Fm S 2 Rl

where FKM is the Kubelka-Munk parameter, K and S are the absorption and scattering coefficients, and R^ is the reflectance from an infinitely thick sample at a given wavelength. When an emulsion is highly colored, the absorption of light dominates (high FKM) and the reflectance is low. As scattering effects become more important (low FKM), the reflectance increases and the emulsion appears "lighter" in color. The scattering coefficient is proportional to the droplet concentration, while the absorption coefficient is proportional to the chromophore concentration. The appearance of an emulsion therefore depends on the concentration of the various components within it.

FIGURE 9.14 Dependence of the refractive index of various aqueous solutions on solute concentration.

The Kubelka-Munk theory can be used to predict the influence of different types of scatterers or chromophores on the overall appearance of an emulsion. It can also be related to the scattering cross-sections of the individual droplets in an emulsion using diffuse scattering theory. It therefore provides a valuable mathematical link between the physicochemical characteristics of the droplets and the appearance of an emulsion.*

9.3.2. Overall Appearance

The overall appearance of an emulsion is a result of the various types of interactions between light waves and foods mentioned in the previous section.

An object which allows all of the light to pass through it is referred to as being transparent, whereas an object which scatters or absorbs all of the light is referred to as being opaque (Clydesdale 1975). Many dilute emulsions fall somewhere between these two extremes and are therefore referred to as being translucent. The opacity of most food emulsions is determined mainly by the scattering of light from the droplets: the greater the scattering, the greater the opacity (Hernandez and Baker 1991, Dickinson 1994). The extent of scattering is determined by the concentration, size, and relative refractive index of the droplets (Section An emulsion becomes more opaque as the droplet concentration or scattering cross-section increases (Equation 9.29).

The scattering of light accounts for the opacity of emulsions that are made from two liquids which are themselves optically transparent (e.g., water and a mineral oil). When a light wave impinges on an emulsion, all of the different wavelengths are scattered by the droplets, and so the light cannot penetrate very far into the emulsion. As a consequence, the emulsion appears to be optically opaque (Farinato and Rowell 1983).

It is extremely difficult for human beings to objectively describe the colors of materials using everyday language (Hutchings 1994). For this reason, a number of standardized methods have been developed to measure and specify color in a consistent way (Francis and Clydesdale 1975, Hutchings 1994). The underlying principle of these methods is that all colors can be simulated by combining three selected colored lights (red, green, and blue) in the appropriate ratio and intensities. This trichromatic principle means that it is possible to describe any color in terms of just three mathematical variables (e.g., hue, value, and chroma) (Francis and Clydesdale 1975). Experimental techniques for measuring these variables are discussed briefly in Section 9.3.3.

The color of an emulsion is determined by the absorption and scattering of light waves from both the droplets and continuous phase (Dickinson 1994). The absorption of light depends on the type and concentration of chromophores present, while the scattering of light depends on the size, concentration, and relative refractive index of any particulate matter. Whether an emulsion appears "red," "orange," "yellow," "blue," etc. depends principally on its absorption spectra. Under normal viewing conditions, an emulsion is exposed to white light from all directions.** When this light is reflected, transmitted, or scattered by the

* Recently, it has been shown how the color of an emulsion can be predicted using the Kubelka-Munk theory from a knowledge of the droplet and dye characteristics (McClements et al. 1998a).

** If an emulsion is placed in a dark room and a white light beam is directed through it, it appears blue when observed from the side and red when observed from the back, because blue light has a lower wavelength than red light and is therefore scattered to a wider angle (Farinato and Rowell 1983).

emulsion, some of the wavelengths are absorbed by the chromophores present. The color of the light which reaches the eye is a result of the nonabsorbed wavelengths (e.g., an emulsion appears red if it absorbs all of the other colors except the red) (Francis and Clydesdale 1975). The color of an emulsion is modified by the presence of the droplets or any other particulate matter. As the concentration or scattering cross-section of the particles increases, an emulsion becomes lighter in appearance because the scattered light does not travel very far through the emulsion and is therefore absorbed less by the chromophores. It is therefore possible to modify the color of an emulsion by altering the characteristics of the emulsion droplets or other particulate matter. Homogeneity

The quality of a food emulsion is often determined by the uniformity of its appearance over the whole of its surface. An emulsion may have a heterogeneous appearance for a number of reasons: (1) it contains particles which are large enough to be resolved by the human eye (>0.1 mm) or (2) it contains particles which have moved to either the top or the bottom of the container because of gravitational separation. Methods of retarding creaming and sedimentation were considered in Chapter 7.

9.3.3. Experimental Techniques Spectrophotometry

A variety of different types of spectrophotometers have been developed to measure the transmission and reflection of light from objects as a function of wavelength in the visible region (Clydesdale 1975, Francis and Clydesdale 1975, Pomeranz and Meloan 1994, Hutchings 1994). These instruments usually consist of a light source, a wavelength selector, a sample holder, and a light detector (Figure 9.15).

Transmission Spectrophotometer. A beam of white light, which contains electromagnetic radiation across the whole of the visible spectrum, is passed through a wavelength selector, which isolates radiation of a specific wavelength (Penner 1994b). This monochromatic wave is then passed through a cell containing the sample, and the intensity of the transmitted wave is measured using a light detector. By comparing the intensity of the light transmitted by the sample with that transmitted by a reference material, it is possible to determine the transmit-tance of the sample (Equation 9.27). A transmittance spectrum is obtained by carrying out this procedure across the whole range of wavelengths in the visible region. Transmission measurements can only be carried out on emulsions which allow light to pass through, and therefore they cannot be used to analyze concentrated emulsions.

Reflection Spectrophotometer. In these instruments, the intensity of light reflected from the surface of a sample is measured (Francis and Clydesdale 1975). The reflectance (R) of a material is defined as the ratio of the intensity of the light reflected from the sample (RS) to the intensity of the light reflected from a reference material of known reflectance (Rr): R = Rs/Rr. The precise nature of the experimental device depends on whether the reflection is specular or diffuse. For specular reflection, the intensity of the reflected light is usually measured at an angle of 90° to the incident wave, whereas for diffuse reflection, the sum of the intensity of the reflected light over all angles is measured using a device called an integrating sphere (Figure 9.15). A reflectance spectrum is obtained by carrying out this procedure across the whole range of wavelengths in the visible region.

The transmittance and reflectance spectra obtained from a sample can be used to calculate the relative magnitudes of the absorption and scattering of light by an emulsion as a function of wavelength. Alternatively, the color of a product can be specified in terms of trichromatic

FIGURE 9.15 Examples of transmission and reflection spectrophotometers.

coordinates by analyzing the spectra using appropriate mathematical techniques (McClements et al. 1998). The details of these techniques have been described elsewhere and are beyond the scope of this book (Francis and Clydesdale 1975, Hutchings 1994). Light Scattering

Light-scattering techniques are used principally to determine the size distribution of the droplets in an emulsion (Chapter 10). A knowledge of the droplet size distribution enables one to predict the influence of the droplets on light scattering and therefore on the turbidity of an emulsion (Hernandez and Baker 1991, Dickinson 1994). Alternatively, the experimentally determined scattering pattern — the intensity of scattered light versus scattering angle — can be used directly to describe the scattering characteristics of the emulsion droplets.

The scattering of light from dilute emulsions is sometimes characterized by a device known as a nephelometer (Hernandez et al. 1991). This device measures the intensity of light which is scattered at an angle of 90° to the incident beam. The intensity of light scattered by a sample is compared with that scattered by a standard material of known scattering characteristics (e.g., formazin) (Hernandez et al. 1991). Because small droplets scatter light more strongly at wide angles than large droplets, the nephelometer is more sensitive to the presence of small droplets than are turbidity measurements. Colorimetry

A large number of instruments have been developed to characterize the color of materials which are based on the trichromatic principle mentioned previously (Francis and Clydesdale 1975, Hutchings 1994, Francis 1995). A simple colorimeter consists of a light source, the sample to be analyzed, a set of three filters (red, green, and blue), and a photocell to determine the light intensity (Figure 9.16). Colorimetry measurements can be carried out in either a transmission or a reflection mode. In the transmission mode, the intensity of a light beam is measured after it has been passed through the sample and one of the color filters. This

FIGURE 9.16 Schematic diagram of a simple colorimeter.

procedure is then repeated for the other two filters, and the sample is characterized by the intensity of the light wave passing through the red, green, and blue filters. In the reflection mode, the light beam is passed through a filter and is then reflected from the surface of a sample. For specular reflection, a photocell is usually positioned at 90° to the incident wave, while for diffuse reflection, an integrating sphere is used to determine the intensity of the reflected light. This procedure is carried out for each of the three color filters, so that the color of the sample is characterized in terms of the intensities of the red, green, and blue lights. Reflectance measurements are most suitable for determining the color of concentrated emulsions, while transmission measurements are more suitable for characterizing dilute emulsions. Sensory Analysis

Ultimately, the appearance of an emulsion must be acceptable to the consumer, and therefore it is important to carry out sensory tests (Hutchings 1994). These tests can be carried out using either trained specialists or untrained individuals. Each individual is given one or more samples to analyze and asked either to compare the appearance of the samples with each other or to rank certain attributes of the appearance of each sample. Sensory tests must be carried out in a room where the light source is carefully controlled to obtain reproducible measurements which correspond to the conditions a person might experience when consuming the product (Francis and Clydesdale 1975).

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