement between the experimental measurements and predictions of Eq. [1] was excellent (Fig. 3). The above equation could be used directly to determine the sucrose concentration in the upper layer because f m 5 0. It could also be used to determine both the sucrose and oil concentration profile in the lower layer, provided we assumed
RESULTS AND DISCUSSION
Ultrasonic velocity profiles. Measurements of the timedependence of the ultrasonic velocity vs height profile for a two-layer system, which initially consisted of a 20 wt% sucrose solution in the upper layer and a 20 wt% oil-in-water emulsion in the lower layer, are shown in Fig. 2. At the beginning of the experiment the ultrasonic velocity had a relatively constant and small value in the lower layer, increased dramatically at the emulsion–sucrose solution boundary, and then had a relatively constant and high value in the upper layer. The ultrasonic velocity is significantly less than that of water in the lower layer because oil has a smaller ultrasonic velocity than water at this temperature (16). On the other hand, it is considerably higher than water in the upper layer because of the presence of the sucrose (17). With time there was an increase in ultrasonic velocity within the lower layer and a
FIG. 3. Dependence of the ultrasonic velocity of oil-in-water emulsions on their sucrose and oil concentration. The curves are predictions made using Eq. [1].
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BASARAN AND MCCLEMENTS
that they followed particular mathematical functions (discussion to follow).
O ~c 2 c~f N
DE 5
i
mi
, S i !! 2 ,
[4]
i51
Determination of Sucrose and Oil Concentration Profiles Ideally, we would have liked to measure both the sucrose and oil concentration profiles directly using the ultrasonic technique. In practice, it was necessary to assume a particular mathematical function for the sucrose and for the oil concentration profile in order to determine them both from ultrasonic velocity versus height measurements. This meant that the results of the analysis depended on the validity of the mathematical functions used. In a previous study, we showed that Fick’s law could be used to describe the diffusion of sucrose through a biopolymer network and so we also used this approach in the current study (14). The variation of oil concentration with height was modeled using a Fermi function, which was found to give a good description of the oil concentration profile in the emulsion containing no sucrose. The concentration of sucrose in the lower layer was assumed to follow the form given by the Fick’s diffusion equation (4) S5
S 0U 2 A9 z erf~B9x!, 2
[2]
where S 0U is the initial sucrose concentration in the upper layer, x is the distance from the emulsion–sucrose solution boundary, and A9 and B9 are constants to be determined experimentally. Initially, we assumed that the oil concentration profile would remain constant throughout the experiment, with f m 5 0 in the upper layer and f m 5 f 0L in the lower layer, where f 0L is the initial oil content in the lower layer. Nevertheless, the experimental ultrasonic velocity vs height profiles indicated that the height of the emulsion within the measurement cell decreased with time (Fig. 2), probably because water diffused from the emulsion into the sucrose solution. This effect was taken into account by assuming that the oil content in the lower layer followed a Fermi distribution function ~ f m 2 f 0L ! f 5 f 0L 1 , 1 1 exp@~ x 2 x B !/0.001#
[3]
where, x B is the distance that the emulsion–sucrose solution boundary moved from its initial location ( x 5 0). We assumed that f 0L remained constant to a first approximation below the emulsion–sucrose solution boundary; however, in practice it should increase slightly as water moved into the upper layer. Sucrose and oil concentration profiles in the lower layer could be determined from Eqs. [2] and [3] once the values of A9, B9, f 0L , and x B were known. These values were determined by finding the best least-squares fit between Eqs. [1] to [3] and the experimental measurements of the ultrasonic velocity profile in the lower layer
where DE is a measure of the closeness of the fit between theory and experiment, c i is the measured ultrasonic velocity of the system at height x i , c( f m , S) is the ultrasonic velocity calculated from Eq. [1], and S i and f mi are the sucrose and oil concentrations at height x i given by Eqs. [2] and [3], respectively. We used the Levenberg–Marquadt method, which is part of a commercial mathematical software package (MathCad 7 Professional, MathSoft, Inc), to find the values of A9, B9, f 0L , and x B that minimized DE. The sucrose and fat concentrations (in wt%) in the lower layer were then calculated as a function of height using Eqs. [2] and [3], while the sucrose concentration in the upper layer was determined directly from the ultrasonic velocity measurements using Eq. [1]. Conversion of Concentration Units The theory used to determine the diffusion coefficients of sucrose in the upper and lower layers assumes that the sucrose concentration is given as wt/vol rather than wt/wt (4). To convert the sucrose concentration into the appropriate units it was necessary to know the density of the sample at each height. The sample density was calculated from
r 5 fr oil 1 ~1 2 f ! r aq,
[5]
where f is the volume fraction of the oil and
r oil 5 920 kg m 23 r aq 5 995.58 1 375.7S/~100 2 f m! 1 148 S 2 /~100 2 f m ! 2 kg m 23. The density of the oil phase was measured in the laboratory. The density of the aqueous phase was taken from empirical equations reported in the literature (17). It should be noted that S is the concentration of sucrose (in wt%) of the overall system, not just the aqueous phase. Time Dependence of Sucrose Concentration Profiles The sucrose concentration profiles (in g per 100 cm 3) were determined from the ultrasonic velocity profiles using the method described above. The time-dependence of the sucrose concentration profiles of a two-layer system which initially consisted of 20 wt% sucrose in the upper layer and 20 wt% oil in the lower layer is shown in Fig. 4. At the onset of the experiment there was a steep increase in the sucrose concentration at the boundary between the lower and upper layers. As
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MONITORING OF SUCROSE DIFFUSION IN EMULSIONS
different diffusion coefficient in each layer then the change in concentration profile with time and vertical height is given by SL ~ x, t! 5 S 0L 2
S 0L 2 S 0U
1 1 ÎD L /D U
S
1 2 erf
2x
2 ÎD L t
D
for x # 0 [6]
SU ~ x, t! 5 S 0U 2
FIG. 4. Time dependence of the sucrose concentration vs height for a two-layer system initially consisting of 20 wt% sucrose in the top layer and 20 wt% oil in the lower layer.
the experiment proceeded, sucrose moved from the upper to the lower layer at a rate that depended on its translational diffusion coefficient. As a consequence there was an appreciable change in the sucrose concentration profile with time, there being a decrease in sucrose concentration in the upper layer and a corresponding increase in the lower layer. By analyzing the time dependence of the concentration profile using a suitable theory it was possible to obtain information about the diffusion coefficient of the sucrose (4). It should be noted that our experiments were carried out using a system that consisted of a more dense sucrose solution above a less dense emulsion. The xanthan network that surrounded the emulsion droplets was highly viscous and therefore the motion of the individual emulsion droplets would be severely restricted. We would therefore not have expected gravitational mixing to be a problem and would have expected to obtain similar results using a system consisting of a more dense sucrose solution below a less dense emulsion. It should also be noted that high concentrations of xanthan are known to promote depletion flocculation in oil-in-water emulsions (14). The measured diffusion coefficients are therefore for the diffusion of sucrose molecules through a suspension of aggregated droplets, which may depend on the size, shape, and internal structure of the flocs. Determination of Sucrose Diffusion Coefficients The diffusion of a solute in a two-layer liquid can be described using Fick’s second law assuming that the two phases act as semiinfinite media with the appropriate boundary conditions (4, 14). If it is assumed that the sucrose has a
S 0U 2 S 0L
1 1 ÎD U /D L
S
1 2 erf
2x
2 ÎD U t
D
for x $ 0, [7]
where S( x, t) is the concentration of sucrose at the vertical position x and time t, and D is the diffusion coefficient of the solute. The subscripts L and U refer to the lower and upper layers, respectively. In the above equations it is assumed that the diffusion coefficient in each layer is independent of time and vertical distance. In practice, the diffusion coefficient of sucrose depends on the sucrose concentration, and therefore it will change with both time and distance as the diffusion process proceeds. For this reason, the diffusion coefficients determined in this work are time-averaged and distance-averaged values. The diffusion coefficients were calculated by finding the best fit between the experimentally measured sucrose concentration profiles and those predicted by Eqs. [6] and [7] for the time range (t 5 24 to 320 h) and vertical distances ( x 5 280 to 180 mm). This was done using the Levenberg–Marquardt routine of a commercial software package (Mathsoft, Mathcad Plus 7.0, Professional Edition) to find the minimum in the relation
O O ~S~ x , t ! 2 S nj
DE 5
ni
i
i
pred
~ x i , t i !! 2 ,
j51 i51
where S ( x i , t j ) and S pred ( x i , t j ) are the measured and predicted concentrations, x i is the ith vertical distance, t j is the jth time, and n i and n j are the total number of distances and
TABLE 1 Experimentally Determined Diffusion Coefficients of Sucrose in the Upper and Lower Layers at 30°C % Oil
D L (310 210 m 2 s 21) 6 0.4
D U (310 210 m 2 s 21) 6 0.4
0 5 10 15 20
4.1 4.2 3.1 3.8 3.1
4.2 3.8 3.3 3.3 3.5
Note. The values shown are the mean and standard deviation of three measurements.
434
BASARAN AND MCCLEMENTS
times used in the analysis. The values of the diffusion coefficients calculated using this method are shown in Table 1. Dependence of diffusion coefficients on oil concentration. The above procedure was carried out for two-layer systems containing the same initial upper layer sucrose concentration (20 wt%), but different lower layer oil concentrations (0 to 20 wt%). The measured sucrose diffusion coefficients varied between 3.1 and 4.2 3 10 210 m 2 s 21, and were therefore slightly smaller than the values of sucrose in pure water (5.8 3 10 210 m 2 s 21) and in 20 wt% sucrose solutions (5.5 3 10 210 m 2 s 21) (4). The results suggest that the diffusion coefficient was similar in the upper and lower layers, but that there was a slight decrease in diffusion coefficient as the oil concentration in the lower layer increased from 0 to 20 wt% (Table 1). This was expected because the sucrose molecules must follow a more tortuous path through the system when emulsion droplets are present, especially if the droplets are flocculated. For a monodisperse emulsion the effective diffusion coefficient of a nonflocculated emulsion is given by the following relationship: D eff 5 D/(1 1 0.5 f ) (18). Thus an increase in oil concentration from 0 to 20% should cause the diffusion coefficient to decrease to about 90% of the value in a droplet free solution, which is of the order of the observed decrease. Our results suggest that the presence of relatively low concentrations of oil droplets in an emulsion only causes a slight decrease in the translational motion of small molecules. It should be noted that the overall concentration of Tween 20 in the upper and lower aqueous phases was kept constant. Nevertheless, some of the Tween 20 in the emulsion layer was absorbed to the surface of the droplets, which could cause a small additional osmotic pressure difference between the sucrose and emulsion layers. This osmotic pressure gradient would have promoted some of the water to move from the emulsion to the sucrose layer, and some of the Tween 20 to move from the sucrose layer to the emulsion. We expect that this effect would not have a significant impact on the experimental measurements because the concentrations of nonabsorbed Tween 20 were relatively low (,1%) compared to the sucrose concentrations. Time dependence of oil concentration profiles. The oil concentration profiles were determined from the ultrasonic velocity profile in the lower layer as explained above (Fig. 5). These measurements showed that the height of the emulsion decreased with time. The most likely reason for the compression of the emulsion was the difference in sucrose concentrations in the upper and lower layers. Due to the osmotic pressure gradient, water molecules will move from the emulsion into the upper layer in order to balance the sucrose concentrations. CONCLUSIONS
Ultrasonic velocity profiling is a powerful method of nondestructively monitoring molecular diffusion in optically
FIG. 5. Time dependence of the oil concentration vs height for a two-layer system initially consisting of 20 wt% sucrose in the top layer and 20 wt% oil in the lower layer.
opaque emulsions. This technique can be used to monitor diffusion in systems that are not amenable to study using traditional methods. Our experiments showed that the addition of up to 20 wt% oil droplets to an aqueous solution caused a slight decrease in the diffusion coefficient of sucrose, which was in agreement with the theory of molecular diffusion in colloidal dispersions. In addition, ultrasonic velocity profiling was able to monitor the compression of emulsions with time because of the diffusion of water molecules into the sucrose solution above them. In this study, we only measured the ultrasonic velocity profile and therefore it was necessary to make assumptions about the mathematical form of the oil and sucrose concentration profiles in order to determine them. It is possible that a combination of ultrasonic velocity and attenuation measurements could be used to determine both the droplet and sucrose concentrations directly, without having to make any assumptions about their concentration profiles. ACKNOWLEDGMENTS This material is based upon work supported by the Cooperative State Research, Education and Extension Service, U.S. Department of Agriculture, under Agreement Number 97-35503-4371.
REFERENCES 1. Snyder, L. R., and Kirkland, J. J., “Introduction to Modern Liquid Chromatography,” 2nd ed. Wiley, New York, 1979. 2. Fan, L. T., and Singh, S. K., “Controlled Release: A Quantitative Treatment.” Springer-Verlag, Berlin, 1990. 3. Kauten, R., and McCarthy, M., in “Food Processing: Recent Developments” (A. Gaonkar, Ed.), p. 1. Elsevier, Amsterdam, 1995. 4. Warin, F., Gekas, V., Voirin, A., and Dejmek, P., J. Food Sci. 62, 454 (1997).
MONITORING OF SUCROSE DIFFUSION IN EMULSIONS 5. Harding, S. E., in “New Physico-Chemical Techniques for the Characterization of Complex Food Systems” (E. Dickinson, Ed.), p. 109. Blackie Academic, London, 1995. 6. Hibberd, D. J., Howe, A. M., and Robins, M. M., Colloids Surf. 31, 347 (1988). 7. Javanaud, C., and Robins, M. M., in “Food Process Monitoring Systems” (A. C. Pinder and G. Godfrey, Eds.). Chapman & Hall, New York, 1993. 8. Povey, M. J. W., “Ultrasonic Techniques for Fluids Characterization.” Academic Press, San Diego, 1997. 9. Robbins, M. M., in “Ultrasound in Food Processing” (M. J. W. Povey and T. J. Mason Eds.), p. 219. Blackie Academic, London, 1998. 10. Basaran, T. K., Demetriades, K., and McClements, D. J., Colloids Surf. 136, 169 (1998).
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11. Sarkar, N., and Wolfe, R. R., Trans. ASAE 26, 624 (1983). 12. Attwood, D., Johansen, L., Tolley, J. A., and Rassing, F., Int. J. Pharm. 9, 285 (1981). 13. Tolley, J. A., and Rassing, J., Int. J. Pharm. 14, 223 (1983). 14. Basaran, T. K., Coupland, J. N., and McClements, D. J., J. Food Sci. 64, 125 (1999). 15. Del Grosso, V. A., and Mader, C. W., J. Acoust. Soc. Am. 52, 1442 (1972). 16. Chanamai, R., Coupland, J. N., and McClements, D. J., Colloids Surf. A 139, 241 (1998). 17. Contreras, N. I., Fairley, P., McClements, D. J., and Povey, M. J. W., Int. J. Food Sci. Tech. 27, 515 (1992). 18. Lonqvist, I., Khan, A., and Soderman, O., J. Colloid Interface Sci. 144, 401 (1991).
Nondestructive Monitoring of Sucrose Diffusion in Oil-in-Water Emulsions by Ultrasonic Velocity Profiling Taygun K. Basaran and D. Julian McClements 1 Biopolymers and Colloids Research Laboratory, Department of Food Science, University of Massachusetts, Amherst, Massachusetts 01003 Received June 10, 1999; accepted September 15, 1999
One of the major problems in studying the diffusion of molecules within colloidal dispersions is the fact that these systems are usually optically opaque. Consequently, it is not possible to use the techniques that have been developed for the analysis of optically transparent systems, such as measuring the absorbance vs height profile by UV-visible spectroscopy (5). Optically opaque systems can be studied by physically sectioning a sample and measuring the concentration of the diffusing molecules in each section (4). The major disadvantage of this technique is that it is destructive and it is not possible to obtain a detailed profile of the change in the concentration with distance. Techniques based on magnetic resonance imaging (MRI) have recently been developed to nondestructively monitor molecular diffusion in optically opaque systems (3). These techniques are extremely powerful; however, their application is limited because of their high cost and need for skilled operators. A number of workers have shown that ultrasonic profiling measurements can be used to monitor mass transport processes in optically opaque materials. Ultrasonic profiling has been used to monitor the creaming of oil droplets in emulsions (6 –10), the sedimentation of pulp in orange juices (11), and the diffusion of small molecules through gels (12–14). These techniques measure either the ultrasonic velocity or attenuation coefficient of a material as a function of its height and then use empirical or theoretical equations to convert the ultrasonic parameters into concentration profiles. In this study, we use an ultrasonic velocity profiling technique to examine the influence of droplet concentration on the diffusion of sucrose through oil-in-water emulsions.
The diffusion of sucrose through an optically opaque oil-inwater emulsion was monitored nondestructively by measuring the ultrasonic velocity as a function of height. Initially, a corn oil-inwater emulsion (0, 5, 10, 15, or 20 wt% oil) stabilized by Tween 20 (1 wt%) and xanthan (1 wt%) was placed in a measurement cell at 30°C. A 20 wt% sucrose solution containing the same concentration of Tween 20 and xanthan as the aqueous phase in the emulsion was placed on top of the emulsion. The ultrasonic velocity of this two-layer system was measured as a function of sample height and time and then converted into sucrose and oil concentration– distance profiles using empirical calibration curves. The translational diffusion coefficient of the sucrose in the upper and lower layers was determined by fitting the experimental data to a Fickian diffusion model. The measured diffusion coefficients of the sucrose molecules decreased as the droplet concentration in the emulsion increased, indicating retardation of the sugar molecule movement. Ultrasonic profiling was also used to monitor the compression of the emulsion due to movement of water molecules into the upper layer. © 1999 Academic Press Key Words: ultrasound; sucrose; emulsion; diffusion coefficient.
INTRODUCTION
The movement of small molecules through colloidal dispersions is important in a variety of scientific and technological applications. The separation and identification of substances using many chromatography and electrophoresis techniques relies on differences in the speeds that different molecules pass through a colloidal dispersion (1). Many types of pharmaceutical products utilize colloidal matrixes to control the rate at which drugs are released in the body (2). The diffusion of small molecules through biopolymer networks and colloidal dispersions is of great importance in the production of many types of foods. The diffusion of salts in cheese curd is an important stage in the manufacture of some cheeses (3). The diffusion of sugars from fruit purees into yogurts containing a network of aggregated milk proteins influences product quality (4). It is therefore of great technological and scientific interest to establish the factors that determine the rate at which small molecules diffuse through colloidal dispersions. 1
EXPERIMENTAL PROCEDURES
Materials
To whom correspondence should be addressed.
Sucrose, sodium azide, and Tween 20 were obtained from the Sigma Chemical Company (St. Louis, MO). The polysaccharide, xanthan, was obtained from Kelco International (London, UK). The corn oil was obtained from a local supermarket. All solutions were prepared with double-distilled and deionized water.
429
0021-9797/99 $30.00 Copyright © 1999 by Academic Press All rights of reproduction in any form reserved.
430
BASARAN AND MCCLEMENTS
Emulsion Preparation An aqueous surfactant solution containing 1 wt% Tween 20 and 0.02 wt% sodium azide (an antimicrobial agent) was prepared. Corn oil-in-water emulsions were prepared by homogenizing weighed amounts of oil (25 wt%) and surfactant solution (75 wt%). A coarse emulsion premix was prepared using a high-speed blender (Waring Model 33BL79, New Hartford, CT). This emulsion was further homogenized by passing it three times through a high-pressure valve homogenizer (APV-Gaulin, Model Mini-Lab 8.30H, Wilmington, MA) at a pressure of 5 3 10 7 Pa. This produced a final droplet mean diameter of ' 0.6 mm. Emulsions with different droplet concentrations were prepared by diluting the initial emulsion with an aqueous solution containing 1 wt% Tween 20 and 0.02 wt% sodium azide; 1 wt% xanthan was also incorporated into all of the emulsions to stabilize the droplets against creaming. Preparation of Two-Layer System A vertical two-layer system was used to study the molecular diffusion of sucrose through the emulsions (Fig. 1a). About 40 cm 3 of emulsion (0, 5, 10, 15, or 20 wt% oil) was carefully poured into the bottom of the measurement cell, avoiding the incorporation of any air bubbles that would interfere with the ultrasonic signal. About 40 cm 3 of aqueous solution consisting of 20 wt% sucrose, 1 wt% Tween 20, 1.0 wt% xanthan, and 0.02 wt% sodium azide was poured on top of the emulsion, being careful to keep the boundary between the upper and lower layers flat. All solutions were prepared at ; 30°C and kept covered at all times to prevent evaporation. Ultrasonic Velocity Profiling
FIG. 1. (a) Diagram of the ultrasonic profiling device used to monitor diffusion in the two-layer systems. The upper layer consisted of 20 wt% sucrose, 1 wt% xanthan, and 1 wt% Tween 20. The lower layer consisted of oil droplets (0, 5, 10, 15, or 20 wt%) dispersed in an aqueous phase that consisted of 1 wt% xanthan and 1 wt% Tween 20. (b) The ultrasonic velocity was determined by measuring the time-of-flight of an ultrasonic pulse across the sample.
The ultrasonic profiler used in this work consisted of (Fig. 1a) a custom-built measurement cell, a 5 MHz broadband ultrasonic transducer (Panametrics, Waltham, MA), a pulse generator (200 MHz computer-controlled ultrasonic pulser– receiver, Model 5900PR, Panametrics, Waltham, MA), a digital storage oscilloscope (Lecroy 9300, Lecroy Instruments, Chestnut Ridge, NY), and a stepper motor capable of moving the transducer in the vertical direction (Ultrapac II, Physical Acoustics Corporation, Princeton, NJ). The pulse generator produced an electrical pulse with an appropriate amplitude, duration, and frequency content, which was converted into an ultrasonic pulse by the transducer. The ultrasonic pulse propagated through the front wall of the measurement cell where it was partly reflected and partly transmitted at the wall-sample boundary. The reflected part traveled back to the transducer where it was converted back into an electrical pulse that was displayed on the oscilloscope. The transmitted part propagated through the sample, was reflected from the back wall of the measurement cell, and then traveled back to the transducer where it was also detected and displayed on the oscilloscope. The ultrasonic velocity was determined by measuring the time-
of-flight ( d t) of the pulse through the sample: c 5 2d/ d t, where d is the sample path length (Fig. 1b). This procedure was repeated over a range of vertical positions by moving the ultrasonic transducer from the bottom to the top of the measurement cell using the stepper motor. The ultrasonic velocity measurements were obtained by manually measuring the time difference between the echoes using the cursors on an oscilloscope. For this reason, a complete velocity profile of the sample took about 30 min to acquire. This time could be reduced to less than a minute if the measurement procedure was fully automated. The measurement cells used in this study were custom made. Each one consisted of a 10 mm thick plexiglass front wall (the “delay line”) and a 20 mm thick brass back wall (the “reflector plate”). The side walls were constructed of aluminum. Each measurement cell had a vertical height of 250 mm, a width of 30 mm, and a path length of approximately 16 mm. The path length was determined accurately at each height of the measurement cell by using distilled water, a liquid of known ultrasonic velocity, as a calibrant: d 5 c waterDt water/2 (15). The
MONITORING OF SUCROSE DIFFUSION IN EMULSIONS
431
decrease within the upper layer because of the downward movement of sucrose into the emulsion. Preparation of calibration curve. To convert the ultrasonic velocity profiles into sucrose and oil concentration profiles it was necessary to construct a calibration curve. Ultrasonic velocity measurements were made at 30°C on a series of emulsions with different oil (0, 5, 10, 15, and 20 wt%) and sucrose concentrations (0, 5, 10, 15, 20, and 22 wt%), but the same aqueous phase xanthan (1 wt%) and Tween 20 (1 wt%) concentrations (Fig. 3). The ultrasonic velocity increased with sucrose concentration and decreased with oil concentration. The relationship between the ultrasonic velocity and composition of the emulsions was described using the empirical relationship c 5 c 0 1 A f m 1 BS 1 CS 2 1 DS f m , FIG. 2. Time dependence of the ultrasonic velocity vs height for a twolayer system initially consisting of 20 wt% sucrose in the top layer and 20 wt% oil in the lower layer.
measurement cells containing the samples were stored in a temperature controlled water bath (30.0 6 0.5°C) throughout the duration of the experiment. The precision of the ultrasonic velocity measurements was 60.3 m s 21, while the accuracy was about 61.5 m s 21. The vertical resolution of the ultrasonic velocity profile was determined by the distance moved by the transducer between each measurement step. In our experiments we used fairly fine intervals (;1 mm) close to the initial boundary position between the upper and lower layers (where the concentration profile was steep) and fairly coarse intervals (;2.5 mm) away from the initial boundary position. Ultrasonic velocity profiles were acquired as a function of time after the upper layer was placed on top of the lower layer.
[1]
where c is the ultrasonic velocity (in m s 21) of the emulsion containing sucrose, c 0 (5 1516.02 m s 21) is the ultrasonic velocity in the absence of sucrose and oil, S is the sucrose concentration (in wt%) and f m is the oil concentration (in wt%). The constants A (5 21.357), B (5 2.922), C (5 0.0177), and D (5 20.0357) were determined by finding the values that gave the best least-squares fit between the experimental measurements and Equation 1 (MathCad 7 Professional, MathSoft, Inc). The agreement between the experimental measurements and predictions of Eq. [1] was excellent (Fig. 3). The above equation could be used directly to determine the sucrose concentration in the upper layer because f m 5 0. It could also be used to determine both the sucrose and oil concentration profile in the lower layer, provided we assumed
RESULTS AND DISCUSSION
Ultrasonic velocity profiles. Measurements of the timedependence of the ultrasonic velocity vs height profile for a two-layer system, which initially consisted of a 20 wt% sucrose solution in the upper layer and a 20 wt% oil-in-water emulsion in the lower layer, are shown in Fig. 2. At the beginning of the experiment the ultrasonic velocity had a relatively constant and small value in the lower layer, increased dramatically at the emulsion–sucrose solution boundary, and then had a relatively constant and high value in the upper layer. The ultrasonic velocity is significantly less than that of water in the lower layer because oil has a smaller ultrasonic velocity than water at this temperature (16). On the other hand, it is considerably higher than water in the upper layer because of the presence of the sucrose (17). With time there was an increase in ultrasonic velocity within the lower layer and a
FIG. 3. Dependence of the ultrasonic velocity of oil-in-water emulsions on their sucrose and oil concentration. The curves are predictions made using Eq. [1].
432
BASARAN AND MCCLEMENTS
that they followed particular mathematical functions (discussion to follow).
O ~c 2 c~f N
DE 5
i
mi
, S i !! 2 ,
[4]
i51
Determination of Sucrose and Oil Concentration Profiles Ideally, we would have liked to measure both the sucrose and oil concentration profiles directly using the ultrasonic technique. In practice, it was necessary to assume a particular mathematical function for the sucrose and for the oil concentration profile in order to determine them both from ultrasonic velocity versus height measurements. This meant that the results of the analysis depended on the validity of the mathematical functions used. In a previous study, we showed that Fick’s law could be used to describe the diffusion of sucrose through a biopolymer network and so we also used this approach in the current study (14). The variation of oil concentration with height was modeled using a Fermi function, which was found to give a good description of the oil concentration profile in the emulsion containing no sucrose. The concentration of sucrose in the lower layer was assumed to follow the form given by the Fick’s diffusion equation (4) S5
S 0U 2 A9 z erf~B9x!, 2
[2]
where S 0U is the initial sucrose concentration in the upper layer, x is the distance from the emulsion–sucrose solution boundary, and A9 and B9 are constants to be determined experimentally. Initially, we assumed that the oil concentration profile would remain constant throughout the experiment, with f m 5 0 in the upper layer and f m 5 f 0L in the lower layer, where f 0L is the initial oil content in the lower layer. Nevertheless, the experimental ultrasonic velocity vs height profiles indicated that the height of the emulsion within the measurement cell decreased with time (Fig. 2), probably because water diffused from the emulsion into the sucrose solution. This effect was taken into account by assuming that the oil content in the lower layer followed a Fermi distribution function ~ f m 2 f 0L ! f 5 f 0L 1 , 1 1 exp@~ x 2 x B !/0.001#
[3]
where, x B is the distance that the emulsion–sucrose solution boundary moved from its initial location ( x 5 0). We assumed that f 0L remained constant to a first approximation below the emulsion–sucrose solution boundary; however, in practice it should increase slightly as water moved into the upper layer. Sucrose and oil concentration profiles in the lower layer could be determined from Eqs. [2] and [3] once the values of A9, B9, f 0L , and x B were known. These values were determined by finding the best least-squares fit between Eqs. [1] to [3] and the experimental measurements of the ultrasonic velocity profile in the lower layer
where DE is a measure of the closeness of the fit between theory and experiment, c i is the measured ultrasonic velocity of the system at height x i , c( f m , S) is the ultrasonic velocity calculated from Eq. [1], and S i and f mi are the sucrose and oil concentrations at height x i given by Eqs. [2] and [3], respectively. We used the Levenberg–Marquadt method, which is part of a commercial mathematical software package (MathCad 7 Professional, MathSoft, Inc), to find the values of A9, B9, f 0L , and x B that minimized DE. The sucrose and fat concentrations (in wt%) in the lower layer were then calculated as a function of height using Eqs. [2] and [3], while the sucrose concentration in the upper layer was determined directly from the ultrasonic velocity measurements using Eq. [1]. Conversion of Concentration Units The theory used to determine the diffusion coefficients of sucrose in the upper and lower layers assumes that the sucrose concentration is given as wt/vol rather than wt/wt (4). To convert the sucrose concentration into the appropriate units it was necessary to know the density of the sample at each height. The sample density was calculated from
r 5 fr oil 1 ~1 2 f ! r aq,
[5]
where f is the volume fraction of the oil and
r oil 5 920 kg m 23 r aq 5 995.58 1 375.7S/~100 2 f m! 1 148 S 2 /~100 2 f m ! 2 kg m 23. The density of the oil phase was measured in the laboratory. The density of the aqueous phase was taken from empirical equations reported in the literature (17). It should be noted that S is the concentration of sucrose (in wt%) of the overall system, not just the aqueous phase. Time Dependence of Sucrose Concentration Profiles The sucrose concentration profiles (in g per 100 cm 3) were determined from the ultrasonic velocity profiles using the method described above. The time-dependence of the sucrose concentration profiles of a two-layer system which initially consisted of 20 wt% sucrose in the upper layer and 20 wt% oil in the lower layer is shown in Fig. 4. At the onset of the experiment there was a steep increase in the sucrose concentration at the boundary between the lower and upper layers. As
433
MONITORING OF SUCROSE DIFFUSION IN EMULSIONS
different diffusion coefficient in each layer then the change in concentration profile with time and vertical height is given by SL ~ x, t! 5 S 0L 2
S 0L 2 S 0U
1 1 ÎD L /D U
S
1 2 erf
2x
2 ÎD L t
D
for x # 0 [6]
SU ~ x, t! 5 S 0U 2
FIG. 4. Time dependence of the sucrose concentration vs height for a two-layer system initially consisting of 20 wt% sucrose in the top layer and 20 wt% oil in the lower layer.
the experiment proceeded, sucrose moved from the upper to the lower layer at a rate that depended on its translational diffusion coefficient. As a consequence there was an appreciable change in the sucrose concentration profile with time, there being a decrease in sucrose concentration in the upper layer and a corresponding increase in the lower layer. By analyzing the time dependence of the concentration profile using a suitable theory it was possible to obtain information about the diffusion coefficient of the sucrose (4). It should be noted that our experiments were carried out using a system that consisted of a more dense sucrose solution above a less dense emulsion. The xanthan network that surrounded the emulsion droplets was highly viscous and therefore the motion of the individual emulsion droplets would be severely restricted. We would therefore not have expected gravitational mixing to be a problem and would have expected to obtain similar results using a system consisting of a more dense sucrose solution below a less dense emulsion. It should also be noted that high concentrations of xanthan are known to promote depletion flocculation in oil-in-water emulsions (14). The measured diffusion coefficients are therefore for the diffusion of sucrose molecules through a suspension of aggregated droplets, which may depend on the size, shape, and internal structure of the flocs. Determination of Sucrose Diffusion Coefficients The diffusion of a solute in a two-layer liquid can be described using Fick’s second law assuming that the two phases act as semiinfinite media with the appropriate boundary conditions (4, 14). If it is assumed that the sucrose has a
S 0U 2 S 0L
1 1 ÎD U /D L
S
1 2 erf
2x
2 ÎD U t
D
for x $ 0, [7]
where S( x, t) is the concentration of sucrose at the vertical position x and time t, and D is the diffusion coefficient of the solute. The subscripts L and U refer to the lower and upper layers, respectively. In the above equations it is assumed that the diffusion coefficient in each layer is independent of time and vertical distance. In practice, the diffusion coefficient of sucrose depends on the sucrose concentration, and therefore it will change with both time and distance as the diffusion process proceeds. For this reason, the diffusion coefficients determined in this work are time-averaged and distance-averaged values. The diffusion coefficients were calculated by finding the best fit between the experimentally measured sucrose concentration profiles and those predicted by Eqs. [6] and [7] for the time range (t 5 24 to 320 h) and vertical distances ( x 5 280 to 180 mm). This was done using the Levenberg–Marquardt routine of a commercial software package (Mathsoft, Mathcad Plus 7.0, Professional Edition) to find the minimum in the relation
O O ~S~ x , t ! 2 S nj
DE 5
ni
i
i
pred
~ x i , t i !! 2 ,
j51 i51
where S ( x i , t j ) and S pred ( x i , t j ) are the measured and predicted concentrations, x i is the ith vertical distance, t j is the jth time, and n i and n j are the total number of distances and
TABLE 1 Experimentally Determined Diffusion Coefficients of Sucrose in the Upper and Lower Layers at 30°C % Oil
D L (310 210 m 2 s 21) 6 0.4
D U (310 210 m 2 s 21) 6 0.4
0 5 10 15 20
4.1 4.2 3.1 3.8 3.1
4.2 3.8 3.3 3.3 3.5
Note. The values shown are the mean and standard deviation of three measurements.
434
BASARAN AND MCCLEMENTS
times used in the analysis. The values of the diffusion coefficients calculated using this method are shown in Table 1. Dependence of diffusion coefficients on oil concentration. The above procedure was carried out for two-layer systems containing the same initial upper layer sucrose concentration (20 wt%), but different lower layer oil concentrations (0 to 20 wt%). The measured sucrose diffusion coefficients varied between 3.1 and 4.2 3 10 210 m 2 s 21, and were therefore slightly smaller than the values of sucrose in pure water (5.8 3 10 210 m 2 s 21) and in 20 wt% sucrose solutions (5.5 3 10 210 m 2 s 21) (4). The results suggest that the diffusion coefficient was similar in the upper and lower layers, but that there was a slight decrease in diffusion coefficient as the oil concentration in the lower layer increased from 0 to 20 wt% (Table 1). This was expected because the sucrose molecules must follow a more tortuous path through the system when emulsion droplets are present, especially if the droplets are flocculated. For a monodisperse emulsion the effective diffusion coefficient of a nonflocculated emulsion is given by the following relationship: D eff 5 D/(1 1 0.5 f ) (18). Thus an increase in oil concentration from 0 to 20% should cause the diffusion coefficient to decrease to about 90% of the value in a droplet free solution, which is of the order of the observed decrease. Our results suggest that the presence of relatively low concentrations of oil droplets in an emulsion only causes a slight decrease in the translational motion of small molecules. It should be noted that the overall concentration of Tween 20 in the upper and lower aqueous phases was kept constant. Nevertheless, some of the Tween 20 in the emulsion layer was absorbed to the surface of the droplets, which could cause a small additional osmotic pressure difference between the sucrose and emulsion layers. This osmotic pressure gradient would have promoted some of the water to move from the emulsion to the sucrose layer, and some of the Tween 20 to move from the sucrose layer to the emulsion. We expect that this effect would not have a significant impact on the experimental measurements because the concentrations of nonabsorbed Tween 20 were relatively low (,1%) compared to the sucrose concentrations. Time dependence of oil concentration profiles. The oil concentration profiles were determined from the ultrasonic velocity profile in the lower layer as explained above (Fig. 5). These measurements showed that the height of the emulsion decreased with time. The most likely reason for the compression of the emulsion was the difference in sucrose concentrations in the upper and lower layers. Due to the osmotic pressure gradient, water molecules will move from the emulsion into the upper layer in order to balance the sucrose concentrations. CONCLUSIONS
Ultrasonic velocity profiling is a powerful method of nondestructively monitoring molecular diffusion in optically
FIG. 5. Time dependence of the oil concentration vs height for a two-layer system initially consisting of 20 wt% sucrose in the top layer and 20 wt% oil in the lower layer.
opaque emulsions. This technique can be used to monitor diffusion in systems that are not amenable to study using traditional methods. Our experiments showed that the addition of up to 20 wt% oil droplets to an aqueous solution caused a slight decrease in the diffusion coefficient of sucrose, which was in agreement with the theory of molecular diffusion in colloidal dispersions. In addition, ultrasonic velocity profiling was able to monitor the compression of emulsions with time because of the diffusion of water molecules into the sucrose solution above them. In this study, we only measured the ultrasonic velocity profile and therefore it was necessary to make assumptions about the mathematical form of the oil and sucrose concentration profiles in order to determine them. It is possible that a combination of ultrasonic velocity and attenuation measurements could be used to determine both the droplet and sucrose concentrations directly, without having to make any assumptions about their concentration profiles. ACKNOWLEDGMENTS This material is based upon work supported by the Cooperative State Research, Education and Extension Service, U.S. Department of Agriculture, under Agreement Number 97-35503-4371.
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