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How Fluids Unmix. Discoveries by the School of Van Der Waals and Kamerlingh Onnes, ,  ---

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4671 Sengers Voorwerkb 23-09-2002 09:17 Pagina I How fluids unmix 4671 Sengers Voorwerkb 23-09-2002 09:17 Pagina II History of Science and Scholarship in the Netherlands, volume The series History of Science and Scholarship in the Netherlands presents studies on a variety of subjects in the history of science, scholarship and academic insti- tutions in the Netherlands. Titles in this series . Rienk Vermij, The Calvinist Copernicans. The reception of the new astronomy in the Dutch Republic, -. , --- . Gerhard Wiesenfeldt, Leerer Raum in Minervas Haus. Experimentelle Natur- lehre an der Universität Leiden, -. , --- . Rina Knoeff, Herman Boerhaave (-). Calvinist chemist and physician. , --- . Johanna Levelt Sengers, How fluids unmix. Discoveries by the School of Van der Waals and Kamerlingh Onnes, , --- Editorial Board K. van Berkel, University of Groningen W.Th.M. Frijhoff, Free University of Amsterdam A. van Helden, Utrecht University W.E. Krul, University of Groningen A. de Swaan, Amsterdam School of Sociological Research R.P.W. Visser, Utrecht University 4671 Sengers Voorwerkb 23-09-2002 09:17 Pagina III How fluids unmix Discoveries by the School of Van derWaals and Kamerlingh Onnes Johanna Levelt Sengers , Koninklijke Nederlandse Akademie van Wetenschappen, Amsterdam 4671 Sengers Voorwerkb 23-09-2002 09:17 Pagina IV © Royal Netherlands Academy of Arts and Sciences No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photo- copying, recording or otherwise, without the prior written permission of the publisher. Edita , P.O. BOX , Amsterdam, the Netherlands [email protected], www.knaw.nl/edita --- The paper in this publication meets the requirements of « -norm () for permanence This study was undertaken with the support of the Koninklijke Hollandsche Maatschappij der Wetenschappen (‘Royal Holland Society of Sciences and Humanities’) as part of its 250th anniver- sary celebrations in 2002. The research for this book was also supported by the Stichting voor Funda- menteel Onderzoek der Materie (). 4671 Sengers Voorwerkb 23-09-2002 09:17 Pagina V Contents . Historical setting: time period and place . Understanding fluid phase behavior – the challenge . A description of the individual chapters . Gas non-ideality in the th century . Andrews and the P-V relation near the critical point . Van der Waals’s background . The Van der Waals equation . The Helmholtz energy according to Van der Waals . Double tangent, tie line, connodal and spinodal . Van der Waals’s career at the University of Amsterdam . Cubic equations . Relation to coming chapters ‒ . The principle of corresponding states from the Van der Waals equation . Van der Waals tests the principle of corresponding states . Importance of the principle of corresponding states for gas liquefaction . Kamerlingh Onnes and the principle of mechanical similarity .. Biographical notes .. Mechanical similarity . Empirical scale factors . The principle of corresponding states as the foundation for a molecular theory of phase separation of fluid mixtures 4671 Sengers Voorwerkb 23-09-2002 09:17 Pagina VI . The principle of corresponding states in the th century .. Two-parameter corresponding states .. Empirical scale factors .. Generalized corresponding states – acentric factor .. Quantum-mechanical corresponding states .. Chain molecules . Outlook ‒ . Early attempts at understanding mixture phase behavior . Andrews, Cailletet, and Van der Waals – the liquefaction of gaseous mixtures . Gibbs and the equilibrium of heterogeneous systems . The equation of Van der Waals for fluid mixtures .. Historical setting .. Molecular theory of a substance composed of two different species . Helmholtz energy for a binary Van der Waals mixture . Double-tangent plane – coexisting phases . Stability of the mixture A(V, x) surface – the spinodal and the plait point .. Taylor expansion .. An exact expression for the spinodal . Plaits on the isothermal Helmholtz energy surface for binary mixtures .. The transverse plait .. The longitudinal plait .. The isothermal Helmholtz energy surface at three-phase coexistence . Other significant results . Concluding remarks ‒ . Korteweg’s origins . The shape of analytic surfaces .. Korteweg’s tools .. Curvature of an analytic surface . On plait points – first part .. Overview .. A look at analytic surfaces near plait points .. Taylor expansion of the surface – curvature and stability .. Taylor expansion at the plait point – flecnodal .. Landau expansion .. How to find a plait point on a surface .. Two kinds of plait points 4671 Sengers Voorwerkb 23-09-2002 09:17 Pagina VII .. Two kinds of double plait points . On plait points – second part .. Korteweg’s method of continuous transformation of surfaces .. The role of homogeneous double plait points in the evolution of plaits . The general theory of plaits () .. Overview .. First theorem – directions of tie line and connodals .. Second theorem – a connodal forms a cusp .. Application to the evolution of a heterogeneous double plait point .. Third theorem – exchange of connectivity of plaits .. Triple-tangent planes .. Accessory plaits .. Quadritangent planes . Assessment and outlook ‒ . The Physics Laboratory at Leiden University . Measurement and calibration of pressure . Thermometry . Measurement of density and observation of phase separation . Kuenen performs the first measurements on gas mixtures .. Kuenen’s background .. The first reliable measurements on fluid mixture phase separation . Kuenen discovers retrograde condensation .. A liquid phase evaporates under pressure .. A controversy with Van der Waals .. Retrograde condensation rediscovered . Kuenen discovers critical azeotropy . Kamerlingh Onnes builds space models . Kuenen moves on ‒ , , . Introduction . Van Konynenburg and Scott (K&S) on the Van der Waals mixtures .. Scope of the work .. The global phase diagram .. The shield region .. The six types of binary fluid phase diagrams .. When were these phase diagrams discovered? . Korteweg and the Van der Waals symmetric mixture .. The model 4671 Sengers Voorwerkb 23-09-2002 09:17 Pagina VIII .. Korteweg’s graphical representations .. Strong attraction between the two components .. Weak attraction between the two components – three- and four-phase equilibria .. Relevance of Korteweg’s work – ternary mixtures and the three-state Potts model .. Was Korteweg right? .. Outlook . Kuenen, in Scotland, discovers new types of phase behavior .. Kuenen’s career .. Aqueous three-phase mixtures .. Three-phase critical endpoint – heteroazeotropy .. Mixtures of ethane and alcohols – discovery of Type-V .. Ethane and methanol – Type III . Van Laar calculates the global phase behavior of the Van der Waals mixture .. Overview – biographical notes .. Partial miscibility in associating mixtures – ‘especially water’ .. ‘The different forms and transformations’ .. ‘An exact expression’ .. Van Laar finds a singularity in the plait point curve .. The case of unequal excluded volumes .. The existence of Type IV .. An assessment - ‒ , , . Historical setting – Keesom . A gas that sinks in a liquid .. A curious experiment .. Azeotropy and barotropy .. Quantifying the barotropic effect . Gas-gas separation . Matters of priority – Van Laar, Kamerlingh Onnes and Keesom . Measuring gas-gas equilibria . A case study of the workings of the Dutch School , , ‒ . Characterization of critical behavior .. What happens at a critical point? .. Power laws and critical exponents 4671 Sengers Voorwerkb 23-09-2002 09:17 Pagina IX .. Modern theory of criticality .. How to measure a coexistence curve . Van der Waals develops the theory of capillarity . De Vries measures the capillary rise near a critical point . Verschaffelt finds that mean-field theory fails at the critical point .. Who was Verschaffelt? .. Verschaffelt measures capillary rise .. Verschaffelt pinpoints a problem with the near-critical surface tension data .. Verschaffelt finds non-classical critical exponents very near the critical point .. Impact, or lack of it . Verschaffelt’s career in the th century . An unrecognized bridge to the modern era . Verschaffelt vindicated - : , , . Andrews-Van der Waals versus older views of fluid criticality . Overview of controversies . Why experiments near critical points are difficult . Ramsay finds evidence of gaseous and liquid molecules . Cailletet liquefies mixtures . Cailletet and Collardeau demonstrate the persistence of the liquid state . Pellat: Andrews’s critical temperature is not that of Cagniard de la Tour . Blurring of the Andrews-Van der Waals view . Experiments by Zambiasi, De Heen, Battelli and Galitzine . Gouy studies gravity effects near the critical point . Kuenen explains Cailletet’s early experiments on phase separation of mixtures . Ramsay does penance and takes the offensive . Kuenen disproves Galitzine’s experiments . De Heen separates the liquid-like from the gas-like molecules . Persistence of the concept of liquidogens . The use of floats as probes of local density .. An experiment by Teichner .. A quantitative treatment of impurity effects near critical points .. Kamerlingh Onnes repeats De Heen’s and Teichner’s experiments . History repeats itself .. Fallow years and rebirth
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  • Arxiv:0710.5227V1 [Physics.Hist-Ph] 27 Oct 2007

    Arxiv:0710.5227V1 [Physics.Hist-Ph] 27 Oct 2007

    THE COLLABORATION BETWEEN KORTEWEG AND DE VRIES | AN ENQUIRY INTO PERSONALITIES BASTIAAN WILLINK Abstract. In the course of the years the names of Korteweg and de Vries have come to be closely associated. The equation which is named after them plays a fundamental role in the theory of non- linear partial differential equations. What are the origins of the doc- toral dissertation of De Vries and of the Korteweg-de Vries paper? Bastiaan Willink, a distant relative of both of these mathemati- cians, has sought to answer these questions. This article is based on a lecture delivered by the author at the symposium dedicated to Korteweg and de Vries at University of Amsterdam in September 2003. Since its rediscovery by Zabusky and Kruskal in 1965, an extensive literature has come to exist on the Korteweg-de Vries equation (KdV equation) which de- scribes the behavior of long-wavelength waves in shallow water. It is not the aim of this paper to add to the discussions concerning the contents of this equation or regarding the genesis of the theory of non-linear partial differential equations. Hereto Eduard de Jager has recently added two papers [1] Earlier Robert Pego and others questioned the originality of the work by De Vries and Korteweg, especially in relation to the work by Boussinesq [2]. De Jager has however made it plausible that although the KdV equation can be deduced from an equation of Boussinesq [Joseph Valentin Boussinesq (1842-1929)] by means of a relatively simple substi- tution, nonetheless Korteweg and De Vries arrived at new and important results through treading a different path than Boussinesq.