Many of us have been fascinated as children by soap bubbles and soap films. Their shapes and colours are beautiful and they are great fun to pay with. With no les intensity, scientists and mathematicians have been interested in the properties of bubbles and films throughout scientific history.
In this book David Lovett describes the properties of soap films and soap bubbles. He then uses their properties to illustrate and elucidate a wide range of physical principles and scientific phenomena in a way that unifies different concepts. The book will appeal not only to students and teachers at school and university but also to readers with a general scientific interest and to researchers studying soap films.
For the most part simple school mathematics is used. Sections containing more advanced mathematics have been placed in boxes or appendices and can be omitted by readers without the appropriate mathematical background.
The text is supported with
* Over 100 diagrams and photgraphs.
* Details of practical experiments that can be performed using simple household materials.
* Computer programs that draw some of the more complicated figures or animate sequences of soap film configurations.
* A bibliography for readers wishing to delve further into the subject.
David Lovett is a lecturer in physics at the University of Essex. His research interests include Langmiur-Blodgett thin films and the use of models as teaching aids in physics. He has been interested in soap films since 1978 and has made a number of original contributions to the subject, particularly in the use of models which change their dimensions and their analogy with phase transitions. He has published three other books including ITensor Properties of Crystals (Institute of Physics Publishing 1989).
John Tilley is also a lecturer in physics at the University of Essex with research interests in theoretical solid-state physics and soap films. He is coauthor of Superfluidity and Superconductivity (Institute of Physics Publishing, 3rd edition, 1990).
Table of Contents
Preface. Introduction: What are soap films? Surface tension and surface energy; A brief history of soap-film studies; Plateau's problem; The shape of minimal surfaces; The saddle-point bifurcation. Two-dimensional soap-film patterns: Introduction; Simple two-dimensional patterns; Bubbles within the two-dimensional patterns; Symmetry of patterns, objects and soap films; Further discussions on geometry; The general Steiner problem. Soap films and first- and second-order phase transitions: A 2D model for a first-order phase transition; Thermodynamics of the phase transition; The water-vapour phase transition; Physics of the four-pin soap-film model; A 2D model for a second-order phase transition; The Ehrenfest classification; The order parameter and symmetry. Soap-film models and catastrophe models: Introduction to catastrophe theory; The fold catastrophe; The cusp catastrophe; The Zeeman catastrophe machine; Illustrating double-cusp catastrophes with soap films; Chapter appendix; phase transitions and Landau theory. Film within a wedge - the catenoidal surface: Film between three pins joining non-parallel plates; Film within a wedge; Setting the wedge apex upwards in a gravitational field; Interference colours; Theory of thin-film interference; Films between two cones; The ^IH-surfaces of revolution; Altering pressure on one side of a film; Films within a helix-the helicoid; Chapter appendix; mathematics of the catenoidal surface. Soap films within three-dimensional frameworks and minimal surfaces: Films within simple prism-shaped frameworks; Films within simple variable frameworks; Film patterns within the regular Platonic polyhedra; Great arc configurations; Minimal surfaces and computers; Examples of minimal surfaces suitable for representation by computer graphics. Fermat's principle and refraction: Fermat's principle; Modelling simple refraction; Prisms and lenses; Mirages; P-waves through the earth; Curvature of space - the Schwarzschild geometry; Bending of light near a black hole. Bubbles: Simple bubbles; Bubbles within fixed frameworks; Bubbles within variable frameworks; Coalescing bubbles; More about bubble patterns; The bubble raft and crystal structure. Analogies within the scientific world: Introduction; Biological unicellular forms and radiolarians; Forms of carbon and the fullerenes; The honeycomb; Cracks and fissures; Equilibrium shapes of crystals; Langmuir-Blodgett films; Application in technology; communications networks; Architectural applications; Concluding comments. Appendices. Construction of the models: The two-dimensional models and the wedge; The frameworks. Soap-film patterns by computer using Mathematical (J Tilley and D Lovett): Computer programs. Bibliography. Index.
"... an attractive book well laid out ... many high quality illustrations. ... useful reference book"
School Science Review
attractive book well laid out ... many high quality illustrations. ... useful reference book"
School Science Review
"This will appeal to everyone with an enquiring mind who is keen to illustrate, by experiments, basic results in science and mathematics. This is a valuable work that will stimulate the reader and introduce the reader to many new concepts and ideas."
ill appeal to everyone with an enquiring mind who is keen to illustrate, by experiments, basic results in science and mathematics. This is a valuable work that will stimulate the reader and introduce the reader to many new concepts and ideas."
"This well-written and lively book will entertain and educate any scientist or science student."
American Journal of Physics
ell-written and lively book will entertain and educate any scientist or science student."
American Journal of Physics