![]()
1
Introduction
Paul Stevenson
1.1 GasâLiquid Foam in Products and Processes
A gasâliquid foam, such as those found on the top of oneâs bath or oneâs beer, is a multiphase mixture that generally exhibits several physical properties that make it amenable to be used in multifarious industrial applications:
1. High specific surface area. The amount of gasâliquid surface area per unit volume of material that is attainable in a foam is greater than that in comparable two-phase systems. This property makes gasâliquid foam particularly attractive for interphase mass transfer operations. Examples of such processes are froth flotation, in which valuable hydrophobic particles are recovered from a slurry, the recovery of oil sands, and the stripping of gases from effluent by absorption into the liquid phase.
2. Low interphase slip velocity. The slip velocity between gas and liquid phases is the absolute velocity of the liquid phase relative to the gas phase, and this is typically much smaller in a foam than in a bubbly gasâliquid mixture. This is because the large specific surface area is able to impart a relatively large amount of shear stress on the liquid phase, thereby limiting the relative slip velocity between phases. A high contact time between gas and liquid phases can be engendered, which can also enhance the amount of mass transfer from liquid to gas, gas to liquid, or liquid to interface.
3. Large expansion ratio. Because the volumetric liquid fraction of a foam can be very low, the expansion ratio (i.e. the quotient of total volume and the volume of liquid used to create that foam) can be very high. This property is harnessed in the use of the material for fighting fires and to displace hydrocarbons from reservoirs.
4. A finite yield stress. Because gasâliquid foams can support a finite shear stress before exhibiting strain, they are very effective for use in delivering active agents contained in liquids in household and personal care products (such as bathroom cleaner and shaving foam), as well as in topical pharmaceutical treatments.
Thus, the geometrical, hydrodynamical and rheological properties of gasâliquid foam can be harnessed to make it a uniquely versatile multiphase mixture for a variety of process applications and product designs. It is therefore a material that is of broad interest to chemical engineers.
However, these physical properties of gasâliquid foam are determined by the underlying physics of the material. The rheology of foam is dependent upon, inter alia, the liquid fraction in the foam, which is in turn dependent of the rate of liquid drainage. This is a function of the rate at which bubbles coalesce and how the bubble size distribution evolves because of inter-bubble gas diffusion. The performance of a froth flotation column is dependent upon the stability of the foam, but the very attachment of particles to interfaces can have a profound influence upon this stability. In fact, the underlying physical processes that dictate the performance of a foam in a process or product application are generally highly interdependent.
It is precisely because of this interdependency, and how the interdependent fundamental physical processes impact upon the applications of foam, that it is hoped that this volume will have utility, for it seems axiomatic that those motivated by applications of foam would need to know about the underlying physics, and vice versa.
1.2 Content of This Volume
This volume is split into two major sections, within which the chapters broadly:
1. Give a treatment of one or another aspect of the fundamental physical nature or behaviour of gasâliquid foam
2. Consider a process or product application of foam
The first part provides a chapter in which the topology of gasâliquid foam is described followed by expositions of how this can change through liquid drainage, inter-bubble gas diffusion and coalescence, although these processes are highly mutually interdependent. Further, there are chapters on the rheology of foam and how particles can enhance stability, since these topics are rooted in fundamental physics, but have an important impact upon applications of foam. There is a chapter on the hydrodynamics of pneumatic foam, which underpins the processes of froth flotation, foam fractionation and gasâliquid mass transfer, and one on the formation and stability of non-aqueous foams. Finally in the âFundamentalsâ section there is a chapter on âSuprafrothâ, which is a novel class of magnetic froth in which coarsening is promoted by the application of a magnetic field and therefore is reversible.
In the second part, âApplicationsâ, there are chapters on processes and products that exploit the properties of foam. Froth flotation, foam fractionation and foam gas absorption are unit operations for different types of separation processes that rely upon pneumatic gasâliquid foam for their operation, and each is treated in an individual chapter. In addition there is a dedicated chapter on the flotation of oil sands because the technical challenges of this process are dissimilar to those of phase froth flotation of minerals and coal and because the supply of hydrocarbon resources from this source is likely to become increasingly important over the next century. However, foams also find utility in the enhanced recovery from oil reservoirs and this is described in a chapter. Foams manifest in a variety of manufacturing processes, and there is a description of foam behaviour and control in the production of glass. One of the most common applications of foam is in firefighting, as is discussed in a dedicated chapter. There is an important chapter on the creation and application of foams in consumer products; such products are typically of high added-value and therefore this field is rich with opportunities for innovation and development. Finally, a chapter on blast-mitigation using foam is given.
1.3 A Personal View of Collaboration in Foam Research
I had been doing postdoctoral work in the UK into multiphase flow through subsea oil flowlines when, in 2002, I travelled to Newcastle, Australia, to commence research on froth flotation of coal. I confess to not knowing what flotation was, but when I was travelling to work by train on my first morning I saw a coal train pass that seemed to be at least one mile long, so I thought it must be a field worthy of engagement. I had never considered foams beyond those encountered in domestic life.
However, once in Australia, it soon became clear to me that there was nothing specific for me to do, so I was left to my own devices from the outset. I inherited a pneumatic foam column that lived in a dingy dark-room, and for six months I would go there each morning and watch foam rise up a column and collect the overflow in a bucket. When it got too hot, I went to the excellent and well-air-conditioned library to read about foam drainage. I especially remember reading articles on drainage of Denis Weaireâs (co-author of Chapter 2 herein) group from Trinity College Dublin, and the work that Stephan Koehler (author of Chapter 3) carried out at Harvard. Despite having had a relatively rigorous education in a good chemical engineering department, I felt totally out of my depth when trying to get to grips with this work. Iâd come across vector notation as an undergraduate, but it still daunted me. One afternoon I read the words âself-similar ansatzâ, and immediately retired for the day. During this time, I shared an office with Noel Lambert (joint author of Chapter 11), now Chief Process Engineer of CleanProTech, who would come into the office coated in coal dust and issue instructions down the telephone to organise the next dayâs flotation plant trials. I found the mathematical approach of Denis and Stephan difficult to comprehend, but Noelâs world was completely alien to me. And yet we were all working on one or another aspect of foam.
I learnt enough from Noel to realise that flotation was an incredibly physically complicated process and that plant experience was of paramount importance when trying to improve and innovate. In this context, methods that claimed to be able to simulate the entire flotation process by numerical solutions of sets of equations based upon oversimplified physics seemed particularly contrived. Similarly, there was a plethora of dimensionally inconsistent data fits in the flotation literature that were by their very nature only relevant to the experiments from which they were developed, but upon which general predictive capability was claimed. It is not surprising that some physicists appear to view some work of engineers with caution.
However, it was a chemical engineer who, arguably, was the first researcher to make significant process in both the fundamental science of gasâliquid foam and the process applications. Among his many achievements, Robert Lemlich of the University of Cincinnati proposed what is often now known as the âchannel-dominated foam drainage modelâ, and he used this to propose a preliminary mechanistic model for the process of foam fractionation. Thus, the desire for a better understanding of a process technology for the separation of surface-active molecules from aqueous solution was the driver for the development of what some regard as the âstandard modelâ of foam drainage. Robert Lemlichâs career was characterised by trying to describe and innovate process technologies that harnessed foam by building a better understanding of the underlying physics. Lemlichâs contributions, which are often not given the credit that they deserve, demonstrate the value of a combined approach of physical understanding and practical application. Lemlich, and his co-workers, were able to effect these developments within their own research group. Those of us who do not possess Lemlichâs skill and insight may not be able to make similar progress single-handedly, but can still benefit from cross-disciplinary collaboration to achieve similar goals.
As a chemical engineer working on the fundamentals of gasâliquid foam and its process applications, I have collaborated with physicists and have found that the biggest impediments to interdisciplinary research in foam are caused by semantic problems. For example, as a former student of chemical engineering, I learnt about Wallisâs models of one-dimensional two-phase flow, and I therefore frequently invoke the concept of a âsuperficial velocityâ (i.e. the volumetric flowrate of a particular phase divided by the cross-sectional area of the pipe or channel). However, I have discovered that this is not a term universally known by the scientific community, and its use by me has caused some consternation in the past. Equally, I am quite sure that I have inadvertently disregarded research studies because I have failed to understand the language and methods correctly. However, I have recently found that perseverance, an open mind and a willingness to ask and to answer what may superficially appear to be trivial questions can overcome some difficulties.
The contributors to this volume may be from differing disciplines of science and engineering, but all are leading experts in their fields and all are active in developing the science and technology of foam fundamentals and applications. It is very much hoped that, in bringing together this diverse cohort of authors into a single volume, genuine cross-disciplinary research will be stimulated that can effectively address problems in the fundamental nature of gasâliquid foam as well as innovate new processes that can harness its unique properties. In addition, it is anticipated that engineering practitioners who design products and processes that rely on gasâliquid foam will benefit from gaining an insight into the physics of the material.
![]()
Part I
Fundamentals
2
Foam Morphology
Denis Weaire, Steven T. Tobin, Aaron J. Meagher and Stefan Hutzler
2.1 Introduction
When bubbles congregate together to form a foam, they create fascinating structures that change and evolve as they age [1], are deformed [2], or lose liquid [3]. Foams are usually disordered mixtures of bubbles of many sizes, but they may also be monodisperse, in which case ordered structures may also be found. They may be relatively wet or dry, i.e. contain a greater or lesser amount of liquid.
While the familiar foams of industry and everyday life are three-dimensional, laboratory experiments create two-dimensional foams of various kinds, offering attractive possibilities of easy experiments, computer simulations and visualizations, and more elementary theory. One form of 2D foam consists of a thin sandwich of bubbles between two glass plates. Let us begin with the 3D case, recognizing its greater practical importance.
2.2 Basic Rules of Foam Morphology
2.2.1 Foams, Wet and Dry
Foams may be classified as dry or wet according to liquid content, which may be represented by liquid volume fraction Ď. This ranges from much less than 1% to about 30%. Engineers call the gas fraction (i.e. 1 â Ď) the foam quality. Foams used in firefighting are classified by their expansion ratio, which is defined by Ď â1. At each extreme (the dry and wet limits) the bubbles come together to form a structure which resembles one of the classic idealized paradigms of natureâs morphology: the division of space into cells in the dry limit and the close-packing of spheres in the wet limit (see Fig. 2.1).