Foam Engineering -  - E-Book

Foam Engineering E-Book

0,0
135,99 €

-100%
Sammeln Sie Punkte in unserem Gutscheinprogramm und kaufen Sie E-Books und Hörbücher mit bis zu 100% Rabatt.

Mehr erfahren.
Beschreibung

Containing contributions from leading academic and industrial researchers, this book provides a much needed update of foam science research. The first section of the book presents an accessible summary of the theory and fundamentals of foams. This includes chapters on morphology, drainage, Ostwald ripening, coalescence, rheology, and pneumatic foams. The second section demonstrates how this theory is used in a wide range of industrial applications, including foam fractionation, froth flotation and foam mitigation. It includes chapters on suprafroths, flotation of oil sands, foams in enhancing petroleum recovery, Gas-liquid Mass Transfer in foam, foams in glass manufacturing, fire-fighting foam technology and consumer product foams. Key features: * Foam fractionation is an exciting and emerging technology, starting to gain significant attention * Discusses a vital topic for many industries, especially mineral processing, petroleum engineering, bioengineering, consumer products and food sector * Links foam science theory to industrial applications, making it accessible to an engineering science audience * Summarizes the latest developments in this rapidly progressing area of research * Contains contributions from leading international researchers from academia and industry

Sie lesen das E-Book in den Legimi-Apps auf:

Android
iOS
von Legimi
zertifizierten E-Readern

Seitenzahl: 1046

Veröffentlichungsjahr: 2012

Bewertungen
0,0
0
0
0
0
0
Mehr Informationen
Mehr Informationen
Legimi prüft nicht, ob Rezensionen von Nutzern stammen, die den betreffenden Titel tatsächlich gekauft oder gelesen/gehört haben. Wir entfernen aber gefälschte Rezensionen.



Contents

About the Editor

List of Contributors

Preface

1 Introduction

1.1 Gas–Liquid Foam in Products and Processes

1.2 Content of This Volume

1.3 A Personal View of Collaboration in Foam Research

Part I Fundamentals

2 Foam Morphology

2.1 Introduction

2.2 Basic Rules of Foam Morphology

2.3 Two-dimensional Foams

2.4 Ordered Foams

2.5 Disordered Foams

2.6 Statistics of 3D Foams

2.7 Structures in Transition: Instabilities and Topological Changes

2.8 Other Types of Foams

2.9 Conclusions

Acknowledgements

3 Foam Drainage

3.1 Introduction

3.2 Geometric Considerations

3.3 A Drained Foam

3.4 The Continuity Equation

3.5 Interstitial Flow

3.6 Forced Drainage

3.7 Rigid Interfaces and Neglecting Nodes: The Original Foam Drainage Equation

3.8 Mobile Interfaces and Neglecting Nodes

3.9 Neglecting Channels: The Node-dominated Model

3.10 The Network Model: Combining Nodes and Channels

3.11 The Carman – Kozeny Approach

3.12 Interpreting Forced Drainage Experiments: A Detailed Look

3.13 Unresolved Issues

3.14 A Brief History of Foam Drainage

4 Foam Ripening

4.1 Introduction

4.2 The Very Wet Limit

4.3 The Very Dry Limit

4.4 Wet Foams

4.5 Controlling the Coarsening Rate

5 Coalescence in Foams

5.1 Introduction

5.2 Stability of Isolated Thin Films

5.3 Structure and Dynamics of Foam Rupture

5.4 What Are the Key Parameters in the Coalescence Process?

5.5 How Do We Explain the Existence of a Critical Liquid Fraction?

5.6 Conclusion

6 Foam Rheology

6.1 Introduction

6.2 Main Experimental and Theoretical Approaches

6.3 Foam Visco-elasticity

6.4 Yielding

6.5 Plastic Flow

6.6 Viscous Dissipation in Steadily Sheared Foams

6.7 Foam–Wall Viscous Friction

6.8 Conclusions

Abbreviations

Acknowledgement

7 Particle Stabilized Foams

7.1 Introduction

7.2 A Summary of Some Empirical Observations

7.3 On the Thermodynamic Stability of Particle Stabilized Foams

7.4 On the Ability of Particles to Stabilize Foams during Their Production

7.5 Design Rules for Particle Stabilized Foams

7.6 Conclusions

Acknowledgement

8 Pneumatic Foam

8.1 Preamble

8.2 Vertical Pneumatic Foam

8.3 Horizontal Flow of Pneumatic Foam

8.4 Pneumatic Foam in Inclined Channels

8.5 Methods of Pneumatic Foam Production

9 Non-aqueous Foams: Formation and Stability

9.1 Introduction

9.2 Phase Behavior of Diglycerol Fatty Acid Esters in Oils

9.3 Non-aqueous Foaming Properties

9.4 Conclusion

Acknowledgements

10 Suprafroth: Ageless Two-dimensional Electronic Froth

10.1 Introduction

10.2 The Intermediate State in Type-I Superconductors

10.3 Observation and Study of the Tubular Intermediate State Patterns

10.4 Structural Statistical Analysis of the Suprafroth

Acknowledgements

Part II Applications

11 Froth Phase Phenomena in Flotation

11.1 Introduction

11.2 Froth Stability

11.3 Hydrodynamic Condition of the Froth

11.4 Detachment of Particles from Bubbles

11.5 Gangue Recovery

11.6 The Velocity Field of Froth Bubbles

11.7 Plant Experience of Froth Flotation

12 Froth Flotation of Oil Sand Bitumen

12.1 Introduction

12.2 Oil Sands

12.3 Mining and Slurrying

12.4 Froth Structure

12.5 Physical Properties of Froths

12.6 Froth Treatment

12.7 Conclusion

Acknowledgements

13 Foams in Enhancing Petroleum Recovery

13.1 Introduction

13.2 Foam Applications for the Upstream Petroleum Industry

13.3 Foam Applications in Wells and Near Wells

13.4 Foam Applications in Reservoir Processes

13.5 Occurrences of Foams at the Surface and Downstream

13.6 Conclusion

14 Foam Fractionation

14.1 Introduction

14.2 Adsorption in Foam Fractionation

14.3 Foam Drainage

14.4 Coarsening and Foam Stability

14.5 Foam Fractionation Devices and Process Intensification

14.6 Concluding Remarks about Industrial Practice

15 Gas–Liquid Mass Transfer in Foam

15.1 Introduction

15.2 Non-overflowing Pneumatic Foam Devices

15.3 Overflowing Pneumatic Foam Devices

15.4 The Waldhof Fermentor

15.5 Induced Air Methods

15.6 Horizontal Foam Contacting

15.7 Calculation of Specific Interfacial Area in Foam

15.8 Hydrodynamics of Pneumatic Foam

15.9 Mass Transfer and Equilibrium Considerations

15.10 Towards an Integrated Model of Foam Gas–Liquid Contactors

15.11 Discussion and Future Directions

Acknowledgements

16 Foams in Glass Manufacturing

16.1 Introduction

16.2 Glass Foams in Glass Melting Furnaces

16.3 Physical Phenomena

16.4 Experimental Studies

16.5 Modeling

16.6 Measures for Reducing Glass Foaming in Glass Melting Furnaces

16.7 Perspective and Future Research Directions

Acknowledgements

17 Fire-fighting Foam Technology

17.1 Introduction

17.2 History

17.3 Applications

17.4 Physical Properties

17.5 Chemical Properties

17.6 Testing

17.7 The Future

18 Foams in Consumer Products

18.1 Introduction

18.2 Creation and Structure

18.3 Sensory Appeal

18.4 Conclusions

19 Foams for Blast Mitigation

19.1 Introduction

19.2 Free Field Tests

19.3 Shock Tube Testing

19.4 Theoretical Approaches

19.5 Conclusions

Plates

Index

This edition first published 2012© 2012 John Wiley & Sons, Ltd

Registered OfficeJohn Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom

For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.

The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher.

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.

Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought.

The publisher and the author make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of fitness for a particular purpose. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for every situation. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read. No warranty may be created or extended by any promotional statements for this work. Neither the publisher nor the author shall be liable for any damages arising herefrom.

Library of Congress Cataloging-in-Publication Data

Foam engineering : fundamentals and applications / [edited by] Paul Stevenson. – 1st ed.p. cm.Includes bibliographical references and index.

ISBN 978-0-470-66080-5 (hardback)1. Foam. 2. Foam–Industrial applications. 3. Foam–Technological innovations. 4. Foamed materials. I. Stevenson, Paul, 1973–QD549.F59 2012620.1–dc23

2011037211

A catalogue record for this book is available from the British Library.

Print ISBN: 9780470660805

About the Editor

Paul Stevenson is a senior lecturer in the Chemical and Materials Engineering Department of the University of Auckland, New Zealand. He took BA (Hons) and MEng degrees in chemical engineering from the University of Cambridge, UK, where he completed doctoral studies in multiphase flow in oil flowlines. After post-doctoral research with the 2nd Consortium on Transient Multiphase Flow at Cambridge, he took a position at the University of Newcastle, Australia, to investigate froth flotation and foam fractionation. He has worked as a process chemist for Allied Colloids and as a chemical engineer for Croda Hydrocarbons and British Steel Technical, all in the UK. In addition he has spent periods as a Japanese convertible bond dealer for the US investment bank D.E. Shaw Securities International and a racecourse bookmaker for his family’s business.

List of Contributors

Kenji Aramaki

Graduate School of Environment and Information Sciences, Yokohama National University, Yokohama, JapanN. BabcsánBAY-ZOLTAN Foundation for Applied Research, Miskolc-Tapolca, Igloói, HungaryG. Ben-DorProtective Technologies R&D Center, Faculty of Engineering Sciences, Ben-Gurion University of the Negev, Beer Sheva, IsraelA. BritanProtective Technologies R&D Center, Faculty of Engineering Sciences, Ben-Gurion University of the Negev,Beer Sheva, IsraelPaul C. CanfieldDepartment of Physics and Astronomy, Ames Laboratory, Iowa State University, Ames, IA, USASylvie Cohen-AddadUniversité Paris 6, Paris, France, and Université Paris-Est, Marne-la-Vallée, FranceAnnie ColinUniversité Bordeaux, Pessac, FranceNikolai D. DenkovDepartment of Chemical Engineering, Faculty of Chemistry, Sofia University, Sofia, BulgariaReinhard HöhlerUniversité Paris 6, Paris, France, and Université Paris-Est, Marne-la-Vallée, FranceS. HutzlerSchool of Physics, Trinity College, Dublin, IrelandE. Eddy IsaacsAlberta Innovates – Energy and Environment Solutions, Calgary, AB, CanadaG. KaptayBAY-ZOLTAN Foundation for Applied Research, Miskolc-Tapolca, Iglói, Hungary, and University of Miskolc, Egyetemváros, Miskolc, HungaryStephan A. KoehlerPhysics Department, Worcester Polytechnic Institute, Worcester, MA, USANoel W.A. LambertClean Process Technologies Pty Ltd, Lower Belford, NSW, AustraliaXueliang LiCentre for Advanced Particle Processing, University of Newcastle, Callaghan, AustraliaPeter J. MartinSchool of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, UKThomas J. MartinChemical Technology and Quality Assurance,Research & Development,Chemguard, Inc.,Mansfield, TX, USAA.J. MeagherSchool of Physics, Trinity College, Dublin, IrelandRandy J. MikulaNatural Resources Canada, Devon, AB, CanadaLaurent PilonHenry Samueli School of Engineering and Applied Science, Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, CA, USAOlivier PitoisUniversité Paris-Est, Laboratoire Navier, IFSTTAR, FranceRuslan ProzorovDepartment of Physics and Astronomy, Ames Laboratory, Iowa State University, Ames, IA, USALaurier L. SchrammSaskatchewan Research Council, Saskatoon, SK, CanadaH. ShapiroProtective Technologies R&D Center, Faculty of Engineering Sciences, Ben-Gurion University of the Negev, Beer Sheva, IsraelLok Kumar ShresthaInternational Center for Young Scientists, WPI Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba Ibaraki, JapanPaul StevensonDepartment of Chemical and Materials Engineering, Faculty of Engineering, University of Auckland, New ZealandSlavka S. TcholakovaDepartment of Chemical Engineering, Faculty of Chemistry, Sofia University, Sofia, BulgariaS.T. TobinSchool of Physics, Trinity College, Dublin, IrelandD. WeaireSchool of Physics, Trinity College, Dublin, Ireland

Preface

I am enormously grateful to all of authors who have contributed to this volume on gas–liquid foam. One of the great pleasures of working with such accomplished scientists and engineers from industry and academia is that everybody has known the level at which to pitch their contributions.

Special thanks are due to Laurie Schramm who, along with co-authors, has contributed two chapters on foams in enhanced oil recovery and flotation of oil sands, and to Thomas Martin who endured initial confusion upon my part to produce a first class chapter on fire-fighting foams. I’d like to express my gratitude to Stephan Koehler for giving me sound advice about the selection of authors for various chapters, and to Denis Weaire who advised upon how to engender more coherence in the volume. Cat Chimney gave sterling assistance in formatting referencing styles of a number of chapters. My former colleague Noel Lambert delivered excellent copy at tremendously short notice despite being in enormous demand by others. Gratitude is due to Sven Schröter (of Schroeter Imagery) for his excellent photography and production of the image on the cover of this volume. I could not have completed this project without the constant and faithful assistance of my doctoral student and friend Xueliang (Bruce) Li. Bruce co-wrote two chapters with me, reviewed other chapters and developed ideas for cover art. He is truly a gentleman and scholar.

Thanks should also go to the staff at Wiley (Chichester), in particular Rebecca Stubbs, Sarah Tilley and Amie Marshall, who first envisaged this project and gave excellent support as the volume developed.

Last but not least I’d like to thank my second daughter, Charlotte, for being born at a perfect time to enable me to claim my nine weeks paternity leave from the University of Auckland, during which I worked upon this volume, as well as my wife Tracey for giving birth to her and my first daughter Emily for being cute.

1

Introduction

Paul Stevenson

1.1 Gas–Liquid Foam in Products and Processes

A gas–liquid foam, such as those found on the top of one’s bath or one’s 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 gas–liquid 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 gas–liquid 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 gas–liquid 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 gas–liquid 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 gas–liquid 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 gas–liquid 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 gas–liquid foam

2. Consider a process or product application of foam

The first part provides a chapter in which the topology of gas–liquid 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 gas–liquid mass transfer, and one on the formation and stability of non-aqueous foams. Finally in the ‘Fundamentals’ section there is a chapter on ‘Suprafroth’, 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, ‘Applications’, 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 gas–liquid 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 Weaire’s (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. I’d come across vector notation as an undergraduate, but it still daunted me. One afternoon I read the words ‘self-similar ansatz’, 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 day’s flotation plant trials. I found the mathematical approach of Denis and Stephan difficult to comprehend, but Noel’s 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 gas–liquid foam and the process applications. Among his many achievements, Robert Lemlich of the University of Cincinnati proposed what is often now known as the ‘channel-dominated foam drainage model’, 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 ‘standard model’ of foam drainage. Robert Lemlich’s career was characterised by trying to describe and innovate process technologies that harnessed foam by building a better understanding of the underlying physics. Lemlich’s 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 Lemlich’s 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 gas–liquid 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 Wallis’s models of one-dimensional two-phase flow, and I therefore frequently invoke the concept of a ‘superficial velocity’ (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 gas–liquid 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 gas–liquid foam will benefit from gaining an insight into the physics of the material.

Part I

Fundamentals

3

Foam Drainage

Stephan A. Koehler

3.1 Introduction

The term foam drainage originally described the process by which fluid flows out of a foam, such as liquid draining out of a soap froth [1, 2], or the draining head on freshly poured beer (see Fig. 3.1a