where Kis the complex propagation constant of the emulsion (= ra/ce + iae), k1 is the complex propagation constant of the continuous phase (= ra/cj + iaj), ra is the angular frequency, c is the ultrasonic velocity, a is the attenuation coefficient, i = V-1, and r is the droplet radius. The A0 and Aj terms are the monopole and dipole scattering coefficients of the individual droplets, which depend on the adiabatic compressibility, density, specific heat capacity, thermal conductivity, cubical expansivity, and viscosity of the component phases, as well as the frequency and droplet size (Epstein and Carhart 1953). Equation 10.10 can be used to calculate the ultrasonic velocity and attenuation coefficient of an emulsion as a function of droplet size and concentration, once the thermophysical properties of the component phases are known, since ce = ra/Re(Ke) and ae = Im(Ke).
The dependence of the ultrasonic velocity and attenuation coefficient of an emulsion on droplet size and concentration is shown in Figure 10.15. The ultrasonic velocity increases with droplet size, while the attenuation per wavelength (aA) has a maximum value at an intermediate droplet size. It is this dependence of the ultrasonic properties of an emulsion on droplet size that enables ultrasound to be used as a particle-sizing technology. An emulsion is analyzed by measuring its ultrasonic velocity and/or attenuation spectra and finding the droplet size and concentration which give the best fit between the experimental data and Equation 10.10. For polydisperse emulsions, the equation has to be modified to take into account the droplet size distribution (McClements 1991). One of the major limitations of the ultrasonic technique is the fact that a great deal of information about the thermophysical properties of the component phases is needed to interpret the measurements, and this information often is not readily available in the literature (Coupland and McClements 1998). In addition, for droplet concentrations greater than about 15%, it is necessary to extend the above equation to take into account interactions between the droplets, which has been done recently (Hemar et al. 1997, McClements et al. 1998b).
The ultrasonic properties of materials can be measured using a number of different experimental techniques (e.g., pulse echo, through transmission, and interferometric) (McClements
FIGURE 10.15 Dependence of the ultrasonic properties of an emulsion on its droplet size and dispersed-phase volume fraction.
FIGURE 10.15 Dependence of the ultrasonic properties of an emulsion on its droplet size and dispersed-phase volume fraction.
1996). The major difference between them is the form in which the ultrasonic energy is applied to the sample and the experimental configuration used to carry out the measurements. In this section, we shall only consider the pulse-echo technique because it is one of the simplest and most widely used techniques to analyze emulsions. The sample to be analyzed is contained within a thermostated measurement cell which has an ultrasonic transducer fixed to one side (Figure 10.16). An electrical pulse is applied to the transducer, which stimulates it to generate a pulse of ultrasound that is directed into the sample. This pulse travels across the sample, is reflected from the back wall of the measurement cell, travels back through the sample, and is then detected by the same transducer (Figure 10.16). The ultrasonic pulse received by the transducer is converted back into an electrical pulse which is digitized and saved for analysis.
The ultrasonic velocity and attenuation coefficient of a sample are determined by measuring the time of flight (t) and amplitude (A) of the ultrasonic pulse which has traveled through it. The ultrasonic velocity is equal to the distance traveled by the pulse (2d) divided by its time of flight: c = 2d/t. The attenuation coefficient is calculated by comparing the amplitude of a pulse which has traveled through the sample with that of a pulse which has traveled through a material whose attenuation coefficient is known: a2 = aj - ln(A2/Aj)/2d, where the subscripts 1 and 2 refer to the properties of the reference material and the material being tested, respectively. The through-transmission technique is very similar to the pulse-echo technique, except that separate transducers are used to generate and receive the ultrasonic pulse (McClements 1996).
To determine the droplet size distribution of an emulsion, it is necessary to measure the frequency dependence of its ultrasonic properties. Two different approaches can be used to measure the dependence of the ultrasonic properties on frequency using the pulse-echo technique. In the first approach, a broadband ultrasonic pulse is used, which is a single pulse that contains a wide range of frequencies. After the pulse has traveled through the sample, it is analyzed by a Fourier transform algorithm to determine the values of t and A (and therefore c and a) as a function of frequency (McClements and Fairley 1991, 1992). To cover the whole frequency range (0.1 to 100 MHz), a number of transducers with different frequencies have to be used. In the second approach, a tone-burst ultrasonic pulse is used, which is a single pulse that contains a number of cycles of ultrasound at a particular frequency (McClements 1996). The transducer is tuned to a particular frequency, and a measurement of the ultrasonic velocity and attenuation coefficient is made. The transducer is then tuned to another frequency and the process is repeated. Because measurements are carried out separately at a number of different frequencies, this approach is more time consuming and laborious than the one which uses broadband pulses. Both of these methods are used to determine the frequency dependence of the ultrasonic properties of emulsions in commercial ultrasonic particle sizers.
Ultrasound has major advantages over many other particle-sizing technologies because it can be used to measure droplet size distributions in concentrated and optically opaque emulsions in situ. In addition, it can be used as an on-line sensor for monitoring the characteristics of food emulsions during processing, which gives food manufacturers much greater control over the quality of the final product. The possibility of using ultrasound to measure droplet sizes in real foods has been demonstrated for casein micelles (Griffin and Griffin 1990), sunflower-oil-in-water emulsions (McClements and Povey 1989), corn-oil-in-water emulsions (Coupland and McClements 1998), salad creams (McClements et al. 1990), and milk fat globules (Miles et al. 1990).
The two major disadvantages of the ultrasonic technique are the large amount of thermophysical data required to interpret the measurements and the fact that small air bubbles can interfere with the signal from the emulsion droplets (McClements 1991, 1996).
Instrumental techniques based on nuclear magnetic resonance (NMR) utilize interactions between radio waves and the nuclei of hydrogen atoms to obtain information about the properties of materials.* An NMR technique has been developed to measure the droplet size distribution of emulsions (Callaghan et al. 1983, van den Enden et al. 1990, Li et al. 1992, Soderman et al. 1992), which is sensitive to particle sizes between about 0.2 and 100 |im (Dickinson and McClements 1995). This technique relies on measurements of the restricted diffusion of molecules within emulsion droplets.
The principles of the technique are fairly complex and have been described in detail elsewhere (Dickinson and McClements 1995, Soderman and Bailnov 1996). Basically, the sample to be analyzed is placed in a static magnetic field gradient and a series of radio-frequency pulses are applied to it. These pulses cause some of the hydrogen nuclei in the sample to be excited to higher energy levels, which leads to the generation of a detectable NMR signal. The amplitude of this signal depends on the movement of the nuclei in the sample: the farther the nuclei move during the experiment, the greater the reduction in the
* NMR techniques can also be used to study the nuclei of certain other isotopes, but these are not widely used for particle sizing.
amplitude. A measurement of the signal amplitude can therefore be used to study molecular motion.
In a bulk liquid, the distance that a molecule can move in a certain time is governed by its translational diffusion coefficient, xrms = (V2Dt). When a liquid is contained within an emulsion droplet, its diffusion may be restricted because of the presence of the interfacial boundary. If the movement of a molecule in a droplet is observed over relatively short times (t<< d2/2D), the diffusion is unrestricted, but if it is observed over longer times, its diffusion is restricted because it cannot move farther than the diameter of the droplet. By measuring the attenuation of the NMR signal at different times, it is possible to identify when the diffusion becomes restricted and thus estimate the droplet size. Because this technique relies on the movement of molecules within droplets, it is independent of droplet flocculation.
This technique has been used to determine the droplet size distribution of a variety of oil-in-water and water-in-oil emulsions, including margarine, cream, and cheese (Callaghan et al. 1983, van den Enden et al. 1990, Li et al. 1992, Soderman et al. 1992). Like ultrasonic spectrometry, it is nondestructive and can be used to analyze emulsions which are concentrated and optically opaque (Dickinson and McClements 1995). It therefore seems likely that NMR instruments specifically designed to measure the particle size distribution of emulsions will be developed and become commercially available in the near future.
Neutron scattering techniques utilize interactions between a beam of neutrons and an emulsion to determine the droplet size distribution (Dickinson and Stainsby 1982, Eastoe 1995). They can also be used to provide information about the thickness of interfacial layers and the spatial distribution of droplets. These techniques have a couple of special features which make them particularly suitable for studying food emulsions (Eastoe 1995). First, the scattering of neutrons from emulsion droplets is very weak, and therefore multiple scattering effects are not appreciable, which means that concentrated emulsions can be analyzed without dilution. Second, the scattering of neutrons from heterogeneous materials depends on the "contrast" between the different components, which can be manipulated by the experimenter. Thus it is possible to selectively highlight specific structural features within an emulsion (see below). Despite its ability to generate information which is difficult to obtain using other techniques, the application of neutron scattering to food emulsions is limited because a nuclear reactor is needed to generate the neutron beam. There are only a small number of neutron-scattering facilities in the world which are generally accessible, and beam time is rather limited and must be scheduled many months in advance of the proposed experiment (Stothart 1995).
In many respects, the measurement principle of neutron scattering is similar to that of static light scattering, except that a beam of neutrons is used instead of light. The sample to be analyzed is placed into a cuvette which is inserted between a source of neutrons and a neutron detector (Stothart 1995). A beam of neutrons is passed through the emulsion, and the intensity of the scattered neutrons is measured as a function of scattering angle (and/or wavelength). Information about the properties of the emulsion is then obtained by interpreting the resulting spectra using an appropriate neutron-scattering theory (Eastoe 1995).
Each type of atomic nuclei scatters neutrons to a different extent, which is characterized by a "scattering cross-section" (Lovsey 1984). The scattering of neutrons from a heterog-enous material, such as an emulsion, depends on the contrast between the scattering cross-sections of the different components: the greater the contrast, the more intense the scattering. One of the most important attributes of neutron scattering is the ability to alter the scattering cross-section of molecules that contain hydrogen atoms (e.g., water, proteins, fats, and carbohydrates) (Eastoe 1995, Stothart 1995). Normal hydrogen (!H) and deuterium (2H) have
Highlight Highlight droplet + interface interface droplet
FIGURE 10.17 Concept of contrast matching of emulsions in neutron-scattering experiments.
significantly different scattering cross-sections, and so by varying the !H:2H ratio of a particular type of molecule, it is possible to increase or decrease its contrast with respect to the other components in an emulsion. As a consequence, it is possible to emphasize specific structural components within an emulsion.
Consider an oil-in-water emulsion (Figure 10.17) which consists of oil droplets covered by an interfacial layer and suspended in an aqueous phase. By altering the ratio of water to deuterated water in the aqueous phase, it is possible to match the aqueous phase to either the interfacial layer or the oil within the droplets. Alternatively, the interfacial layer could be matched to the droplet by partial deuteration of either the oil or emulsifier molecules. Thus it is possible to obtain information about the thickness of the interfacial layer, the oil droplet, or the droplet + interfacial layer.
This technique depends on the dielectric response of an emulsion during the application of an electromagnetic wave (Clausse 1983, Asami 1995, Sjoblom et al. 1996). The possibility of using dielectric spectroscopy to determine the droplet size distribution of concentrated emulsions was recently demonstrated (Garrouch et al. 1996). The dielectric permittivity of an emulsion is measured over a wide range of electromagnetic frequencies, and the resulting spectra are analyzed using a suitable theory to determine the droplet size distribution. The major limitation of this technique is that it can only be used to determine droplet size distributions in emulsions that contain charged particles. Even so, it can be used to simultaneously measure the zeta potential and droplet size distribution, and it can be used to analyze emulsions which are concentrated and optically opaque without the need for any sample dilution. It may therefore have some important applications in the food industry. Nevertheless, dielectric spectroscopy is still in its infancy, and a lot more research is still required before the technique becomes more widely accepted and utilized.
The droplet size distribution of emulsions that contain charged droplets can be determined using electroacoustic techniques (O'Brien et al. 1995, Carasso et al. 1995, Dukhin and Goetz 1996). These techniques use a combination of electric and acoustic phenomena to determine both the size and zeta potential of emulsion droplets (Section 10.6.3). Instruments based on this principle have recently become commercially available and are capable of analyzing droplets with sizes between about 0.1 and 10 (Hunter 1998). These instruments are capable of analyzing emulsions with high droplet concentrations (<40%) without any sample dilution. The major limitation of the electroacoustic technique is that measurements rely on the droplets having an electrical charge, the surrounding liquid must be Newtonian, and there must be a significant density contrast between the droplets and the surrounding liquid. These conditions are not always met for food emulsions, which means that electroacoustics may only have limited application within the food industry.
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