Foam Engineering
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Contributors xvii
Preface xix
1 Introduction 1
Paul Stevenson
1.1 Gas-Liquid Foam in Products and Processes 1
1.2 Content of This Volume 2
1.3 A Personal View of Collaboration in Foam Research 3
Part I Fundamentals 5
2 Foam Morphology 7
D. Weaire, S.T. Tobin, A.J. Meagher and S. Hutzler
2.1 Introduction 7
2.2 Basic Rules of Foam Morphology 7
2.2.1 Foams, Wet and Dry 7
2.2.2 The Dry Limit 9
2.2.3 The Wet Limit 11
2.2.4 Between the Two Limits 11
2.3 Two-dimensional Foams 11
2.3.1 The Dry Limit in 2D 11
2.3.2 The Wet Limit in 2D 12
2.3.3 Between the Two Limits in 2D 12
2.4 Ordered Foams 15
2.4.1 Two Dimensions 15
2.4.1.1 The 2D Honeycomb Structure 15
2.4.1.2 2D Dry Cluster 15
2.4.1.3 2D Confinement 15
2.4.2 Three Dimensions 16
2.4.2.1 3D Dry Foam 16
2.4.2.2 3D Wet Foam 17
2.4.2.3 Ordered Columnar Foams 18
2.5 Disordered Foams 19
2.6 Statistics of 3D Foams 20
2.7 Structures in Transition: Instabilities and Topological Changes 21
2.8 Other Types of Foams 22
2.8.1 Emulsions 22
2.8.2 Biological Cells 22
2.8.3 Solid Foams 23
2.9 Conclusions 24
3 Foam Drainage 27
Stephan A. Koehler
3.1 Introduction 27
3.2 Geometric Considerations 29
3.3 A Drained Foam 33
3.4 The Continuity Equation 35
3.5 Interstitial Flow 36
3.6 Forced Drainage 38
3.7 Rigid Interfaces and Neglecting Nodes: The Original Foam Drainage Equation 41
3.8 Mobile Interfaces and Neglecting Nodes 43
3.9 Neglecting Channels: The Node-dominated Model 46
3.10 The Network Model: Combining Nodes and Channels 48
3.11 The Carman-Kozeny Approach 50
3.12 Interpreting Forced Drainage Experiments: A Detailed Look 51
3.13 Unresolved Issues 53
3.14 A Brief History of Foam Drainage 54
4 Foam Ripening 59
Olivier Pitois
4.1 Introduction 59
4.2 The Very Wet Limit 59
4.3 The Very Dry Limit 61
4.3.1 Inter-bubble Gas Diffusion through Thin Films 61
4.3.2 von Neumann Ripening for 2D Foams 62
4.3.3 3D Coarsening 64
4.4 Wet foams 65
4.5 Controlling the Coarsening Rate 69
4.5.1 Gas Solubility 69
4.5.2 Resistance to Gas Permeation 70
4.5.3 Shell Mechanical Strength 70
4.5.4 Bulk Modulus 71
5 Coalescence in Foams 75
Annie Colin
5.1 Introduction 75
5.2 Stability of Isolated Thin Films 76
5.2.1 Experimental Studies Dealing with Isolated Thin Liquid Films 76
5.2.2 Theoretical Description of the Rupture of an Isolated Thin Liquid Film 77
5.3 Structure and Dynamics of Foam Rupture 78
5.4 What Are the Key Parameters in the Coalescence Process? 81
5.5 How Do We Explain the Existence of a Critical Liquid Fraction? 86
5.6 Conclusion 89
6 Foam Rheology 91
Nikolai D. Denkov, Slavka S. Tcholakova, Reinhard Höhler and Sylvie Cohen-Addad
6.1 Introduction 91
6.2 Main Experimental and Theoretical Approaches 93
6.3 Foam Visco-elasticity 95
6.3.1 Linear Elasticity 95
6.3.1.1 Monodisperse Dry Foam 95
6.3.1.2 Effects of Bubble Polydispersity and Liquid Content 96
6.3.2 Non-linear Elasticity 98
6.3.3 Linear Relaxations 99
6.3.3.1 Slow Relaxation 99
6.3.3.2 Fast Relaxation 101
6.3.4 Shear Modulus of Particle-laden Foams 102
6.4 Yielding 103
6.5 Plastic Flow 105
6.6 Viscous Dissipation in Steadily Sheared Foams 106
6.6.1 Predominant Viscous Friction in the Foam Films 108
6.6.2 Predominant Viscous Friction in the Surfactant Adsorption Layer 111
6.7 Foam-Wall Viscous Friction 112
6.8 Conclusions 114
7 Particle Stabilized Foams 121
G. Kaptay and N. Babcsán
7.1 Introduction 121
7.2 A Summary of Some Empirical Observations 123
7.3 On the Thermodynamic Stability of Particle Stabilized Foams 125
7.4 On the Ability of Particles to Stabilize Foams during Their Production 131
7.5 Design Rules for Particle Stabilized Foams 135
7.6 Conclusions 138
8 Pneumatic Foam 145
Paul Stevenson and Xueliang Li
8.1 Preamble 145
8.2 Vertical Pneumatic Foam 145
8.2.1 Introduction 145
8.2.2 The Hydrodynamics of Vertical Pneumatic Foam 147
8.2.2.1 Pneumatic Foam with Constant Bubble Size Distribution 148
8.2.2.2 The Introduction of Capillary Forces to Give a Liquid Fraction Profile 149
8.2.2.3 Liquid Fraction Profile with Changing Bubble Size Distribution with Height 150
8.2.2.4 Addition of Washwater to a Pneumatic Foam 151
8.2.3 The 'Vertical Foam Misapprehension' 152
8.2.4 Bubble Size Distributions in Foam 153
8.2.5 Non-overflowing Pneumatic Foam 153
8.2.6 The Influence of Humidity upon Pneumatic Foam with a Free Surface 155
8.2.7 Wet Pneumatic Foam and Flooding 155
8.2.8 Shear Stress Imparted by the Column Wall 157
8.2.9 Changes in Flow Cross-Sectional Area 158
8.3 Horizontal Flow of Pneumatic Foam 158
8.3.1 Introduction 158
8.3.2 Lemlich's Observations 159
8.3.3 Wall-slip and Velocity Profiles 160
8.3.4 Horizontal Flow Regimes 161
8.4 Pneumatic Foam in Inclined Channels 162
8.5 Methods of Pneumatic Foam Production 162
9 Non-aqueous Foams: Formation and Stability 169
Lok Kumar Shrestha and Kenji Aramaki
9.1 Introduction 169
9.1.1 Foam Formation and Structures 169
9.1.2 Foam Stability 170
9.2 Phase Behavior of Diglycerol Fatty Acid Esters in Oils 173
9.3 Non-aqueous Foaming Properties 174
9.3.1 Effect of Solvent Molecular Structure 174
9.3.2 Effect of Surfactant Concentration 177
9.3.2.1 Particle Size Distribution 179
9.3.2.2 Rheological Properties of Particle Dispersion 179
9.3.2.3 Equilibrium Surface Tension 181
9.3.3 Effect of Hydrophobic Chain Length of Surfactant 181
9.3.3.1 Foaming of C12G2 in Liquid Paraffin, Squalene, and Squalane 182
9.3.3.2 Foaming of C12G2 in Olive Oil 182
9.3.4 Effect of Headgroup Size of Surfactant 187
9.3.5 Effect of Temperature 189
9.3.6 Effect of Water Addition 191
9.3.6.1 Effect of Water on Foamability 191
9.3.6.2 Effect of Water on Foam Stability 192
9.3.7 Non-aqueous Foam Stabilization Mechanism 201
9.4 Conclusion 203
10 Suprafroth: Ageless Two-dimensional Electronic Froth 207
Ruslan Prozorov and Paul C. Canfield
10.1 Introduction 207
10.2 The Intermediate State in Type-I Superconductors 208
10.3 Observation and Study of the Tubular Intermediate State Patterns 211
10.4 Structural Statistical Analysis of the Suprafroth 215
Part II Applications 227
11 Froth Phase Phenomena in Flotation 229
Paul Stevenson and Noel W.A. Lambert
11.1 Introduction 229
11.2 Froth Stability 233
11.3 Hydrodynamic Condition of the Froth 235
11.4 Detachment of Particles from Bubbles 236
11.5 Gangue Recovery 238
11.6 The Velocity Field of the Froth Bubbles 241
11.7 Plant Experience of Froth Flotation 242
11.7.1 Introduction 242
11.7.2 Frother-constrained Plant 242
11.7.3 Sampling, Data Manipulation and Data Presentation 244
11.7.4 Process Control 245
11.7.5 The Assessment of Newly Proposed Flotation Equipment 246
11.7.6 Conclusions about Froth Flotation Drawn from Plant Experience 246
12 Froth Flotation of Oil Sand Bitumen 251
Laurier L. Schramm and Randy J. Mikula
12.1 Introduction 251
12.2 Oil Sands 251
12.3 Mining and Slurrying 253
12.4 Froth Structure 265
12.5 Physical Properties of Froths 272
12.6 Froth Treatment 274
12.7 Conclusion 278
13 Foams in Enhancing Petroleum Recovery 283
Laurier L. Schramm and E. Eddy Isaacs
13.1 Introduction 283
13.2 Foam Applications for the Upstream Petroleum Industry 284
13.2.1 Selection of Foam-Forming Surfactants 284
13.3 Foam Applications in Wells and Near Wells 287
13.3.1 Drilling and Completion Foams 287
13.3.2 Well Stimulation Foams: Fracturing, Acidizing, and Unloading 288
13.4 Foam Applications in Reservoir Processes 289
13.4.1 Reservoir Recovery Background 289
13.4.1.1 Sweep Efficiency 290
13.4.1.2 Capillary Trapping 291
13.4.2 Foam Applications in Primary and Secondary Oil Recovery 292
13.4.3 Foam Applications in Enhanced (Tertiary) Oil Recovery 293
13.4.3.1 Foams in Carbon Dioxide Flooding 294
13.4.3.2 Foams in Hydrocarbon Flooding 294
13.4.3.3 Foams in Steam Flooding 297
13.5 Occurrences of Foams at the Surface and Downstream 298
13.6 Conclusion 299
14 Foam Fractionation 307
Xueliang Li and Paul Stevenson
14.1 Introduction 307
14.2 Adsorption in Foam Fractionation 310
14.2.1 Adsorption Kinetics at Quiescent Interface 311
14.2.2 Adsorption at Dynamic Interfaces 314
14.3 Foam Drainage 315
14.4 Coarsening and Foam Stability 316
14.5 Foam Fractionation Devices and Process Intensification 317
14.5.1 Limitations of Conventional Columns 317
14.5.2 Process Intensification Devices 319
14.5.2.1 Adsorption Enhancement Methods 319
14.5.2.2 Drainage Enhancement Methods 322
14.6 Concluding Remarks about Industrial Practice 324
15 Gas-Liquid Mass Transfer in Foam 331
Paul Stevenson
15.1 Introduction 331
15.2 Non-Overflowing Pneumatic Foam Devices 334
15.3 Overflowing Pneumatic Foam Devices 336
15.4 The Waldhof Fermentor 338
15.5 Induced Air Methods 340
15.6 Horizontal Foam Contacting 341
15.7 Calculation of Specific Interfacial Area in Foam 342
15.8 Hydrodynamics of Pneumatic Foam 343
15.9 Mass Transfer and Equilibrium Considerations 345
15.9.1 Gas-Liquid Equilibrium 345
15.9.2 Rate of Mass Transfer 345
15.9.3 Estimation of Mass Transfer Coefficient 346
15.10 Towards an Integrated Model of Foam Gas-Liquid Contactors 347
15.11 Discussion and Future Directions 349
16 Foams in Glass Manufacturing 355
Laurent Pilon
16.1 Introduction 355
16.1.1 The Glass Melting Process 356
16.1.2 Melting Chemistry and Refining 359
16.1.2.1 Redox State of Glass 359
16.1.2.2 Melting Chemistry 360
16.1.2.3 Refining Chemistry 360
16.1.2.4 Reduced-pressure Refining 362
16.1.3 Motivations 362
16.2 Glass Foams in Glass Melting Furnaces 363
16.2.1 Primary Foam 363
16.2.2 Secondary Foam 363
16.2.3 Reboil 364
16.2.4 Parameters Affecting Glass Foaming 365
16.3 Physical Phenomena 365
16.3.1 Glass Foam Physics 365
16.3.1.1 Mechanisms of Foam Formation 365
16.3.1.2 Glass Foam Morphology 367
16.3.2 Surface Active Agents and Surface Tension of Gas/Melt Interface 368
16.3.3 Drainage and Stability of a Single Molten Glass Film 369
16.3.4 Gas Bubbles in Molten Glass 370
16.3.4.1 Bubble Nucleation 370
16.3.4.2 Stability of a Single Bubble at the Glassmelt Surface 370
16.3.4.3 Bubble Rise through Molten Glass 371
16.4 Experimental Studies 373
16.4.1 Introduction 373
16.4.2 Transient Primary and Secondary Glass Foams 374
16.4.2.1 Experimental Apparatus and Procedure 374
16.4.2.2 Experimental Observations 375
16.4.3 Steady-state Glass Foaming by Gas Injection 383
16.4.3.1 Experimental Apparatus and Procedure 383
16.4.3.2 Experimental Observations and Foaming Regimes 383
16.4.3.3 Onset of Glass Foaming 384
16.4.3.4 Steady-state Foam Thickness 385
16.5 Modeling 386
16.5.1 Introduction 386
16.5.2 Dynamic Foam Growth and Decay 386
16.5.2.1 Foaming by Thermal Decomposition 386
16.5.2.2 Foaming by Gas Injection 387
16.5.3 Steady-State Glass Foams 389
16.5.3.1 Onset of Foaming 389
16.5.3.2 Steady-state Foam Thickness 390
16.5.4 Experiments and Model Limitations 394
16.6 Measures for Reducing Glass Foaming in Glass Melting Furnaces 395
16.6.1 Batch Composition 396
16.6.2 Batch Conditioning and Heating 397
16.6.3 Furnace Temperature 397
16.6.4 External and Temporary Actions 397
16.6.5 Atmosphere Composition and Flame Luminosity 398
16.6.6 Control Foaming in Reduced-Pressure Refining 399
16.7 Perspective and Future Research Directions 400
17 Fire-Fighting Foam Technology 411
Thomas J. Martin
17.1 Introduction 411
17.2 History 413
17.3 Applications 415
17.3.1 Foam Market 415
17.3.2 Hardware 415
17.4 Physical Properties 416
17.4.1 Mechanism of Action 417
17.4.2 Class A Foams 422
17.4.3 Class B Foams 422
17.5 Chemical Properties 430
17.5.1 Ingredients and Purpose 430
17.5.1.1 Water 431
17.5.1.2 Organic Solvents 431
17.5.1.3 Hydrocarbon Surfactants 433
17.5.1.4 Fluorosurfactants 439
17.5.1.5 Polymers 444
17.5.1.6 Salts, Buffers, Preservatives and Other Additives 446
17.5.2 Example Recipes 447
17.6 Testing 448
17.6.1 Lab Test Methods 449
17.6.1.1 Expansion and Quarter Drain Time 449
17.6.1.2 pH 450
17.6.1.3 Specific Gravity (SG) 450
17.6.1.4 Refractive Index (RI) 450
17.6.1.5 Brookfield Viscosity 450
17.6.1.6 Film Formation 451
17.6.1.7 Surface Tension (ST), Interfacial Tension (IFT), Spreading Coefficient (SC), and Critical Micelle
Concentration (CMC) 451
17.6.1.8 Proportioning Rate 451
17.6.1.9 Deluge-Resistance Time 451
17.6.1.10 Degree of Surfactant Retention in Foam 452
17.6.1.11 Drave's Wetting Rate 452
17.6.2 Fire Test Standards 452
17.6.2.1 UL 162 Fire Tests 452
17.7 The Future 453
18 Foams in Consumer Products 459
Peter J. Martin
18.1 Introduction 459
18.1.1 Foams and Consumer Appeal 459
18.1.2 Market Descriptions and Directions 461
18.1.3 The Scope of This Chapter 463
18.2 Creation and Structure 463
18.2.1 Surfactants and Their Application 464
18.2.2 Creation 466
18.2.3 Growth 468
18.2.4 Application of structure 469
18.2.5 Maintenance of Structure 469
18.2.6 Summary 470
18.3 Sensory Appeal 470
18.3.1 Visual 471
18.3.2 Auditory 472
18.3.3 Mouth Feel 473
18.3.4 Summary 473
18.4 Conclusions 473
Index
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 φ. This ranges from much less than 1% to about 30%. Engineers call the gas fraction (i.e. 1 − φ) the foam quality. Foams used in firefighting are classified by their expansion ratio, which is defined by φ −1. 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 nature’s 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).
Fig. 2.1 Shown are examples of 3D dry and wet foams, as obtained from experiment (a and c) and computer simulations (b and d). Typical 3D foams are polydisperse, consisting of bubbles of many different sizes. (a) Reproduced with kind permission of M. Boran. (d) Reproduced with permission from Wiley-VCH Verlag GmbH & Co. KGaA. (b) and (d) are simulations carried out by A. Kraynik [4].
Bubble size is important in determining which picture is more relevant in equilibrium under gravity. If the average bubble diameter is less than the capillary length l 0, defined as
where γ is the surface tension of the liquid, g is acceleration due to gravity and Δ ρ is the density difference of the gas and liquid, a thin layer of foam consisting of small bubbles will be wet (i.e. have a liquid fraction larger than about 20%). Larger bubbles in equilibrium under gravity form a dry foam.
Fig. 2.2 Plateau’s rules of equilibrium require tetrahedral junctions for dry foams. They are prevalent for small values of liquid fraction, but wet foams can contain junctions of more then four edges (or six cells) [7].
2.2.2 The Dry Limit
In the dry limit the soap films that constitute the interface between bubbles may be idealized as infinitesimally thin curved surfaces, which are generally not simply spherical. These surfaces constitute the faces of polyhedral cells. Many varieties of polyhedra are found in equilibrated dry foams, as enumerated, for example, in the classic observations of Matzke [5] (see Fig. 2.21). But they are subject to important geometrical and topological restrictions, first stated by Plateau [6],1 foam morphologist par excellence. His rules, illustrated in Fig. 2.2, are as follows.
- Faces (films) must meet three at a time. The angles at which they meet must everywhere be 120 degrees, so that three cells are joined symmetrically at a cell edge.
- Edges must meet four at a time. The angles between edges are arccos (−1/3) ≈ 109.43 degrees, the Maraldi angle, where six cells meet symmetrically at every corner.
It may seem intuitively reasonable that such rules follow somehow from local equilibrium of surface tension forces at the points in question. In part this is indeed true, but it is not obvious upon naive consideration why conjunctions of more than six cells are not possible. Plateau observed only tetrahedral junctions in the soap film configurations that he created in wire frames; in due course a colleague, Lamarle [8], supplied a very longwinded mathematical proof. We still await something more expeditious. Taylor [9] has provided a more refined and rigorous modern proof, but it is even less transparent.
Returning to the surfaces that constitute the cell faces, there is a further rule, well known as the Laplace–Young law in the general context of fluid interfaces. It expresses the balance of forces on a small element of soap film in terms of a pressure difference Δ p,
Fig. 2.3 A photograph of the surface of a foam. The curvatures of the films are made visible by the reflections of light on the surface.
Fig. 2.4 Simulations of foams are usually carried out with K. Brakke’s Surface Evolver [10]. This software approximates surfaces with a triangulated mesh or tessellation. This mesh can be refined (i.e. the number of triangles used can be increased) to improve the accuracy of the approximation. (a) to (c) show the same surfaces as the refinement of the tessellation is increased. Note how the curvature of the surfaces becomes much smoother.
Here γ is surface tension and r is the mean radius of curvature. It is related to the two principal radii of curvature, R 1 and R 2, by the expression
In the general case R 1 differs from R 2; for the case of a sphere R 1 = R 2.
The surface is therefore free to have a complicated form, difficult to formulate mathematically; see Fig. 2.3. It is for this reason that almost all detailed descriptions of dry foam structures are numerical in character, consisting of some sort of tessellation, as shown in Fig. 2.4. In modern times they are usually carried out with the freely available Surface Evolver software of Ken Brakke [10].2
2.2.3 The Wet Limit
In the wet limit, the bubbles are spherical (see Fig. 2.1c, d). There are some restrictions on the possibilities for such a packing of hard spheres, familiar in the idealized models used in the field of granular materials. Each sphere must be in contact with at least three others (with the rare exception of ‘rattlers’, small spheres trapped in large cages). The average number of these contacts is six in disordered packings. The latter result, from the elementary theory of mechanical constraints that was originated by James Clerk Maxwell, is not to be considered exact, but is generally valid in practice (at least approximately).
2.2.4 Between the Two Limits
A real foam must lie somewhere between these two idealized limiting cases. Let us start from the dry end, first considering the addition of an amount of liquid that is large enough that we may still neglect the liquid content of the films, but nevertheless still close to the dry limit. The liquid occupies the interstitial space associated with the cell edges. These swell to form what are called Plateau borders.
For a small enough liquid fraction, Plateau’s rules should still apply in some approximate sense. They are progressively violated as the liquid fraction is increased, and our understanding of this intermediate regime is limited. Progressing towards the wet limit we reach a regime in which the cells are slightly deformed spheres, but these are not easy to describe, other than by simulation or rather over-idealized models. For example, the bubbles are sometimes represented by overlapping spheres [4] (or circles in 2D [11]).
2.3 Two-dimensional Foams
The merits of the much simpler 2D foam may now be obvious. Its structure may be modelled using only circular arcs, with curvatures consistent with local gas and liquid pressures. It was C.S. Smith [12] who did most to promote this system as an object of study, although many before him, including Lord Kelvin, had occasional recourse to it.
2.3.1 The Dry Limit in 2D
In the dry limit the 2D foam consists of polygonal cells, as in Fig. 2.5. Since the vertices can only be threefold (a Plateau condition), it follows easily that the average number of sides of a cell is exactly six (Euler’s theorem) [13].
Fig. 2.5 Examples of experimental and simulation images of 2D dry foam. Recently there has been renewed interest in experiments with various types of 2D foam, in particular with regard to their rheological properties [14–17].
Fig. 2.6 Examples of experimental and simulation images of a 2D wet foam. In contrast to the dry system shown in Fig. 2.5, the Plateau borders between bubbles can touch four or more bubbles. As with Fig. 2.5(b), the simulation was carried out with the PLAT [18] software, and includes periodic boundary conditions.
2.3.2 The Wet Limit in 2D
In the wet limit, the cells are touching circular disks, as shown in Fig. 2.6. Just as in the 3D case, we make contact with close-packed...
