List of Principal Symbols

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Hilary Miles
6 years ago
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1 Symbol Quantity First appearance on page Upper-case characters A Vector of the cell boundary area between wall and fluid 23 in the calculation domain C Coordinate position of the cell centroid 23 C c Cunningham or slip correction factor 14 D p Particle diffusion coefficient 13 D v Binary vapour diffusion coefficient 10 Dv T Thermal (Soret) diffusion coefficient 10 F Coordinate position of the face centroid 23 F Helmholtz free energy 65 G Gibbs free energy 65 H Enthalpy 65 L Length of the flow tube 7 L v Latent heat of evaporation 11 M Molar weight of the vapour-carrier gas 11 M g Molar weight of air 11 M p,i Particle / droplet mass concentration of component i 13 M s Molar weight of the solute 15 M v Molar weight of water vapour 11 M w Molar weight of water; M w = M v 15 N p Total particle / droplet number concentration 7 Q Heat energy 64 Q rev Heat energy of a reversible process 64 R Universal gas constant 15 R i Inner tube radius 7 R o Outer tube radius 7 vii

2 viii List of Symbols R v Specific gas constant for water vapour 14 S Entropy 64 S h Source term in energy equation 11 S h, wall Latent heat source at tube wall 25 S i Saturation ratio at tube inlet 7 S p Saturation ratio at the particle / droplet surface 14 S r Water vapour saturation ratio in the tube 14 S v Water vapour sink in the vapour mass transport equation 10 S ' Source / sink term in general ' equation 12 T Temperature 10 T i Temperature at the tube inlet 7 T v Water vapour temperature 66 T w Liquid water temperature 66 T wall Temperature at the tube wall 7 U Internal energy 63 V Viscosity vector, V = (V x ;V r ) 17 V Volume 63 V c Volume of a cell in a computational grid 25 V r Viscosity term in radial direction in the momentum equation 10 V x Viscosity term in axial direction in the momentum equation 10 W Work 64 Lower-case charaters a Droplet radius 16 a k Activity of component k in a non-ideal 72 a s Activity of salt in an aqueous solution 72 a w Activity of water in an aqueous solution 72 c Number of components in the system considered 63 c p Specific heat capacity at constant pressure 11 d p Particle / droplet diameter 14 d p,eq Equilibrium diameter 33 d p,i Initial seed particle diameter (dry) 7 e Water vapour pressure 14 e a Water vapour pressure above a droplet with radius a 67

3 ix e sat,dp Saturation water vapour pressure above an aqueous solution 14 droplet e sat,s Saturation water vapour pressure above an aqueous salt 70 solution e sat,w Saturation water vapour pressure above a plane surface 14 of water f Heat Heat transition transfer function 14 f Mass Mass transition transfer function 14 f k Rational activity coefficient of component k in a nonideal 72 f s Rational activity coefficient of salt in an aqueous solution 72 f w Rational activity coefficient of water in an aqueous solution 72 g Gravitational acceleration 10 g Mean molar Gibbs free energy 65 g k Partial molar Gibbs free energy of component k 65 g r r-component of the gravitational acceleration 10 g x x-component of the gravitational acceleration 10 h Specific enthalpy 11 jv Vapour mass flux relative to mass average velocity 10 k Counter (k; k = 1; 2;:::;c) for components in the system 63 considered k Al Heat conductivity of aluminium (Al) 26 k Si2 O Heat conductivity of quartz glass (Si 2 O) 26 k B Boltzmann s constant 14 k mix Heat (or thermal) conductivity of the vapour-carrier gas 11 m mol Molality 45 m p,i Mass concentration of component i in the particle 13 / droplet m s Mass of solute in the droplet 15 m w Mass of water in the droplet 15 n Total number of moles in the system considered 65 n d Normal distance between face and cell centroid 23 n k Number of moles of component k 63 n s Number of moles of solute in an aqueous salt solution 73 n w Number of moles of water in an aqueous salt solution 73

4 x List of Symbols p Pressure 64 p k Partial pressure of component k in a gas 70 pv Partial pressure of water vapour 66 pw Partial pressure of liquid water 66 q Heat flux 11 qh, wall Heat flux 24 r Radial coordinate in the flow tube 10 s Vector difference between the face and cell centroid 23 s Mean molar entropy 65 s k Specific entropy of component k 65 sv Specific entropy of water vapour 66 sw Specific entropy of liquid water 66 t Time 13 u Mass average velocity vector 10 u x-component of u 10 v r-component of u 10 v k Specific volume of component k 65 vm Mean molar volume 65 vv Specific volume of water vapour 66 vw Specific volume of liquid water 66 x Axial coordinate in the flow tube 10 Greek characters ' Diffusion coefficient of the general dependent variable, ' 12 ff Thermal diffusivity 11 ffv,g Thermal diffusion factor 10 " V Volume fraction of the soluble part of the condensation 15 nucleus Dynamic viscosity 10 Mean free path 14 μ k Chemical potential of component k in a 64 μ k;0 Standard chemical potential of component k in a gas 70 μ k;l Chemical potential of component k in a solution 70 μ ffi k;l Standard chemical potential of the pure species k 70 μv Chemical potential of water vapour 66 μw Chemical potential of liquid water 66

5 xi ν Dissociation factor 15 οs Solute mass fraction in the droplet 16 οv Water vapour mass fraction 10 οw Water mass fraction in the droplet 16 %g Density of the vapour-carrier gas 10 %sol Density of the solution droplet 15 %w Density of water 15 ffa Surface tension between a bulk phase of water and air 68 ffsol Surface tension of the solution droplet 15 ffv Surface tension between a bulk phase of water and water 67 vapour ' General dependent variable 12 's Molal or pracitcal osmotic coefficient of the solute 15 ψ k Mole fraction of component k 65 ψ k;l Mole fraction of component k in a solution 70 ψs Solute mole fraction in the droplet 15 ψw Water mole fraction in the droplet 15 Other symbols Kn Knudsen number 14 Pe Péclet number 60 End of List of Symbols

TABLE OF CONTENTS CHAPTER TITLE PAGE

v TABLE OF CONTENTS CHAPTER TITLE PAGE TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS LIST OF APPENDICES v viii ix xii xiv CHAPTER 1 INTRODUCTION 1.1 Introduction 1 1.2 Literature Review