Surface and Interfacial Tension

Measurement, Theory, and Applications

Stanley Hartland

• Publisher: CRC Press
• Year: 2004
• Print ISBN: 9780824750343
• eBook ISBN: 9781135537401
• Topic: Physical Sciences
• Subtopic: Chemistry
• Index: Chemistry

This edited volume offers complete coverage of the latest theoretical, experimental, and computer-based data as summarized by leading international researchers. It promotes full understanding of the physical phenomena and mechanisms at work in surface and interfacial tensions and gradients, their direct impact on interface shape and movement, and t

1.
Drainage and Collapse in Standing Foams

ASHOK BHAKTA Aspen Technology Inc., Cambridge, Massachusetts, U.S.A.

ELI RUCKENSTEIN State University of New York at Buffalo, Buffalo, New York, U.S.A.

I. INTRODUCTION

Foams are highly concentrated dispersions of gas (dispersed phase) in a liquid (continuous phase). Concentrated emulsions (biliquid foams) are similar systems in which the dispersed phase is a liquid. The terms “foam” and “concentrated emulsion” are often used interchangeably in the literature because the phenomena responsible for their behavior are essentially the same.

Foams have several very interesting and unusual properties that make them useful in many industrial applications. The large gas/liquid interfacial area available is exploited in foam fractionation to efficiently separate surface-active substances, such as proteins, from their solutions [1–5]. Foams are also being considered for use in enhanced oil recovery [6, 7], insulation, and reduction of the impact of explosions [6]. On the other hand, foams can often be a nuisance [8, 9] in the chemical process industry. When they last long enough, they interfere with physical and chemical processes and adversely impact productivity and efficiency. Liquid-liquid concentrated emulsions have received relatively less attention in literature. However, interest in them is growing. Concentrated emulsions have been used to prepare high-molecular-weight polymers and composites as well as membranes for separation [10, 11].

The structure of a foam depends on the relative proportions of the gas and liquid. Bubbles are spherical in foams containing a large amount of liquid (>25%). As the percentage of liquid decreases, the bubbles become less spherical. Foams with less than 2% liquid are almost completely polyhedral. For monodispersed foams (composed of identical bubbles), a gas volume fraction of 0.74 is considered to be the limit beyond which the bubbles cease to be spherical. This is because the highest volume fraction that identical spheres can occupy is 0.74. It must be emphasized, however, that this criterion for determining the onset of polyhedricity is applicable only to mono-disperse foams. In poly disperse foams, the bubbles can remain spherical at much higher volume fractions. Although foams are almost never mono-disperse, it is possible to produce foams with a narrow-enough size distribution that the assumption of monodispersity in theoretical models is often reasonable.

Polyhedral foams have a complex structure composed of liquid films (formed between the faces of adjacent polyhedral bubbles) and Plateau border (PB) channels (formed at the edges). Although the dimensions of the films and Plateau border channels vary almost randomly in a typical foam, all foams are known to obey a set of geometrical rules formulated by the Belgian scientist Plateau:

1. Three and only three films meet at an edge at an angle of 120°.
2. Four and only four PB channels meet at a node at an angle of approximately 109°.

The PB channels, which contain most of the liquid, form a complex interconnected network within the framework of Plateau’s laws. Fig. 1 shows a typical foam column, a polyhedral bubble, and the cross-section of a typical Plateau border channel formed where three films meet.

For purposes of modeling foam decay, the details of foam structure are relevant only to the extent that they are useful in determining the mean dimensions of the PB channels and films in terms of the bubble volume that can be measured experimentally. Kelvin’s Tetrakaidecahedron (four quadrilateral, four pentagonal, and six hexagonal faces) is the only space-filling regular polyhedron that satisfies Plateau’s laws. However, it has become common practice to assume a foam to consist of regular pentagonal dodecahedra for modeling purposes. Although it is not space-filling, the regular pentagonal dodecahedron comes remarkably close to satisfying Plateau’s laws. The angle between the faces is about 116° and the angle between the edges is about 108°. In fact, in his experimental study of agglomerations of monodispersed bubbles, Matzke [13] found that a majority of the polyhedra had 12 faces, and pentagonal faces were the most common. In any case, because the structure assumed for the polyhedron is only likely to affect a few geometrical constants to a small extent, it is probably not worth the effort to refine these assumptions. Several interesting discussions of foam structure are available in the literature [12–20].

Foams are metastable. They show a spontaneous tendency to separate into two distinct phases. The time scale for the disi...

Table of contents

• Cover Page
• Surfactant Science Series
• Title Page
• Copyright Page
• Preface
• Contributors
• 1. Drainage and Collapse in Standing Foams
• 2. Foam Film Stability in Aqueous Systems
• 3. Liquid Drops at Surfaces
• 4. Simulation of Bubble Motion in Liquids
• 5. Role of Capillary Driven Flow in Composite Manufacturing
• 6. Surfactant Solution Behavior in Quartz Capillaries
• 7. Contact Angle and Surface Tension Measurement
• 8. Contact Angle Measurements on Fibers and Fiber Assemblies, Bundles, Fabrics, and Textiles
• 9. Bubble Nucleation and Detachment
• 10. Thermodynamics of Curved Interfaces in Relation to the Helfrich Curvature Free Energy Approach