Traditional foam properties measurement techniques

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Chapter 2. Background and literature review

Foam properties

In order to better understand the relationships between polarised light scattering and foam characteristics discussed in the later chapters, some essential foam properties will be reviewed firstly in this section.Foam is a two phase system composing of gas bubbles packed in a smaller amount of liquid or solid [1]. The solid foams are typically solidified liquid foams and hence retain a related structure. The current research conducts only on the liquid foam, so the remainder of the chapter deals only with discussions of liquid foams. A detailed description of cellular solids can be found in Gibson and Ashby [27]. Liquid foams have novel properties owing to their lightness and their very large specific surface area. These properties often meet the somewhat contradictory requirements of a number of industrial applications [28] (See Table 2.1). Now liquid foams have a wealth of uses, of which some are surprising such as aerated food industry, personal care products,enhanced oil recovery, firefighting, waste water treatment, mineral flotation and various other separation processes [29]. Furthermore, a foam, under carefully controlled conditions, often serves as a model system for a cellular material or a biological tissue [30].Liquid foams are broadly divided into “wet” and “dry”, based on the volume proportion of liquid contained in the foam. The wet foams typically have a liquid fraction ε in the range 0.1-0.2, while in theory the upper limit is set at 0.36, calculated on the basis of a closed packed sphere type configuration [20, 31]. In the dry limit, ε < 0.01, the foam consists of polyhedral bubbles with curved walls [32]. For most practical purposes, the foams are treated as being neither completely dry nor completely wet. The typical bubble size can range from 10 µm to some centimetres, and their surface separation distance (i.e. the liquid film thickness) can range from 0.1-2 µm [1]. Liquid foams are continuously evolving systems far from equilibrium. On the aging of a foam, the foam properties such as foam structure, liquid fraction, bubble size distribution etc. change due to the drainage, coarsening and coalescence.These phenomena will be discussed in the following sections. The complex behaviours of foam at various scales have attracted the interest of a wide range of researchers in physics, chemistry and engineering (Figure 2.1)

Foam structure

Foam is a random, space-filling arrangement of spherical to polyhedral bubbles. Although the arrangement is random, it is not arbitrary as foams evolve in order to minimise the surface area of the films between bubbles, which gives rise to a certain universal distribution of polyhedron sizes and shapes [33, 34]. A bubble in the centre of a dry foam is polyhedral in shape because of interaction with its neighbours. Its faces are thin films that are gently curved either because of the pressure differences between the bubbles, or simply because its perimeter does not lie in one plane. In a foam the films of different bubbles intersect in threes along the edges (Figure 2.2), which are liquid–carrying channels known as Plateau borders.The curvature of the gas/liquid interfaces must remain finite by the Laplace-Young law,which imposes a non-zero thickness on the Plateau borders. When two bubbles with a difference in pressure of ∆p share a common face, the pressure-curvature relationship is given Where, σ is the surface tension and r is the local radius of curvature of the film surface. The cross-section of each Plateau border is a small triangle with concave sides (Figure 2.3). Four Plateau borders intersect at the vertices (or nodes) of each polyhedral bubble [35].The amount of liquid contained in a foam is defined by the liquid volume fraction ε, the ratio of the volume of liquid to the total volume of the foam (See Equation (2-2)).Depending on the liquid fraction, different types of foams possess different types of structure. For a bubbly liquid, the bubbles are spherical and do not touch each other; For a wet foam,the bubbles touch and take the shape of a squashed sphere at each bubble/bubble contact; For a dry foam, the bubbles are polyhedral and the Plateau borders have a negligible cross-section.The basic rules of foam geometry were first described by a Belgian scientist, Joseph Antoine Ferdinand Plateau in the 19th century. The rules, known as the Plateau’s law, are: i) Equilibrium of faces: the films are smooth and have a constant mean curvature which is determined by the Laplace-Young law (Equation (2-1)); ii) Equilibrium of edges: the films always meet in threes along edges, forming angles of arccos(-1/2) = 120°; iii) Equilibrium of vertices: the edges meet four-fold at vertices or nodes, forming angles of arccos(-1/3) ≈ 109.5°. These three laws are a necessary and sufficient condition to ensure mechanical equilibrium of an ideal foam and provide the basis for describing the foam structure. One simple idealised foam structure is the Kelvin foam [36, 37], which is a collection of regular tetrakaidecahedral bubbles.

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Foam production

Foams are formed when a gas and liquid are mixed, leading to the formation of bubbles which rise due to their lower density and arrange themselves in a space filling network of liquid with gas entrained in them. Foams made out of a pure liquid such as water have an imperceptibly short life span. This is because the curvature of the Plateau borders causes them to have a much lower pressure than the liquid films (according to the Laplace-Young law), as a result of which the liquid drains rapidly from the films into the Plateau borders causing the films to rupture [38]. The same can be explained using the energy argument in terms of surface energy of the liquid films. However, the life time of such foams can be prolonged by adding surface-active agents such as surfactants or proteins into the liquid. As the bubbles move through the solution before coming together as a space filling network,they adsorb the surface active macromolecules which reduce the surface energy by lowering the surface tension. When the bubbles come together, the surface active material redistributes through the network owing to surface tension gradients due to non-uniform bubble sizes and/or adsorption. Although, film drainage is not eliminated, it is smaller and much slower to rupture the film. The film shrinks to a thin state which is stabilised by the opposing force of electrostatic repulsion between the same charged polar heads of the surfactant floating in the
liquid phase.

Abstract
Acknowledgements
Table of Contents
List of Figures
List of Tables
List of Abbreviations
Chapter 1. Introduction
1.1 Research objectives
1.2 Organization of the dissertation
Chapter 2. Background and literature review
2.1 Foam properties
2.1.1 Foam structure
2.1.2 Foam production
2.1.3 Coarsening
2.1.4 Liquid drainage
2.1.5 Rupture/Coalescence
2.2 Traditional foam properties measurement techniques
2.2.1 Bubble size and distribution measurement
2.2.2 Liquid fraction measurement
2.3 Light scattering techniques
2.3.1 Light scattering-background
2.3.2 Application of light scattering techniques in foams
2.4 Polarised light scattering techniques
2.4.1 Polarised light background
2.4.2 Application of polarised light scattering techniques in foams
2.5 Implications from literature review
2.5.1 Implications from foam properties literature review
2.5.2 Implications from light scattering literature review
2.5.3 Implications to present work
Chapter 3. Method and materials
3.1 Experiment setup
3.2 Experimental procedures
3.2.1 Foaming solution preparation
3.2.2 Instrument calibration
3.2.3 Foam production
3.2.4 Polarised light scattering measurement
3.3 Measurement of Stokes parameters
3.4 Measurement of Mueller matrix elements
3.5 Measurement of liquid fraction
3.6 Measurement of bubble size distribution
Chapter 4. Effect of SDS (Sodium dodecyl sulphate) foam on polarised light characteristics
4.1 Introduction
4.2 Evolution of liquid fraction
4.3 Evolution of bubble size distribution
4.4 Effect of SDS foam properties on the degree of polarisation, P
4.5 Effect of SDS foam properties on the degree of linear polarisation, PL
4.6 Effect of SDS foam properties on the degree of circular polarisation, PC
4.7 Effect of SDS foam properties on the orientation angle, ψ
4.8 Effect of SDS foam properties on the ellipticity angle,
4.9 Conclusions
Chapter 5. Correlation between Mueller matrix elements and SDS foam properties
5.1 Introduction
5.2 Evolution of liquid fraction
5.3 Evolution of bubbles
5.3.1 Evolution of bubble size distribution
5.3.2 Evolution of the bubble geometrical shape
5.4 Correlation between Mueller matrix elements and liquid fraction
5.4.1 Correlation between Mueller matrix elements and liquid fraction of Foam I
5.4.2 Correlation between Mueller matrix elements and liquid fraction of Foam II
5.4.3 Correlation between Mueller matrix elements and liquid fraction of Foam III
5.5 Correlation between Mueller matrix elements and thickness of bubble sides
5.6 Conclusions
Chapter 6. Effect of Casein foam on polarised light characteristics
6.1 Introduction
6.2 Evolution of liquid fraction
6.3 Evolution of bubble size distribution
6.4 Coalescence in Casein foams
6.5 Effect of Casein foam properties on the degree of polarisation, P
6.5.1 Changes of degree of polarisation with time
6.5.2 Multiple regression analysis
6.6 Effect of Casein foam properties on the degree of linear polarisation, PL
6.7 Effect of Casein foam properties on the degree of circular polarisation, PC
6.8 Effect of Casein foam properties on the orientation angle,
6.9 Effect of Casein foam properties on the ellipticity angle, χ
6.10 Conclusions
Chapter 7. Correlation between Mueller matrix elements and Casein foam properties
7.1 Introduction
7.2 Evolution of liquid fraction
7.3 Evolution of bubble size distribution
7.4 Correlation between M11 and Casein foam properties
7.5 Correlation between M12 and Casein foam properties
7.6 Correlation between M22 and Casein foam properties
7.7 Correlation between M33 and Casein foam properties
7.8 Correlation between M34 and Casein foam properties
7.9 Correlation between M44 and Casein foam properties
7.10 Conclusions
Chapter 8. Conclusions and recommendations
8.1 Conclusions
8.2 Recommendations for future work