An investigation of the critical thickness of film rupture and drainage phenomena using dual wavelength ellipsometry

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Abstract

The effect of viscosity on the critical thickness of film rupture has been investigated using the new technique of dual wavelength ellipsometry. This technique enables accurate film thickness determination of a draining film between an approaching droplet and a liquid/liquid interface. Film drainage data for a polybutene/decane film between a water droplet and a bulk water phase was obtained over a range of film viscosities. Critical film thicknesses showed a dependence upon the film viscosity, and ranged from 1950 to 3454 Å for polybutene/decane film viscosities of 6.48–29.30×10−3 N s m−2 respectively. The magnitude of these critical film thickness values indicate that short range van der Waals forces do not control the rupturing process in the systems studied in this investigation.

Introduction

The quality of many food and industrial products depends on the stability of an emulsion system. When two droplets approach each other in an emulsion system, a thin liquid film forms between the two droplets. If the system is unstable, this film then thins to a certain thickness, termed the critical thickness, at which point an instability develops, rupture occurs, and the two droplets coalesce. In order for the stability of such systems to be properly controlled, an understanding of the properties that effect coalescence are necessary.

Owing to the complex nature of the coalescence process, most researchers have examined the coalescence of a single droplet at a flat interface and related these results to coalescence phenomena. The coalescence process is said to take place in a number of consecutive stages [1]. These stages, however, are not well defined, but are helpful in understanding the coalescence process. The first stage, when the droplet is a large distance from the interface, its approach is controlled by the bulk hydrodynamics of the two liquid phases [2]. After the drop undergoes damped oscillation at the interface, a thin liquid film is formed between the drop and the bulk phase. The rate at which the droplet approaches the interface is controlled by the film drainage process. In unstable emulsions this is usually the slowest process and consequently, is rate controlling. When the film becomes sufficiently thin, ≈100 nm, the effects of Van der Waals and electrostatic forces become significant. Depending on the sign and magnitude of the disjoining pressure attributable to these forces, the drainage of the film may be either retarded or enhanced. In those systems in which an unstable film is present, the film will continue to thin down to a certain thickness, termed the critical thickness, at which point an instability will develop and rupture of the film will occur. The time that lapses between film formation and film rupture is not constant, but rather has a range of possible values owing to the statistical nature of the rupturing process [3]. The final stage in which the contents of the droplet are transferred to its bulk phase completes the coalescence process.

Although coalescence phenomena have been the focus of many investigations, experimental data are few. Knowledge of the thickness at which a film between a deformable droplet and a liquid/liquid interface ruptures would give further insight into the coalescence process as a whole, and therefore also into the mechanisms controlling emulsion stability.

A liquid/liquid interface is inherently rough owing to the presence of capillary waves which result from thermal fluctuations. It is thought that the mechanism controlling rupture of a film between two liquid phases involves the amplification of these waves at the interface of each liquid boundary. As a result of Van der Waals interactions, the amplitude of these waves increases with decreasing separation of the two surfaces [4]. Unless there is a significant repulsive force between the two surfaces hindering further film drainage, rupture of the intervening film will occur on contact of the boundaries. The probability of rupture is dependent upon the frequency and amplitude of these waves as well as the thickness of the film [5]. Factors such as the disjoining pressure, interfacial tension, presence of a solute, mechanical vibrations, etc. are also important in determining the thickness at which film rupture occurs. The position at which a film ruptures has been shown to be varied. Both central and off-centre rupture, as well as some cases of simultaneous rupture in two separate places, have been observed experimentally [6].

It has been established, that the general thickness range of unstable films at the point of rupture is between 0 and 1000 Å, but owing to experimental limitations precise determination of film thicknesses at the point of rupture has been unobtainable. Early work by Hartland [7]involved the study of film rupture between a deformable droplet and a liquid/liquid interface by using photography and by measuring the electrical capacitance of the film. Critical thicknesses obtained, however, were larger than those determined by other workers and of the order of 10−3 cm. Burrill and Woods [8], and Scheludko and Manev [9]also performed experiments using photographic methods to monitor the process of film drainage. The studies of Scheludko and Manev on the critical thickness of rupture for circular microscopic foam films suggest that the critical thickness is independent of the viscosity of the film. They obtained critical film thicknesses in the range of 300–500 Å for both the aniline and chlorobenzene films studied. Burrill and Woods investigated the effect of surfactant on film drainage in the system of a rising oil droplet coalescing at a bulk oil/water interface. The light interference pattern produced from illumination of the film between a droplet and an interface was photographed, and film thicknesses up to the point of film rupture were extracted. Critical thicknesses of 300–500 Å were obtained; however, for thicknesses <1000 Å, the accuracy of this technique is limited, as the interference colours progress from white to increasing shades of grey as film thicknesses decrease in this thickness region. Grading of this grey scale is therefore required in order to extract the thicknesses at which film rupture occurs. MacKay and Mason [10]employed the technique of interferometry to investigate film drainage and determined critical thicknesses to be in the region of 500 Å. They also proposed that critical thicknesses of rupture were independent of droplet size.

The aim of our present study is to obtain a precise and accurate determination of the thickness of rupture of thin films between an approaching droplet and an interface. The technique we have chosen is ellipsometry since it has the vertical resolution to determine accurately (±2 Å) thicknesses of thin films. Ellipsometry is an optical technique in which the changes in polarisation of light due to reflection from a film-covered surface are analysed in terms of the thickness and refractive index of the film. Previously, ellipsometry has been applied to characterise a diverse range of interfaces and films, with particular interest in adsorption and wetting phenomena. As film drainage is a dynamic process, fast time resolution is required for a study of this type. Additionally, two different wavelengths are required for precise determination of the thicknesses as which a film ruptures. Hence, in this study, a new technique involving the use of an ultra-fast ellipsometer, was developed to study film drainage between an approaching droplet and a liquid/liquid interface up to the point of film rupture, i.e. dual wavelength ellipsometry.

Dual wavelength ellipsometry is similar to conventional ellipsometry, but differs in that two light sources of different wavelength are used rather than only one light source of single wavelength. The technique of dual wavelength ellipsometry uses a similar concept to that of interferometry. Interferometry involves illumination of a film with monochromatic light. Illumination of a film between an approaching droplet and an interface results in the production of a set of interference oscillations, otherwise known as fringes. Each oscillation signifies a specific change in film thickness, which is dependent upon the wavelength of the incident beam. Former studies, utilising the concept of interference fringes, have encountered difficulties in determining critical film thicknesses due to problems in ascertaining the order of the fringe at which film rupture occurs. For example, Fisher et al. [11]employed interferometry to investigate film thinning between an air bubble and a hydrophilic or slightly hydrophobic silica surface. Film thinning rates rather than absolute thicknesses were reported for the hydrophobic plate systems for the reason mentioned above. The use of two wavelengths in our method of dual wavelength ellipsometry eliminates any uncertainty in fringe order and hence any uncertainty in film thickness determination.

In the work presented in this study, we have developed and utilised dual wavelength ellipsometry to investigate the dependence of the critical thickness of rupture on the viscosity of the continuous phase. The system investigated was that of a water droplet approaching a bulk water phase through a continuous medium of polybutene. A viscosity range in the continuous phase of 6.48–29.30×10−3 N s m−2 was achieved by varying the concentration of decane in solution.

Section snippets

Dual wavelength ellipsometry

Ellipsometry [12]is a polarimetric technique which involves the measurement of changes in polarisation of monochromatic light upon reflection from a film-covered surface. Consider a system in which an aqueous droplet is approaching an oil/water interface as shown in Fig. 1. An incident beam is reflected and refracted at the oil/water interface (inset to Fig. 1). The refracted portion of light is then reflected from the oil/droplet interface, and, as a result, suffers a phase change, β, in

Film drainage

Film drainage data were obtained up to the point of rupture for the system of a water droplet approaching a polybutene/water interface in a continuous phase of varying viscosity. The viscosity of the polybutene was varied over a range from 6.48×10−3 to 29.30×10−3 N s m−2, corresponding to a range in droplet radius from 0.191 to 0.228 cm respectively (Table 1).

As a water droplet approached the polybutene/water interface, a set of interference fringes was produced. Fig. 5(a) shows the changes in

Summary

A dual wavelength ellipsometry technique is presented which enables accurate film thickness determination of a draining liquid film from between a droplet and a free surface. This has been used to obtain information on film thicknesses at the point of rupture for an aqueous droplet coalescing in a viscous Newtonian fluid containing polybutene and decane. The results show a much larger critical thickness than previously observed, indicating short range van der Waals forces are not controlling

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Acknowledgements

Financial support from the Australian Food Industry Science Centre is gratefully acknowledged.

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