Xer

Large Droplets

\ Small i Droplets

Frequency

FIGURE 10.12 The distribution of frequency shifts can be related to the using suitable theories: small particles move more rapidly and therefore cause particle size distribution a greater frequency shift.

FIGURE 10.13 Experimental technique for measuring the Doppler shift of particles based on the heterodyne measurement technique.

Doppler shifted. The remainder of the laser beam propagates into the sample, and part of it is scattered back up the waveguide by the particles in its immediate vicinity (~100 |im path length). This backscattered light is frequency shifted by an amount that depends on the velocity of the particles. The difference in frequency between the reflected and scattered waves is equivalent to the Doppler shift.

The variation of the power, P(ra), of the scattered waves with angular frequency (ra) has the form of a Lorentzian function:

where /0 and </S> are the reference and scattered light intensities, and ra0 is a characteristic frequency that is related to the scattering efficiency and diffusion coefficient of the particles: ra0 = DQ2. Particle size is determined by measuring the variation of P(ra) with ra, and then finding the value of the diffusion coefficient which gives the best fit between the measured spectra and that predicted by Equation 10.5. For polydisperse systems, it is necessary to take into account that there is a distribution of particle sizes. The calculation of particle size requires that the analyst input the refractive indices of the continuous and dispersed phases and the viscosity of the continuous phase. Because the path length of the light beam in the sample is so small (about 100 | m), it is possible to analyze much more concentrated emulsions (up to 40%) than with static light scattering or PCS techniques (Trainer et al. 1992), although some form of correction factor usually has to be applied to take into account the influence of the droplet interactions on the diffusion coefficient (Horne 1995). Commercial instruments are available that are easy to use and which can analyze an emulsion in a few minutes. The major limitations of dynamic light-scattering techniques are that they can only be used to analyze droplets with sizes smaller than about 3 | m and that the viscosity of the aqueous phase must be Newtonian, which is not the case for many food emulsions, especially those that contain thickening agents.

10.3.4. Electrical Pulse Counting

Electrical pulse counting techniques are capable of determining the size distribution of particles with diameters between about 0.6 and 400 | m (Hunter 1986, Mikula 1992) and are therefore suitable for analyzing most food emulsions. These instruments have been commercially available for many years and are widely used in the food industry. The emulsion to be analyzed is placed in a beaker that has two electrodes dipping into it (Figure 10.14). One of

Emulsion Drawn Through Tube j t

Current Measurement

Electrolyte solution

Electrodes

Hole

FIGURE 10.14 An electrical pulse counter. The decrease in current is measured when an oil droplet passes through a small hole in a glass tube.

Hole

* Droplets

Electrolyte solution

Electrodes

FIGURE 10.14 An electrical pulse counter. The decrease in current is measured when an oil droplet passes through a small hole in a glass tube.

the electrodes is contained in a glass tube which has a small hole in it, through which the emulsion is sucked. When an oil droplet passes through the hole, it causes a decrease in the current between the electrodes because oil has a much lower electrical conductivity than water. Each time a droplet passes through the hole, the instrument records a decrease in current, which it converts into an electrical pulse. The instrument controls the volume of liquid that passes through the hole, and so the droplet concentration can be determined by counting the number of electrical pulses in a known volume. When the droplets are small compared to the diameter of the hole, the droplet size is simply related to the height of the pulses: d3 = kP, where d is the droplet diameter, P is the pulse height, and k is an instrument constant which is determined by recording the pulse height of a suspension of monodisperse particles of known diameter.

To cover the whole range of droplet sizes from 0.6 to 400 |m, it is necessary to use glass tubes with different sized holes. Typically, droplets between about 4 and 40% of the diameter of the hole can be reliably analyzed. Thus a tube with a hole of 16 |im can be used to analyze droplets with diameters between about 0.6 and 6 |m.

There are a number of practical problems associated with this technique which may limit its application to certain systems. First, it is necessary to dilute an emulsion considerably before analysis so that only one particle passes through the hole at a time; otherwise, a pair of particles would be counted as a single larger particle. As mentioned earlier, dilution of an emulsion may alter the structure of any flocs present, especially when the attraction between the droplets is small. Second, the emulsion droplets must be suspended in an electrolyte solution (typically 5 wt% salt) to ensure that the electrical conductivity of the aqueous phase is sufficiently large to obtain accurate measurements. The presence of an electrolyte alters the nature of the colloidal interactions between charged droplets, which may change the extent of flocculation from that which was present in the original sample. Third, any weakly flocculated droplets may be disrupted by the shear forces generated by the flocs as they pass through the small hole. Fourth, if an emulsion contains a wide droplet size distribution, it is necessary to use a number of glass tubes with different hole sizes to cover the full size distribution. Nevertheless, in those emulsions where it can be applied, electrical pulse counting is usually considered to be more reliable and accurate than light scattering.

10.3.5. Sedimentation Techniques

Sedimentation techniques can be used to determine the size distribution of particles between about 1 nm and 1 mm, although a number of different types of instruments have to be used to cover the whole of this range (Hunter 1986, 1993). Particle size is determined by measuring the velocity at which droplets sediment (or cream) in a gravitational or centrifugal field.

10.3.5.1. Gravitational Sedimentation

The velocity that an isolated rigid spherical particle suspended in a Newtonian liquid moves due to gravity is given by Stokes' equation:

where p2 is the density of the droplets, p1 and n1 are the density and viscosity of the continuous phase, g is the acceleration due to gravity, and r is the droplet radius. The droplet size can therefore be determined by measuring the velocity at which the particle moves through the liquid once the densities of both phases and the viscosity of the continuous phase are known. The movement of the droplets could be monitored using a variety of experimental methods, including visual observation, optical microscopy, light scattering, nuclear magnetic resonance, ultrasound, and electrical measurements (Mikula 1992, Pal 1994, Dickinson and McClements 1995). The Stokes equation cannot be used to estimate droplet sizes less than about 1 |im because of their Brownian motion (Hunter 1986). The gravitational forces acting on a droplet cause it to move in a certain direction, either up or down, depending on the particle density relative to the continuous phase. On the other hand, Brownian motion tends to randomize the spatial distribution of the particles. This effect is important when the distance a particle moves due to Brownian motion is comparable to the distance it moves due to sedimentation or creaming in the same time. In a quiescent system, the average distance (root mean square displacement, xrms) that a sphere moves due to Brownian motion is given by (Hunter 1993):

v rms

Thus, a 1-|m oil droplet (p2 = 920 kg m-3) moves about 0.7 |im s-1 due to Brownian motion when suspended in pure water, whereas it will move about 2 | m in the same time due to creaming. Thus, even for a droplet of this size, the thermal motion can have a pronounced influence on its creaming rate. In addition, temperature gradients within a sample can lead to convective currents that interfere with the droplet movement. For these reasons, gravitational sedimentation techniques have limited application for determining droplet sizes in emulsions. Instead, the droplets are made to move more rapidly by applying a centrifugal force, so that the problems associated with Brownian motion and convection are overcome.

10.3.5.2. Centrifugation

When an emulsion is placed in a centrifuge and rotated rapidly, it is subjected to a centrifugal force that causes the droplets to move inward when they have a lower density than the surrounding liquid (e.g., oil-in-water emulsions) or outward when they have a higher density (e.g., water-in-oil emulsions). The velocity, v(x), at which the droplets move through the surrounding liquid depends on the angular velocity (ra) at which the tube is centrifuged and their distance from the center of the rotor (x) The droplet motion can be conveniently characterized by a sedimentation coefficient, which is independent of the angular velocity and location of the droplets (Hunter 1993):

ro2 x

The radius of an isolated spherical particle in a fluid is related to the sedimentation coefficient by the following equation:

By measuring the droplet velocity at different positions within a centrifuge tube, it is possible to determine S and therefore the droplet radius.

The sedimentation coefficient is related to the distance from the rotor center: ln^/x^ = Sra 2(t2 - t1), where x is the position of the particle at time t (Hunter 1993). Thus a plot of ln(x) versus time at a fixed rotation speed can be used to determine S. For oil-in-water emulsions with sizes between 0.1 and 100 |m, S varies between about 2 ns and 2 ms. The position of the droplets is usually determined by optical microscopy or light scattering. Modern instruments are capable of measuring the full droplet size distribution of emulsions by analyzing the velocity at which a number of different droplets move. Instruments that utilize this principle are commercially available and are used in the food industry.

10.3.6. Ultrasonic Spectrometry 10.3.6.1. Principles

Ultrasonic spectrometry utilizes interactions between ultrasonic waves and particles to obtain information about the droplet size distribution of an emulsion (McClements 1991, 1996; Dukhin and Goetz 1996; Povey 1995, 1997). It can be used to determine droplet sizes between about 10 nm and 1000 | m. Particle-sizing instruments based on ultrasonic spectrom-etry have recently become available commercially and are likely to gain wide acceptance in the food industry in the near future because they have a number of important advantages over alternative technologies (e.g., they can be used to analyze emulsions which are concentrated and optically opaque, without the need for any sample preparation).

As an ultrasonic wave propagates through an emulsion, its velocity and attenuation are altered due to its interaction with the droplets. These interactions may take a number of different forms: (1) some of the wave is scattered into directions which are different from that of the incident wave; (2) some of the ultrasonic energy is converted into heat due to various absorption mechanisms (e.g., thermal conduction and viscous drag); and (3) there is interference between waves which travel through the droplets, waves which travel through the surrounding medium, and waves which are scattered. The relative importance of these different mechanisms depends on the thermophysical properties of the component phases, the frequency of the ultrasonic wave, and the concentration and size of the droplets.

As with light scattering, the scattering of ultrasound by a droplet can be divided into three regimes according to the relationship between the particle size and the wavelength of the radiation: (1) the long-wavelength regime (r < X/20), (2) the intermediate-wavelength regime (X/20 < r < 20X), and (3) the short-wavelength regime (r > 20X). The wavelength of ultrasound (10 |im to 10 mm) is much greater than that of light (0.2 to 1 |im), and so ultrasonic measurements are usually made in the long-wavelength regime, whereas light-scattering measurements are made in the intermediate-wavelength regime. As a consequence, light-scattering results are often more difficult to interpret reliably because of the greater complexity of the scattering theory in the intermediate-wavelength regime.

In the long-wavelength regime, the ultrasonic properties of fairly dilute emulsions (^ < 15%) can be related to their physicochemical characteristics using the following equation:

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