Nucleation of N-nonane in mixtures of methane, propane, and carbon dioxide Citation for published version (APA): Labetski, D. G. (2007). Nucleation of N-nonane in mixtures of methane, propane, and carbon dioxide. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR624554 DOI: 10.6100/IR624554 Document status and date: Published: 01/01/2007 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: 02. Oct. 2021 NUCLEATION OF N-NONANE IN MIXTURES OF METHANE, PROPANE, AND CARBON DIOXIDE Copyright c 2007 D. Labetski Omslagontwerp: P. Verspaget, D. Labetski Druk: Universiteitsdrukkerij, TUE CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN Labetski, Dzmitry Nucleation of n-nonane in mixtures of methane, propane, and carbon dioxide / by Dzmitry Labetski. - Eindhoven : Technische Universiteit Eindhoven, 2007. - Proefschrift. - ISBN 978-90-386-2222-4 NUR 910 Trefw.: condensatie / druppelvorming / gasdynamica / aardgas. Subject headings: condensation / nucleation / gas dynamics / natural gas. NUCLEATION OF N-NONANE IN MIXTURES OF METHANE, PROPANE, AND CARBON DIOXIDE PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op donderdag 22 maart 2007 om 16.00 uur door Dzmitry Labetski geboren te Smolevichi, Belarus Dit proefschrift is goedgekeurd door de promotoren: prof.dr.ir. M.E.H. van Dongen en prof.dr.ir. A. Hirschberg This research was financially supported by Twister B.V. and by the Dutch Technol- ogy Foundation STW, grant ESF.6472. Facts do not cease to exist because they are ignored. Aldous Huxley Contents 1 Introduction 1 1.1 Thermodynamics and kinetics of homogeneous nucleation ...... 2 1.2 Experimental studies on homogeneous nucleation . ..... 5 1.3 Application ................................. 7 1.4 Thesisoverview............................... 8 References ..................................... 9 2 Wave tube experimental method 11 2.1 Nucleation pulse method . 12 2.2 Pulse expansion wave tube . 13 2.3 Determination of pulse conditions: pressure, temperature, time du- ration..................................... 17 2.4 Detection of macroscopic droplets . 22 2.5 Mixture preparation and initial mixture compositions . ........ 31 2.6 Experimental procedure . 36 References ..................................... 37 3 Nucleation and droplet growth 39 3.1 Kinetics of homogeneous nucleation . 39 3.2 Nucleationtheories ............................. 48 3.3 Nucleationtheorem............................. 54 3.4 Dropletgrowth ............................... 58 References ..................................... 68 4 Gradient-theory computation of surface tension and nucleation rate for n-nonane clusters 71 4.1 Theory .................................... 72 4.2 Surface tension and the work of formation . 77 4.3 Nucleationrate ............................... 81 4.4 Comparisons................................. 83 4.5 Conclusions ................................. 86 4.6 Thermophysical properties of n-nonane . 86 References ..................................... 87 5 Results and discussion 91 5.1 n-Nonane nucleation in methane . 91 5.2 n-Nonane nucleation and droplet growth in methane/propane car- riergasmixtures............................... 99 5.3 n-Nonane nucleation and droplet growth in methane/carbon diox- idemixtures .................................104 References .....................................109 vii CONTENTS 6 Conclusions and recommendations 111 A Phase equilibrium and surface tension in multicomponent mixtures 115 A.1 Phase equilibrium in two-phase system . 115 A.2 Equationsofstate ..............................116 A.3 Supersaturation of vapor diluted in the carrier gas . .......117 A.4 Surface tension in mixtures . 117 References .....................................118 B Simultaneous nucleation and droplet growth in the expansion wave tube119 B.1 Characteristic depletion time . 119 B.2 Simultaneous nucleation and droplet growth model . 121 B.3 Comparison of model predictions with experimental data .......122 References .....................................125 C Experimental data 129 Summary 137 Samenvatting 141 Acknowledgments 145 Curriculum Vitae 147 viii Chapter 1 Introduction Condensation is a phenomenon that is a common-life experience. Imagine your- self taking a milk bottle (or a beer bottle if you prefer) from your refrigerator. Left untouched, after some time the bottle will be covered with tiny droplets. Wait a little more and droplets will grow to bigger sizes. What happens is that the wa- ter vapor present in the air contacts with the bottle surface and is cooled down. At this lower temperature it cannot exist in the gas phase and has to transform into liquid. So, condensation is a transition process from one phase to another. Because condensation takes place on a surface it is called heterogeneous conden- sation. Heterogeneous condensation is a phase transition process which occurs on foreign particles such as ions, dust particles, or at some solid surface. Fig. 1.1: Water vapor condensation near the open refrigerator. CHAPTER 1. INTRODUCTION If you are curious, you may continue "experimenting". Put the bottle back into the refrigerator and and turn the knob to decrease the temperature inside. After a while, take the bottle out, put it on the table and observe what is going to hap- pen. You will see that now the condensation is more intense, more droplets are formed on the surface and they are growing faster. From this observation, you can conclude that the more remote the vapor state from its liquid state at the bottle sur- face the more intense the condensation is. In this particular case, the remoteness from equilibrium or the vapor supersaturation can be characterized by the temper- ature difference between two states. Let us continue to decrease the temperature, at some point the temperature will be so low that when you open the refrigera- tor the condensation will start at once. The cold air from the refrigerator will mix with air in the room, cool it down and you will see the formation of very small droplets which manifest themselves as a dense white mist (Fig. 1.1). What you just have observed is a combination of heterogeneous condensation on aerosols and homogeneous condensation – the vapor supersaturation may become so high that foreign particles or surfaces are not always needed. The spontaneous gathering of a few vapor molecules will play the role of a droplet growth nucleus. Because the condensation is not limited by the presence of foreign particles, homogeneous condensation may become a very intense process. The droplet formation rate or nucleation rate strongly depends on supersaturation. In this thesis only homoge- neous nucleation will be considered and studied. 1.1 Thermodynamics and kinetics of homogeneous nu- cleation When the vapor is brought into a thermodynamically unstable state, it adjusts it- self to a new condition through a transition process – condensation. During con- densation, the nuclei or clusters of the new condensed phase are formed and then these clusters start to grow forming macroscopic droplets, and eventually the bulk liquid phase. The energy of cluster formation is a key parameter in the nucleation process. In the simple case of unary nucleation, the energy of cluster formation consists of bulk and liquid terms [1, 2]: W = n(µgas µeq) + aσn2/3, (1.1) − − where n is the number of molecules in the cluster, µgas is the actual chemical poten- tial of the gas phase and µeq that of the liquid (and vapor) phase at equilibrium, a is the cluster surface per molecule, and σ is the surface tension. The bulk term, the first in the right hand side (rhs), characterizes how much energy is gained when 2 1.1. THERMODYNAMICS