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Nucleation and Condensation in Gas-Vapor Mixtures of Alkanes and Water

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Nucleation and Condensation in Gas-Vapor Mixtures of Alkanes and Water Nucleation and condensation in gas-vapor mixtures of alkanes and water Citation for published version (APA): Peeters, P. (2002). Nucleation and condensation in gas-vapor mixtures of alkanes and water. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR559332 DOI: 10.6100/IR559332 Document status and date: Published: 01/01/2002 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. 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If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim. Download date: 23. Sep. 2021 Nucleation and Condensation in Gas-Vapor Mixtures of Alkanes and Water Copyright c 2002 P. Peeters Omslagontw°erp: Paul Verspaget Druk: Universiteitsdrukkerij, TUE CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN Peeters, Paul Nucleation and Condensation in Gas-Vapor Mixtures of Alkanes and Water / by Paul Peeters. - Eindhoven : Technische Universiteit Eindhoven, 2002. - Proefschrift. - ISBN 90-386-2039-x NUR 910 Trefw.: condensatie / druppelvorming / gasdynamica / aardgas. Subject headings: condensation / nucleation / gas dynamics / natural gas. Nucleation and Condensation in Gas-Vapor Mixtures of Alkanes and Water PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magni¯cus, prof.dr. R.A. van Santen, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op donderdag 31 oktober 2002 om 16.00 uur door Paul Peeters geboren te Weert Dit proefschrift is goedgekeurd door de promotoren: prof.dr.ir. M.E.H. van Dongen en prof.dr.ir. H.W.M. Hoeijmakers A clever person solves a problem. A wise person avoids it. Albert Einstein Contents 1 Introduction 1 1.1 Nucleation and growth rate . 1 1.2 Motivation of this research . 3 1.3 Thesis overview . 5 References . 6 2 Phase equilibrium 9 2.1 Thermodynamics of phase equilibrium . 9 2.1.1 Fugacity . 10 2.2 Equations of state . 11 2.2.1 CPA . 12 2.3 Mixtures of methane, n-nonane, and/or water . 14 2.3.1 Pure components . 14 2.3.2 Mixtures . 15 2.3.3 Liquid versus vapor fraction . 16 References . 25 3 Nucleation 27 3.1 Cluster distribution . 27 3.2 Steady nucleation rate . 30 3.3 Dilute vapor in a high pressure carrier gas . 33 3.4 Heterogeneous nucleation . 35 3.4.1 Wetting and contact angles . 36 3.5 Mixtures of methane, n-nonane, and/or water . 36 3.5.1 Supersaturation ratio . 36 3.5.2 Ternary nucleation . 37 3.6 Nucleation theorem . 40 References . 41 4 Droplet growth 43 4.1 Homogeneous droplet model . 44 4.1.1 Continuum region . 45 4.1.2 Knudsen layer . 47 vii viii Contents 4.1.3 Complete set of equations . 50 4.2 Layered droplet model . 51 4.2.1 Molar fluxes in liquid layer . 51 4.2.2 Complete set of equations . 52 4.3 Mixtures of methane, n-nonane and/or water . 53 4.3.1 Binary mixtures . 53 4.3.2 Ternary mixtures . 54 References . 55 5 Wave tube experiments 57 5.1 Nucleation pulse method . 57 5.2 Pulse-expansion wave tube . 58 5.2.1 Pressure pro¯le . 60 5.2.2 Bursting of the diaphragm . 62 5.2.3 Thermodynamic state . 63 5.3 Droplet detection . 64 5.3.1 Light scattering by dielectric particles . 65 5.3.2 Scattering intensity . 67 5.3.3 Light extinction . 69 5.3.4 Layered droplets . 69 5.4 Mixture preparation . 69 5.4.1 Saturation section . 71 5.4.2 Flushing through the HPS . 74 5.5 Experimental procedure . 75 References . 76 6 Experimental results and discussion 79 6.1 Nucleation . 79 6.1.1 Binary mixtures . 79 6.1.2 Ternary mixtures . 83 6.2 Droplet growth . 86 6.2.1 Droplet growth rates . 87 6.2.2 Droplet growth model . 92 References . 99 7 Nucleation of ice 101 7.1 Introduction . 101 7.2 Nucleation . 101 7.3 Surface energy of ice . 102 7.4 Experiment . 103 7.5 Results and discussion . 105 7.6 Conclusions . 112 References . 112 Contents ix 8 Conclusions and recommendations 115 A Physical properties 119 References . 122 B Energy of cluster formation 125 C Droplet growth; derivation of equations 127 C.1 Incoming mass flux . 127 C.2 Energy flux . 128 C.3 Liquid layer . 129 D Tables of experimental data 131 E Droplet growth curves 135 Summary 145 Samenvatting 147 Nawoord 149 Curriculum Vitae 151 x Contents Chapter 1 Introduction In this thesis vapor to liquid nucleation and subsequent droplet growth is studied. Nu- cleation and droplet growth are processes that bring a system that is not at a state of thermodynamic equilibrium (i.e. is in a supersaturated state), to a new equilibrium, by means of the formation of a new phase. Homogeneous nucleation refers to the formation of small stable clusters of vapor molecules, and the nucleation rate is the rate at which these homogeneous condensation nuclei are formed. We will ¯rst give a short description of the physical processes that determine the nucleation rate and the subsequent droplet growth rate. Then, the choice of the system studied, and the conditions at which it is studied will be motivated. In the ¯nal section an overview of this thesis is given. 1.1 Nucleation and growth rate The process of nucleation is a statistical process. It involves the formation of clusters of molecules of a new phase. These clusters are formed at subsaturated as well as supersatu- rated conditions. When the parent phase is not supersaturated, these cluster are unstable and therefore disappear again. When the system is supersaturated, the clusters of the new phase can become stable if they have a certain minimum size. This can be explained as follows. When a system is supersaturated it can lower its energy by forming the new phase. This decrease of energy is proportional to the volume of the new phase. However, the formation of the new phase also involves the formation of an interface between the old (parent) phase and the new phase, which increases the total energy in proportion to the area of this interface. Hence, the di®erence in the energy of a system with and without a cluster of the new phase has a maximum as a function of the cluster size. This maxi- mum forms an energy barrier for the formation of the new stable phase. The maximum height of this energy barrier is called the energy of (cluster) formation, and it depends on the degree of supersaturation of the system. The clusters of size corresponding to this maximum are called the critical clusters. The further away from equilibrium the system is, the lower the energy barrier will be, and the smaller the critical clusters will be. The probability of obtaining a critical cluster is proportional to the Boltzmann factor with the 1 2 Introduction Figure 1.1: Calculations for water vapor to liquid nucleation at 1 bar and 298 K, using the classical nucleation theory. Left: Energy of cluster formation as a function of the cluster size n, for di®erent constant values of the supersaturation S. Right: Nucleation rate J as a function of the supersaturation S. energy of formation in the exponent. This was ¯rst formulated by Volmer and Weber in 1926 [1]. Later, the rate at which critical clusters are formed was included by Becker and DÄoring [2]. The description of the nucleation rate, as formulated by Volmer and Weber, and Becker and DÄoring, is now known as the classical nucleation theory. This theory was extended by Reiss [3] to describe two-component nucleation, and over the years, many modi¯cations to the theory have been made. An up to date discussion of the theory is given by Kashchiev [4]. As an example, ¯gure (1.1) shows the energy barrier W=kBT for the nucleation of water vapor to liquid water as a function of the number of molecules in the cluster, for di®erent values of the supersaturation. Also shown is the corresponding nucleation rate J as a function of the supersaturation S. The curves are calculated using the classical nucleation theory with the capillarity approximation, at a pressure of 1 bar and temperature of 298 K.
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