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Ac I<n owl edge me nts Many people have contributed to the continuing programme of research on which this book draws. First and foremost is Pier Ugo Foscolo, with- out whom there would be no question of the work having got off the ground. His was the driving force which turned what for me would prob- ably have been just a passing curiosity into a positive crusade. His insight, analytical skill and patient probing of the research literature eventually uncovered the elements of an accessible theory waiting to be assembled. We have worked together throughout the developments described in this book. That our initial focus was the forces acting on individual fluidized particles is an indication of the influence of Peter Rowe, who provided facilities, advice and constant encouragement throughout the early stages of this work in the Chemical Engineering Department laboratories at the University College London. He had long recognized the importance of such interactions and had subjected them to pioneering experimental study, of direct relevance to the present programme, many years earlier at the United Kingdom Atomic Energy Authority research laboratories at Harwell. One of the undoubted satisfactions of academic life is that of witnessing the progress of certain research students from eager beginners, struggling to make some sort of sense of the ill-defined open-ended problems they have been handed, to polished professionals, patiently explaining in simple terms to their advisors the steps taken in arriving at momentous conclusions. It does not happen all that often, but three clear instances in the course of this programme call for emphatic acknowledgement: Renzo Di Felice, Acknowledgements now Professor of Chemical Engineering at the University of Genova, and an established international authority on liquid fluidization, for his continuing active participation in experimental and theoretical aspects of the work too numerous to individualize; Stefano Brandani, formerly of the University of L'Aquila, now Reader in Chemical Engineering at University College London, for initiating the 'jump condition' analysis reported in Chapter 14 (his doctoral research was supervised by the late Gianni Astarita, whose inspired contributions to this and other areas of the work are also gratefully acknowledged); and Zumao Chen, who as my doctoral student at L'Aquila worked on aspects of slugging fluidization described in Chapter 15, and who subsequently, on his own initiative, embarked on the two-dimensional numerical simulation studies reported in Chapter 16, which have now come to represent the starting point for new programmes of computational research. From its inception, the work has involved close collaboration between the fluidization research teams of L'Aquila and UCL, accompanied by shuffling of staff and exchange of students. This remains as strong as ever thanks to the active participation of John Yates, who heads the UCL team. Past members of that group who deserve special mention for their contributions to the initial stages of the work are Simon Waldram and Ijaz Hossain; a more recent addition to the team is Paola Lettieri, who maintains strong connections with L'Aquila; David Cheeseman provides continuity and experimental expertise. Major contributors from L'Aquila include Sergio RapagnS., now Professor of Chemical Engineering at the University of Teramo, Nader Jand and Paolo Antonelli. I am especially grateful to Yuri Sergeev, Professor of Engineering Mathematics at the University of Newcastle, for his contribution to the 'jump condition' studies, and also for his frequently solicited advice on technical problems encountered along the way. His careful reading of the original draft manuscript resulted in many suggestions for improvement, all of which have been adopted. Finally, the man who laid the foundation from which we were able to build: Graham Wallis. His unpublished 1962 paper, which he sent me following the appearance of our early applications of his stability criter- ion, contains a wealth of insight and analysis that, together with his book One-Dimensional Two-Phase Flow, we have drawn on repeatedly through- out the course of this work. His direct participation in the programme, at UCL in 1990, provided an invaluable opportunity to clarify aspects of the theory, and to repeat the key 'raining-down' experiments for measuring xii Acknowledgements dynamic wave speed, which he devised and first performed in Peter Rowe's laboratory in Harwell, and only reported in the unpublished 1962 paper; the method is described in Chapter 9, along with his original results and our more recent ones. xiii