Theoretical prediction of emulsion color

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Abstract

The perceived quality of many commercial products that are based on emulsions is determined by their color. In this article, a theory is presented to relate the color of emulsions to their composition and microstructure. First, the scattering characteristics (Qs and g) of individual droplets are calculated using Mie Theory. Second, the scattering (S) and absorption (K) coefficients of a concentrated emulsion are calculated using radiative transfer theory. Third, the reflectance spectrum (R) of the emulsion is calculated using Kubelka–Munk Theory. Finally, the tristimulus coordinates (XYZ, or L*a*b*) of the emulsion are calculated using color theory. There is excellent agreement between theoretical predictions and experimental measurements of the influence of droplet and chromophore characteristics on the tristimulus coordinates of concentrated oil-in-water emulsions.

Introduction

The perceived quality of emulsion-based products, such as foods, pharmaceuticals, petrochemicals, health care products and cosmetics, is determined by a combination of physicochemical characteristics such as stability, rheology and appearance [2], [3], [4], [32], [27]. A great deal of theoretical and experimental work has been carried out to establish the factors that determine the stability and rheology of emulsions [18], [19], [20], [21], [31], [33]. On the other hand, there have been few studies on the factors that determine the overall appearance of emulsions. This is surprising given the obvious importance of optical properties in determining the perceived quality of emulsion-based products. The appearance of an object is the first sensory impression that a person normally experiences of its quality. If the appearance of the product does not fall within the expected range it may be rejected. A better understanding of the relationship between the appearance of emulsions and their composition and microstructure would aid in the design of emulsion-based products with improved quality.

The appearance of a material is determined by a combination of factors, including the nature of the light source, the detector and the material [23], [36]. A change in the characteristics of any of these three factors alters the perceived appearance of the material. For example, the appearance of a material is determined by the intensity, wavelength and polarization of the electromagnetic radiation generated by the light source; by the geometry, composition and microstructure of the material; by the sensitivity and specificity of the detector; and by the relative location of the light source, material and detector. In this manuscript we will focus primarily on the influence of the composition and microstructure of the emulsion on its overall appearance. Even so, it must be stressed that the same emulsion will appear differently when observed using different light sources or detectors.

Before presenting a theory that can be used to predict the color of emulsions it is useful to give a brief overview of the physical processes that occur when a light wave encounters an emulsion. When a beam of white light is incident upon the outer surface of an emulsion some of the light is transmitted and some of the light is reflected [14], [15], [25], [35]. The relative proportions of transmitted and reflected light depend on the geometry, composition and microstructure of the emulsion, as well as the nature of the container that holds it [6], [24], [25]. That part of the light that is transmitted into the emulsion travels through the continuous phase and interacts with the droplets. When chromophoric substances are present in either the continuous or dispersed phases some of the light wave is absorbed. The extent of absorption depends on the concentration and absorbtivity of the chromophores and on the wavelength of the light used. Some wavelengths are absorbed more strongly than others so that the color of the light emerging from the emulsion is no longer white. For example, if light is absorbed strongly at the wavelengths corresponding to yellow-to-indigo, then the emerging light would appear red [29]. When a light wave that enters an emulsion encounters a droplet, part of the wave is transmitted and part of the wave is scattered [6], [24], [34]. The fraction of the wave that is scattered and the direction that the scattered waves travel depends on the refractive index of the droplets and continuous phase, as well as on the size of the droplets relative to the wavelength of light. In a dilute emulsion, a light wave that travels through the emulsion may only encounter a single droplet before emerging (single scattering). In a concentrated emulsion, a light wave scattered from one droplet may be scattered by a number of other droplets before it emerges from an emulsion (multiple scattering) [1]. In a highly concentrated emulsion, a significant fraction of the incident light may travel back to the surface of an emulsion through multiple scattering events and emerge as diffusely reflected light [25]. The overall appearance of an emulsion is therefore determined by a combination of light scattering and absorption phenomena. Scattering is largely responsible for the turbidity, opacity or lightness of an emulsion, whereas absorption is largely responsible for the chromaticness (blueness, greenness, redness, etc.).

Section snippets

Theoretical relationship between emulsion color and droplet characteristics

Human beings have great difficulty in objectively quantifying the precise color of objects, even though they can easily subjectively discriminate between objects of similar color [22]. For this reason, the color of a material is normally quantified instrumentally in terms of tristimulus coordinates, such as the XYZ or L*a*b* systems specified by the Commission International de l'Eclairage (CIE) [23], [36]. The advantage of using a coordinate system is that the color of an object can be

Numerical calculations of emulsion color

The light scattering theory described above provides manufacturers of emulsion-based products with a powerful tool for predicting the influence of composition and microstructure on the optical properties of their products. The theory could be used to optimize product color without having to carry out time-consuming and laborious experiments. In this section the theory is used to investigate some of the major factors that influence the color of concentrated oil-in-water emulsions: droplet

Comparison of theory with experimental measurements

The experimental data presented in the following section are taken from recent studies performed in our laboratory on the influence of composition and microstructure on emulsion color [8], [9], [26].

Conclusions

The tristimulus coordinates of emulsions can be predicted from a knowledge of their composition and microstructure using the light scattering theory. The predicted dependence of emulsion color on droplet characteristics (radius, concentration, refractive index) and chromophore characteristics (absorptivity, concentration) is in good qualitative agreement with experimental measurements. Excellent quantitative agreement between predicted and measured emulsion color can be obtained when the

Acknowledgements

The author thanks Prof. Clydesdale for many useful discussions and Drs Chanamai and Chantrapornchai for their excellent performance of the experimental measurements reported in this manuscript.

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