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The Influence of Electric Charge and Electric Fields on the Formation and Duration of Water Boules

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The Influence of Electric Charge and Electric Fields on the Formation and Duration of Water Boules The Influence of Electric Charge and Electric Fields on the Formation and Duration of Water Boules. by Jeremy Clive Ahern Being a thesis submitted for the degree of Doctor of Philosophy Brunel University Department of Design and Systems Engineering October 2003 The Influence of Electric Charge and Electric Fields on the Formation and Duration of Water Boules. by Jeremy Clive Ahern Being a thesis submitted for the degree of Doctor of Philosophy Brunel University Department of Design and Systems Engineering October 2003 ABSTRACT Consideration is given to the conditions under which floating drops of water, here referred to as water boules, form, exist and coalesce. Particular emphasis is placed on the part played by electric charge and electric fields in these processes. The literature is reviewed in terms of both the phenomenon of floating drops and of the development of hydrostatics, hydrodynamics and electrohydrodynamics as applicable to the subject. Experimental investigations to ascertain the boundary conditions to the influence of such electrical forces are described, together with observations of the connected electrical events. It is confirmed that boules will fail to form at all, i) under conditions of high humidity, and ii) in the presence of an electric field greater than a certain value. This is investigated experimentally, and shown to be approximately 34kV/m, this figure being about two-thirds that previously reported. Boules traversing a plane water surface are demonstrated to acquire additional charge in the process. In the case of drops dispensed from a grounded source, forming boules and crossing a bulk water surface some 15cm wide, the additional charge gathered is significant. Boules of 0.055g mass were found to have a mean charge of 1.6 x 10-12C on leaving a water surface, having arrived as drops with an average charge of 5.8 x 10-14C. Possible charging mechanisms are discussed. The origin of the initial drop charge is considered, and measurements of this are presented from (i), conventional Faraday cup determinations, and (ii), induction methods applied to free-falling drops. Experimental investigation of the time-dependent electrical records of the coalescence of a dispensed drop with a plane water surface shows the whole coalescence process to have a two- part form. This detail is commonly hidden within more conventional charge-transfer measurements. For the coalescences investigated experimentally an small initial event is shown to occur, involving a charge transfer in the range 1.2 – 4.8 x 10-12C. Oscillograms taken from a large number of coalescences show this preliminary event to be a general feature of the coalescence process, with a number of such traces being appended to the thesis. This initial event is followed by a larger one where the signs of the signals from the drop and the bulk surface are opposite to those of the initial event, and whose potential magnitude is broadly in agreement with that anticipated by double layer disruption. The interfacial potential difference necessary for the onset of instability and subsequent coalescence in the case of closely opposed drops is shown to be dependent on the relative humidity of the ambient air. Consideration is given to G I Taylor’s equation describing the critical potential for the onset of instability between closely spaced drops, and this is shown experimentally to require correction for different humidities. It is demonstrated that the critical potential, Vc, at a relative humidity of 100% is approximately 50% of that at 40% RH. Possible reasons for this are discussed, drawing attention to the problem of establishing an accurate DC relative permittivity value for vapour-laden air in small interfacial gaps. The rôle of evaporation in modifying the system geometry is considered experimentally and theoretically, and shown to be significant only for humidities < 50%. The complex nature of the interface in the case of very small air-gaps is discussed, together with the implications of these investigations for the interfacial stability of a floating drop or boule system. A theoretical model based on a consideration of the complex liquid-air-liquid interface as a capacitive system is developed, and shown to be in good agreement with practical observations. This model demonstrates that the parts played by electrical forces, together with environmental factors, are likely to be significant in terms of coalescence at stages prior to gap thinning to the point where London/van-der-Waals forces become dominant. Interfacial potentials are calculated in a boule system at a number of times between 0.1 and 10 seconds, and shown to be sufficient to promote instability and coalescence. Full data based on a number of values of instability potentials is appended to the thesis. Development of the model raises questions concerning the validity of currently accepted values both for interfacial stability in small gaps and for the relative permittivity of humid air in similar situations. Suggestions are made for future work in such areas, together with possible methodologies. The phenomenon of floating water drops is therefore shown to be compatible with the general coalescence process, the event time being modified by such diverse factors as the impact energy with the surface, the ambient humidity and the magnitude of the initial drop charge. The latter is shown to be the dominant factor in the case of drops arriving on a clean surface with low kinetic energies, with the small charge inherent on any water drop being sufficient to produce potentials adequate to promote eventual instability. DECLARATION I declare that no part of the work referred to in this thesis has been submitted in support of an application for another degree or qualification in this or any other university or other institution of learning. Jeremy C Ahern. October, 2003. DEDICATION To the Memory of Bartolomeo Bizio, Venetian natural philosopher and polymath, who in 1818 watched drops falling from his boatman’s oars and floating on the Venice Lagoon, and wondered . i FRONTISPIECE Frontispiece. Water Boules. “..un fenomeno ch’offrono in vari casi le gocciole cadenti sulla superfice di un liquido omologo..” B. Bizio, 1818. ii ACKNOWLEDGEMENTS On reaching the end of a piece of extended research such as is detailed in this thesis, one is deeply aware of the debt of gratitude that has been building up over time. In many cases assistance and encouragement has been both prolonged and consistent, whilst there have been other instances of brief chance meetings and conversations that have exercised a profound effect on the course of the research. To recall everything is both a difficult and perhaps unnecessary task. The present writer is therefore confining these acknowledgements to individuals and institutions who stand out in his memory as those without whom this research would either never have happened, or else been much the poorer. _____________ A particular debt of gratitude is owed to Professor Wamadeva Balachandran both for his initial encouragement of the research and for his continued wise counsel, involvement and enthusiasm throughout its course. Dr. Colin Pounder of Ilkeston, Derbyshire, has been both a staunch friend and valued sounding-board for developing ideas throughout, as well as being a source of considerable encouragement to undertake the work. Mrs Irena McCabe and Dr. Frank James, past and present librarians of the Royal Institution, were both kind and helpful in the search for early and obscure material, and in the loan of rare texts, such as Plateau’s works, for private reading. The staff of the British Library and the Document Supply Centre gave great assistance in helping to trace early serials and in providing copies of papers from all periods. Yale University Library microfilmed the only known extant copy of Leidenfrost’s works. iii Professor Henri Gibert of the Embassy of France in London gave useful assistance in obtaining material on Boutigny from the Bibliothéque Nationale. The Instrument Loan Pool (EPSRC) at the Rutherford Appleton Laboratory made available a Memrecam C³ and a Kodak 4050 High-speed Video system at different times, and Dr. Adrian Walker of the Loan Pool kindly explained their intricacies. Dr. Anatol Jaworek of the Institute of Fluid Flow Machinery in Gdansk kindly sent copies of earlier Soviet papers. Finally, the writer would like to record his deepest thanks to his wife, Mave, for her constant affectionate support, and her cheerful toleration over some years not only of her husband’s frequent preoccupation, but also of the sprawling domestic laboratory in which most of the experiments here recorded were performed. iv CONTENTS Table of Contents. Dedication i Frontispiece ii Acknowledgements iii Chapter 1 – General Introduction, Thesis Structure and Contributions To Knowledge 1.1 General introduction 1 1.1.1 Aims and objectives of the research 3 1.2 The structure of the thesis 4 1.2.1 Review of literature relevant to water boules 4 1.2.2 Methods of boule production and initial investigations 5 1.2.3 Water molecules and the electrical double layer 6 1.2.4 Charges transferred by boules and disrupted drops 7 1.2.5 Electrical events accompanying coalescence 8 1.2.6 The effect of humidity variation on the critical coalescence potential between two closely-spaced drops 9 1.2.7 Coalescence of water boules 10 1.2.8 Summary and recommendation for further study 12 v 1.3 Contributions to knowledge 12 Chapter 2 – A review of the Literature relevant to Water Boules and
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