Vaporisation of single and binary component droplets in heated flowing gas stream and on solid sphere

Vaporisation of single and binary component droplets in heated flowing gas stream and on solid sphere A thesis submitted for the degree of Doctor of Philosophy By Thi Bang Tuyen Nguyen Discipline of Chemical Engineering School of Engineering Faculty of Engineering & Built Environment The University of Newcastle March, 2018 DECLARATIONS I hereby certify that the work embodied in the thesis is my own work, conducted under normal supervision The thesis contains no material which has been accepted, or is being examined, for the award of any other degree or diploma in any university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, except where due reference has been made in the text I give consent to the final version of my thesis being made available worldwide when deposited in the University’s Digital Repository, subject to the provisions of the Copyright Act 1968 and any approved embargo i ACKNOWLEDGEMENTS Firstly, I would like to express my sincere gratitude to Prof Geoffrey M Evans who brought me to Australia, to pursue my desired PhD program I would like to thank my supervisors, Prof Geoffrey M Evans, Dr Subhasish Mitra and Dr Mayur Sathe, for their continued support and guidance I would also like to express my sincere appreciation to Dr Subhasish Mitra for being a supportive senior colleague prior to his currently supervising role and for his great effort in self-fabricating a number of delicate experimental setups in our laboratory I am grateful to all my friends in Nier A Block for keeping a friendly atmosphere and being an everyday life support I would also like to acknowledge the financial support provided through the linkage project from British Petroleum, Kwinana refinery, Western Australia and Australian Research Council that made this work possible Finally, I would like to thank my daughter Binh-Minh, who recently has asked me “Are you a doctor, mummy? – not yet but really soon – oh no I don’t like needles.”, and “why you keep putting party pies in my lunch box everyday mummy?”; my baby boy Quang-Minh, whose face expressions can clear all the work’s hardship when I am home every day and my husband Cuong, for his daily support, encouragement and love ii SELF-PUBLISHED WORK INCLUDED IN THE THESIS No Full bibliography Journal/ Conference Status Contribution to thesis Nguyen, T T B., Mitra, S., Sathe, M J., Pareek, V., Joshi, J B., & Evans, G M (2018a) Evaporation of a sessile binary droplet on a heated spherical particle Experimental Thermal and Fluid Science Journal, Exp Therm Fluid Sci Published Chapter Nguyen, T T B., Mitra, S., Sathe, M J., Pareek, V., Joshi, J B., & Evans, G M (2018) Evaporation of a suspended binary mixture droplet in a heated flowing gas stream Experimental Thermal and Fluid Science, 91(Supplement C), 329-344 Journal, Exp Therm Fluid Sci Published Chapter Nguyen, T T B., Mitra, S., Pareek, V., Joshi, J., Journal, & Evans, G (2015) Comparison of ChERD vaporization models for feed droplet in fluid catalytic cracking risers Chemical Engineering Research and Design, 101, 82-97 Published Chapter Nguyen, T T B., Mitra, S., Pareek, V., Joshi, J B., & Evans, G M (2016) Modelling evaporation of mono and binary component alkane droplets in different convective flow conditions Paper presented at the Proceedings of the 10th Australasian Heat and Mass Transfer Conference (AHMT 2016) Brisbane, Qld 14-15 July, 2016 http://hdl.handle.net/1959.13/1329006 Conference, AHMT Presented Chapter Mitra, S., Nguyen, T B T., Doroodchi http://hdl.handle.net/1959.13/1329006, E., Pareek, V., Joshi, J B., & Evans, G M (2016) On wetting characteristics of droplet on a spherical particle in film boiling regime Chemical Engineering Science, 149, 181-203 Journal, CES Published Chapter Nguyen, T B T., Mitra, S., Pareek, V., Joshi, J B., & Evans, G M (2017) Evaporation at the three phase contact line of a highly wetting droplet on a superheated surface Chemeca conference 2017 Conference, Chemeca Presented Appendix F iii TABLE OF CONTENTS DECLARATIONS i ACKNOWLEDGEMENTS ii SELF-PUBLISHED WORK INCLUDED IN THE THESIS iii TABLE OF CONTENTS iv LIST OF TABLES .vii LIST OF FIGURES viii ABSTRACT xiii NOMENCLATURE xvi Notation xvi Dimensionless numbers xvii Greek letters xviii Subscripts xix Chapter Introduction 1.1 Background of the study 1.2 Homogeneous vaporisation 1.3 Heterogeneous vaporisation 1.4 Problem statement 1.5 Objectives of thesis 1.6 Thesis outline Chapter Literature review 11 2.1 Vaporisation of droplets in multiphase (gas-solid fluidised bed) system 11 2.2 Vaporisation of a suspended droplet in heated flowing gas stream 18 2.3 Vaporisation of a droplet on a heated substrate 29 2.4 Internal convections inside an evaporating droplet 34 Chapter Comparison of vaporization models for feed droplet in fluid catalytic cracking risers 38 3.1 Homogeneous vaporization models 39 3.1.1 Governing equations: 39 3.1.2 Homogeneous models: 41 3.1.3 Estimation of thermos-physical properties: 44 3.2 Heterogeneous vaporization models 46 3.2.1 Existing heterogeneous models 46 3.2.2 Proposed heterogeneous droplet-particle collision (DPC) model 48 3.3 Results and Discussions 57 3.3.1 Validation of homogeneous vaporization models 57 3.3.2 Predictions of vaporization time for gas oil droplets by homogeneous models 61 3.3.3 Heterogeneous vaporization time predictions for gas oil droplets 67 3.4 Conclusions 74 Chapter Evaporation of a suspended binary mixture droplet in a heated flowing gas stream 76 4.1 Modelling 77 4.1.1 Droplet evaporation rate 77 iv 4.1.2 Droplet temperature 80 4.1.3 Estimation of thermo-physical properties 81 4.2 Experimental 83 4.2.1 Apparatus 83 4.2.2 Procedure 84 4.2.3 Materials 87 4.2.4 Image analysis 88 4.3 Results and discussions 90 4.3.1 Evaporation of hydrocarbon mixtures 90 4.3.2 Evaporation of water-glycerol mixtures 99 a) Reduction in droplet size 99 b) Variation in droplet temperature 109 4.4 Scaling analysis 112 4.4.1 Internal motions in the droplet 112 4.4.2 Unsteady heating/cooling stage of the droplet 115 4.5 Conclusions 117 Chapter Evaporation of sessile binary droplet on a heated spherical particle 120 5.1 Experimental 121 5.1.1 Apparatus 121 5.1.2 Image analysis 125 5.2 Results and discussion 130 5.2.1 Droplet evaporation rate 131 5.2.2 Droplet temperature 138 5.2.3 Unsteady heating-up stage 145 5.2.4 Wetted contact area 147 5.2.5 Transient variation in contact angle 155 5.2.6 Internal motion within droplet 163 5.3 Conclusion 168 Chapter Conclusions and recommendations 171 6.1 Conclusions 171 6.2 Recommended future work 175 6.2.1 Evaporation model accounting for internal motions in binary droplets on a heated curved substrate 175 6.2.2 Effect of surface curvature on the sessile droplet evaporation on heated substrate 175 6.2.3 Temperature dependency of contact angle in non-boiling evaporation 175 6.2.4 Evaporation at the three-phase contact line 176 REFERENCES 178 Appendix A Evaporation rate of a suspended droplet 189 Appendix B Evaporation rate of a sessile droplet 191 Appendix C Temperature dependent physical properties of fluids 194 Appendix D Lennard–Jones Potential Model Constants 198 Appendix E Contact angle of an evaporating sessile droplet 199 Appendix F Evaporation at the three-phase contact line 202 v F.1 Background 202 F.2 Modelling 203 F.3 Results and Discussion 207 F.4 Conclusions 211 Appendix G Supplementary results of Chapter 212 G.1 Standard deviations used for error bars 212 G.2 Additional results of water-glycerol, water-IPA and water-butanol droplets 215 vi LIST OF TABLES Table 2.1 Typical numerical studies including the droplet vaporisation under film boiling regime, particularly in FCC riser and fluid coker operating conditions 13 Table 2.2 Development of heat and mass transfer correlations for droplet evaporation 19 Table 2.3 A comparative summary of modelling studies on multicomponent droplet evaporation 24 Table 2.4 Summary of experimental studies on multicomponent droplet evaporation 28 Table 2.5 Experimental contact angle of water droplet on metal surface at different temperature 32 Table 3.1 Homogeneous models for droplet vaporization 41 Table 3.2 FCC feed (vacuum gas oil) liquid and vapour properties in a typical FCC riser (Buchanan, 1994) 62 Table 3.3 Operating conditions of a typical FCC riser (Buchanan, 1994; Nayak et al., 2005)63 Table 3.4 Droplet vaporization times (ms) for different size of FCC feed droplets predicted by homogeneous models (operating conditions are: d p = 65 µm, T d0 = 561 K, T B = 700 K, T G = T p = 922 K) 66 Table 3.5 Vaporization times (ms) predicted by the heterogeneous models for FCC feed droplet (Operating conditions are: d p = 65µm, T d0 = 561K, T B = 700K, T G = T p = 922K).69 Table 4.1 Physical properties of the liquid and gas mixture 82 Table 4.2 Operating conditions of binary hydrocarbon droplet evaporation 90 Table 4.3 Operating conditions of the water-glycerol systems 99 Table 4.4 Time scales for droplet internal motion 114 Table 4.5 Comparisons between characteristic time scales and actual unsteady heating times 116 Table 5.1 Case studies 131 Table 5.2 Comparison of liquid-solid interface temperature predicted with experimental measurement Operating conditions: 90 % water - 10 % glycerol droplet T S = 323-358 K, d p = 10 mm, T a = 296 K, RH = ~ 50 % d = 2.75 mm 141 Table 5.3 Comparison of thermal diffusion time with the actual heating time (case “gly10”) 147 Table 5.4 Duration of pinning mode at different concentrations (T S = 323 K) 149 Table 5.5 Parameters evaluating the convection inside droplet 166 Table 5.6 Reduction in surface tension subject to temperature and glycerol concentration 167 vii LIST OF FIGURES Figure 1.1 Schematic of the two feed droplet vaporisation regimes in a typical FCC unit Figure 2.1 Schematic of a suspended evaporating droplet 18 Figure 3.1 Droplet-particle collision mechanism 49 Figure 3.2 Validation of the four homogeneous model predictions with the vaporization data of water (Ranz & Marshall, 1952b) Conditions are: T d0 = 282 K T G = 298 K T B = 373.15 K d d0 = 1.1 mm Re d0 = (a) Vaporization data of hexane (Downingm, 1966) Conditions are: T d0 = 281 K T G = 437 K T B = 344.6 K d d0 = 1.76 mm Re d0 = 110 (b) Vaporization data of heptane (Nomura et al., 1996) Conditions are: T d0 = 298 K T B = 371.42 K T G = 741 K d d0 = 0.80 mm Re d0 = (c) Vaporisation data of decane (Wong & Lin, 1992) Conditions are: T d0 = 315 K T G = 1000 K T B = 447.1 K d d0 = mm Re d0 = 17 (d) 58 Figure 3.3 Comparison of transient change of decane droplet temperature predicted by homogeneous models and experimental data of Wong and Lin (1992) Conditions are: T d0 = 315 K T G = 1000 K T B = 447.1 K d d0 = mm Re d0 = 17 (a) Temporal change of volume averaged temperature T d versus surface temperature T ds of decane droplet predicted by FTC model Conditions are: T d0 = 315 K T G = 1000 K T B = 447.1 K d d0 = mm Re d0 = 17 (b) 59 Figure 3.4 Transient change of FCC feed droplet diameter predicted by four different homogeneous models - ITC, AS, FTC & ETC compared with the base case of Buchanan [Buc (1)] Conditions are: d d0 = 300 µm, d p = 65 µm, T d0 = 561 K, T B = 700 K, T G = T p = 922K (a) Conditions are: d d0 = 300 µm, d p = 65 µm, T d0 = 561 K, T B = 700 K, T G = T p = 922 K (b) 65 Figure 3.5 Transient change of FCC feed droplet diameter predicted by the four heterogeneous models – Buc (2), Buc (3), Nayak (phi = 14) and DPC Conditions are: d d0 = 50µm, d p = 65µm, T d0 = 561K, T B = 700K, T G = T p = 922K (a) Conditions are: d d0 = 50µm, d p = 65µm, T d0 = 561K, T B = 700K, T G = T p = 922K All the model predictions could be seen attaining the saturation temperature limit (b) 68 Figure 3.6 FCC feed droplet vaporization time predicted by the proposed DPC model with two different formulation of the droplet-particle contact time Conditions are: d = 50 µm, d p = 65µm, T d0 = 561K, T B = 700K, T G = T p = 922K Larger vaporization time is predicted when the contact time of droplet on particle surface decreases 71 Figure 3.7 Effect of advancing contact angle variation on FCC feed droplet vaporization time in the proposed DPC model Conditions are: d d0 = 50 µm, d p = 65 µm, T d0 = 561K, T B = 700K, T G = T p = 922K Vaporization time varies insignificantly when the advancing contact angle of the droplet on particle surface changes from 150o to 180o 73 Figure 4.1 Experimental setup (1) rotameter, (2) column, (3) inline heater, (4) temperature controller, (5) stainless-steel needle, (6) one-way control valve, (7) silicon tube, (8) syringe, (9) syringe pump, (10) droplet, (11) high speed camera, (12) transparent quartz windows, (13) back light, (14) computer, (15) pitot tube, (16) T-type thermocouple, (17) manometer, (18) data logger 84 Figure 4.2 Image analysing process - a) raw nozzle image b) raw nozzle-and-droplet image c) binary image d) logical image e) holes filled image f) nozzle-free-droplet binary-scale image viii g) droplet boundary and nozzle polynomial fitting curve h) polynomials fitting curve on left and right side of droplet boundary 89 Figure 4.3 Model predictions of temporal diameter and temperature validated against experimental data of a decane droplet reported by Daif et al (1999) Operating conditions of Case 1: d = 1.386 mm; T G = 348 K; T d0 = 317 K; Re d0 = 215 91 Figure 4.4 predictions of temporal droplet size and temperature validated against experimental data of a heptane-decane mixture droplet (75 % heptane and 25 % decane) reported by Daif et al (1999) Operating conditions of Case 2: d = 1.334 mm; T G = 348 K; T d0 = 293 K; Re d0 = 214 93 Figure 4.5 Model prediction in temporal change of evaporation rate (a) and mass fraction of species (b) of heptane-decane mixture droplet (75 % heptane and 25 % decane) Operating conditions of Case 2: d = 1.334 mm; T G = 348 K; T d0 = 293 K; Re d0 = 214 95 Figure 4.6 Predicted variation in droplet (75 % heptane and 25 % decane) diameter profile based on both ideal and non-ideal assumption, max standard deviation ~ 0.8×10-3 (a) Activity coefficient of each species in the liquid mixture (b) Operating conditions of Case 2: d = 1.334 mm; T G = 348 K; T d0 = 293 K; Re d0 = 214 96 Figure 4.7 Model prediction of temporal reduction of heptane-decane mixture droplet (20 % heptane and 80 % decane), validated against experimental data of Gökalp et al (1994) and modelling of Zhang and Kong (2010) Operating conditions of Case 3: d = 1.563 mm; T G = 372 K; T d0 = 295 K; Re d0 = 107 97 Figure 4.8 Temporal reduction in droplet size for hexane-decane droplets at different compositions (operating conditions of Case 3: d = 1.563 mm; T G = 372 K; T d0 = 295 K; Re d0 = 107) 98 Figure 4.9 Model prediction of temporal change of droplet size and temperature of waterglycerol mixture droplet (82.5 % water and 17.5 % glycerol), validated against experimental data of Davies et al (2012) Operating conditions of Case 4: d = 0.042 mm; T G = 298 K; T d0 = 298 K; Re d0 = 1.07 100 Figure 4.10 Comparison of model predicted droplet diameter reduction for pure water system with present experimental data (Error: 0.073 – 0.104 mm in 95% confidence interval) Inset plot shows high-speed visualizations of droplet size reduction Operating conditions of Case 5: d = 2.61 mm; T G = 353 K; T d0 = 310 K; Re d0 = 714 102 Figure 4.11 Model prediction for temporal droplet (70 % water and 30 % glycerol) diameter reduction validated against present experimental data (a); and predicted change in species mass fraction with time (b) (Error: 0.013 to 0.05 mm in 95% confidence interval); inset plot shows a complete evaporation Operating conditions of Case 6: d = 2.61 mm; T G = 353 K; T d0 = 317 K; Re d0 = 708 103 Figure 4.12 Temporal variation of evaporation rate for a) water species and b) glycerol species in the binary mixture droplet (70 % and 30 % glycerol) Operating conditions of Case 6: d = 2.61 mm; T G = 353 K; T d0 = 317 K; Re d0 = 708 105 Figure 4.13 Transient change in droplet diameter predicted using ideal and non-ideal assumptions A max standard deviation of 0.0023 mm (more visible in the inset) is the difference between these two assumptions (a), variation in activity coefficient of each species in the liquid mixture (b) Operating conditions of Case 6: d = 2.61 mm; T G = 353 K; T d0 = 317 K; Re d0 = 708 106 ix The mass flux through the liquid-vapour interface can be obtained from the heat flux via the heat of vaporization, LV m = q LV (F.7) Lubrication approximation (laminar flow and one dimension) is used for the liquid flow to achieve the mass flux, m , in Eq (F.7) One-dimensional incompressible quasi-stable NavierStokes equation is applied for the transverse fluid flow due to vaporisation in the microregion: −ν∇ 2u = − ∇p ρ (F.8) Non-slip boundary condition at liquid-solid interface and shear-free at the liquid-vapour interface are used to obtain the mass flux: m = − d  ∂p   δ  3ν L dx  ∂x  (F.9) The pressure term in Eq (F.9) is a second order ordinary differential equation (ODE) of the liquid filmδ(x), as shown in Eq (F.2) Therefore, the mass flux is a forth order ODE of the film thickness, which can be transformed into a system of four first order equations as follows: Appendix F 205 dδ =δ ' dx (F.10) d δ ' (1 + δ ' ) = dx σ 3/ pc (F.11) 3ν Q dp = − L3 dx LV δ (F.12) dQ = q dx (F.13) where Q is the integrated heat flux introduced for the transformation The ODEs system including four equations from Eq (F.10) to Eq (F.13) can be solved by Runge-Kutta method using Matlab R2015b to obtain the film thickness, curvature, pressure and heat flux changing along the integration domain The corresponding boundary conditions for the above four equations are given as below 1/3 δ bc   A =  ρ L (T / T − 1)   L V S B  (F.14) δ bc' = (F.15) pbc = A / δ bc3 (F.16) Qbc = (F.17) Contact angle (CA) is defined as the slope of the film along horizontal axis ( d δ / dx ) the thickness of which is inversely proportional to the attractive force Appendix F 206 F.3 Results and Discussion The present work investigates the heat transfer occurring in heat pipe using ammonia NH3 as a liquid Thermo-physical properties of liquid NH are taken from the study of Stephan and Busse (1992) Table F.1 Properties of liquid NH3 Parameter Value Unit Specific heat of vaporisation LV 1180 × 103 J/kg Density of saturated vapour ρV 9.0 Kg/m3 Density of liquid ρ L 600 Kg/m3 Surface tension σ 0.020 N/m kinematic viscosity of liquid 2.16×10-6 m2/s Hamaker constant 2×10-21 J Accommodation coefficient - Appendix F 207 0.3 delT=1K 0.005 delT=2K delT=4K delT=8K delT=15K 0.2 δ (µm) 0 0.05 0.1 0 0.1 0.2 0.3 x (µm) Figure F.3 Change in film thickness along the horizontal axis at different wall superheats Figure F.3 presents the film thickness increasing along the x-axis at different superheats from to 15 degree It is obvious that the higher superheat results in a smaller film thickness (visible in the inset), which is ~ nm at 15 K to ~ 10 nm at K superheat, while the thickness is larger at the end of the domain When the superheat is increased, the evaporation of the liquid film (in the micro-region) is stronger, therefore more liquid is provided to feed the evaporation which results in increasing in the curvature (see Figure F.4) The curvature at different superheats shown in Figure F.4 indicates a higher curvature for a higher superheat which is due to the larger amount of liquid delivered to feed the intensive evaporation near the adsorbed film as mentioned Appendix F 208 100 delT=1K delT=2K 80 Curvature (1/µm) delT=4K delT=8K 60 delT=15K 40 20 0 0.1 x (µm) 0.2 Figure F.4 Change in curvature along the horizontal axis at different wall superheats The local contact angle which is simply the slope of the film thickness along the xaxis is shown in Figure F.5 The apparent contact angle is which is defined as the contact angle at the end of the integration domain The apparent contact angle is found larger for a higher superheat of the wall due to the increase in curvature as discussed Figure F.5 shows that the contact angle only changes near the adsorbed film region (within approximately 100nm) and remains almost unchanged afterward In the present conditions, results does not change for a larger integration domain Therefore, evaluation of the apparent contact angle is independent of the integration domain selected for the micro-region Apparent contact angle increases from ~ 16o at K to ~ 43o at 15 K superheat under the operating conditions stated in Table F.1 Appendix F 209 50 Contact angle (deg) 40 30 20 Apparent contact angle 10 delT=1K delT=4K delT=15K delT=2K delT=8K 0 0.1 x (µm) 0.2 0.3 Figure F.5 Change in contact angle along the horizontal axis at different wall superheats 1.0E+09 8.0E+08 delT=1K q (W/m2) delT=2K delT=4K 6.0E+08 delT=8K delT=15K 4.0E+08 2.0E+08 0.0E+00 0.1 0.2 0.3 x (µm) Appendix F 210 Figure F.6 Change in heat flux along the horizontal axis at different wall superheats The heat, q , is computed using Eq (F.13) It is shown in Figure F.6 that q is greater at a higher temperature under super-heated conditions Near the beginning for the integration domain the heat flux is almost zero due to the strong adhesion forces near the adsorbed film The heat flux increases and reaches a maximum value before drops to zero at the end of the domain due to increasing in film thickness For a 0.3 µm length selected for micro-region domain, the total heat transferred per unit length is Q ~ 5.0 W/m at K superheat while it is Q ~ 37 W/m at 15 K superheat F.4 Conclusions A numerical approach using lubrication approximation accounting for capillary forces, van der Waals forces and coupling with heat transfer were applied in the microscopic threephase contact line to numerically obtain the macroscopic contact angle, which is practically found in bubble detachment from or droplet impingement on the heated wall Apparent contact angle obtained at different superheats of the highly wetting liquids increases with the increasing the superheat Heat transfer is found to reach a maximum value near the adsorbed film and reduce afterward Appendix F 211 Appendix G Supplementary results of Chapter This appendix provides the following results in addition to the section Results and Discussion of Chapter (1) A few demonstrations where standard deviations from three different datasets are used to plot error bars whilst, in Chapter 5, only average standard deviations were mentioned to focus on the main reported data (2) Additional data on temporal change in droplet volume and temperature of the water-glycerol system are presented as here to avoid repetition in chapter V Data for water 96 % - butanol % system was also shown here; concentration of butanol at % was found as the highest concentration that provided consistent experimental data (although it was reported that the solution is still well mixed at butanol concentration up to %) Lower concentrations were not presented as they gave insignificant difference compared with pure water G.1 Standard deviations used for error bars Standard deviation (SD) at any data point which was calculated from at least three different values of each data point The average standard deviations mentioned in most of the figures in Chapter were the arithmetic average of the SD of every data points Figure G.1, G.2 and G.3 demonstrate the error bars of the experimental data Appendix G 212 Figure G.1 Standard deviations from three different datasets are used to plot error bars for data of temporal reduction in equivalent diameter of the “gly00” droplet Operating conditions: T S = 343 K, d p = 10 mm, T a = 296 K, relative humidity RH = 50 % Appendix G 213 Figure G.2 Standard deviations from three different datasets are used to plot error bars for data of temporal reduction in contact angle of the “gly10” droplet Operating conditions: T S = 323 K, d p = 10 mm, T a = 300 K, relative humidity RH = 50 % Appendix G 214 Figure G.3 Standard deviations from three different datasets are used to plot error bars for data of temporal increase in temperature of the “IPA10” droplet Operating conditions: T S = 353 K, d p = 10 mm, T a = 300 K, relative humidity RH = ~ 50 % G.2 Additional results of water-glycerol, water-IPA and water-butanol droplets Effects of liquid mixture on the temporal reduction in droplet size (equivalent spherical diameter and droplet cap height) of glycerol-water droplet was shown in Figure G.4 (at surface temperature of 323 K) Pure water droplet has a sharp decrease in droplet size at the last stage of evaporation whilst higher glycerol concentration droplets show a plateau trend toward the end due to the very less volatility of glycerol component Appendix G 215 Figure G.4 Transient reduction of equivalent diameter and liquid cap height with time Mixture of purified water and glycerol with glycerol concentration from 0.0 to 35.0 % Average standard deviations ‘std.’ (in metre unit) that were calculated from three experimental sets are mentioned in brackets Operating conditions: T S = 323 K, d p = 10mm, T a = 296 K, relative humidity RH = 50 %; The evaporation behaviour of the more volatile system butanol-water droplet is shown in Figure G.5 The transition is supposed to take place nearly at the end of the droplet lifetime when the more volatile component water (occupying 96% in the mixture) completes its evaporation However, this stage was not captured due to the large uncertainties in the image analysis process (as explained in Section 5.1.2 of Chapter 5) Appendix G 216 Figure G.5 Transient reduction of equivalent diameter Mixture of 96 % purified water and 4% butanol Average standard deviations ‘std.’ that were calculated from three experimental sets are mentioned in brackets Operating conditions: d p = 10mm, T a = 296 K, relative humidity RH = 50 %; Figure G.6 shows the slope at 0.89 of contact angle with pinned wetted diameter, for solid temperatures from 323 - 353 K and IPA concentrations from – 15 % Temporal change in temperature of the droplet was plotted in Figure G.7 (with error bars) which also indicate a less than 10 s heating period A sharp reduction was observed after the heat-up and before the equilibrium stage which is thought due to the governance of heat loss due to evaporation compared with heat gain from the solid surface This phenomenon will be investigated in future research Appendix G 217 Figure G.6 Experimental relationship between the pinned spreading diameter and contact angle at solid temperatures from 323 - 353 K and IPA concentrations from – 15 % Operating conditions: d p = 10 mm, T a = 296 K, relative humidity RH = ~ 50 %; Appendix G 218 Figure G.7 Transient increase in droplet temperature Mixture of 96 % purified water and 4% butanol Average standard deviations ‘std.’ that were calculated from three experimental sets are mentioned in brackets Operating conditions: d p = 10mm, T a = 296 K, relative humidity RH = 50 %; Appendix G 219 ... 2.1 Vaporisation of droplets in multiphase (gas- solid fluidised bed) system 11 2.2 Vaporisation of a suspended droplet in heated flowing gas stream 18 2.3 Vaporisation of a droplet on a heated. .. review of previous studies on droplet vaporisation in gas- solid fluidised bed Next, selected studies on the vaporisation of both single and binary mixture droplets in a heated convective environment... have been conducted on homogeneous vaporization of droplets involving both mono and multi -component droplets especially in relation to the spray combustion in internal combustion engines and liquid