The growth of mycobacterium leprae on eagles medium enriched by the sonic extract of a saprophytic mycobacterium

Graduate Theses, Dissertations, and Problem Reports 2011 Study on Surface Tension and Evaporation Rate of Human Saliva, Saline, and Water Droplets Tian Zhang West Virginia University Follow this and additional works at: https://researchrepository.wvu.edu/etd Recommended Citation Zhang, Tian, "Study on Surface Tension and Evaporation Rate of Human Saliva, Saline, and Water Droplets" (2011) Graduate Theses, Dissertations, and Problem Reports 2271 https://researchrepository.wvu.edu/etd/2271 This Thesis is protected by copyright and/or related rights It has been brought to you by the The Research Repository @ WVU with permission from the rights-holder(s) You are free to use this Thesis in any way that is permitted by the copyright and related rights legislation that applies to your use For other uses you must obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/ or on the work itself This Thesis has been accepted for inclusion in WVU Graduate Theses, Dissertations, and Problem Reports collection by an authorized administrator of The Research Repository @ WVU For more information, please contact researchrepository@mail.wvu.edu Study on Surface Tension and Evaporation Rate of Human Saliva, Saline, and Water Droplets Tian Zhang Thesis submitted to the College of Engineering and Mineral Resources at West Virginia University In partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Ismail B Celik, Ph.D., Chair Alejandro Posada, Ph.D Hailin Li, Ph.D Jagannath Nanduri, Ph.D Mechanical and Aerospace Engineering Department Morgantown, West Virginia 2011 Keywords: saliva, droplet, surface, evaporation ABSTRACT Study on Surface Tension and Evaporation Rate of Human Saliva, Saline, and Water Droplets Tian Zhang Cough, sometimes shedding plenty of germs and virus, is the human body’s way of cleaning the breathing passages The virus and germs spread rapidly through ambient air among humans and may cause infection To reduce ultimately the infections caused by the germs and virus contained in human saliva droplets, it is necessary to understand the vaporization process of human saliva and its role on virus transmission Virus-laden droplets, shed by an infected person through coughing and sneezing, evaporate until becoming droplet nuclei which will remain airborne for a long time and can infect other people In other words, evaporation rate is an important factor affecting the transmission of virus and germ contained in human saliva Accordingly, the present research focuses the evaporation of human saliva droplets, the carriers of virus Experiments and numerical methods are utilized in this research to study surface tension and evaporation rate In order to determine which component influences the surface tension and evaporation rate of droplet, different solutions are evaluated Capillary tubes and a high performance camera are used for measuring the surface tension of these solutions Evaporation measurements were carried out by taking pictures of droplets hanging vertically from a thin needle or laying on a flat surface These images were later postprocessed using an in-house developed Matlab code to obtain the evaporation rate A more general evaporation equation was derived to determine numerically the evaporation rate of the different solutions and then used to analyze the evaporation process of multi-component droplets Eventually, the numerical results compare reasonably well with the experimental measurements These findings will help understand the role of temperature and relative humidity of ambient air in virus transmission Acknowledgements First and foremost, I would like to acknowledge and extend my most heartfelt gratitude to my advisor, Dr Ismail B Celik He encouraged me vitally from the start to the end and has given me opulently inestimable trust and advice, without which I could not complete my research I appreciate to Dr Alejandro Posada, who was guiding me most of the time, without any impatience I am grateful to my other committee members, Dr Jagannath Nanduri and Dr Hailin Li, for all their constant reminds and contributions I would like to broaden my appreciation to the other members of the CFD group of CEMR in WVU, for their help and inspiration in my life and study Specially thank John, who I never met but gave me persistent help through email I would also like to thank the help and support from my other friends, especially Lina in Civil Engineering Lab who gave me most useful tips of performing experiments Lastly, I would like to thank my parents, for their patience and efforts of raising me all the past 24 years, and their incessantly self-giving and categorical love iv Table of Contents Chapter 1: Introduction 1.1 Importance of droplets on the transmission of infectious diseases 1.2 Effect of droplet properties on evaporation 1.3 Literature review Chapter 2: Measurement of Surface Tension 2.1 Methodology 2.1.1Equipment 2.1.2 Liquids to be measured 2.2 Results and Discussion 23 Chapter 3: Measurement of Evaporation Rate 25 3.1 Experimental Set-up and Procedure 25 3.2 Image Analysis 27 Chapter 4: Mathematical Model of Evaporation 33 Mathematical Model 33 Chapter 5: Results and discussion 41 Chapter 6: Conclusions 54 References 56 Appendix I 60 Appendix II 61 Appendix III 64 v List of Tables Table Equipments used in the measurement Table 2 Measured mass of water and NaCl for three concentrations of NaCl water solutions Table Measured data of mass of water and glucose for two concentrations of glucose water solutions 10 Table Measured data of mass of water and milk of the two concentrations of milk water solutions 10 Table Measured mass data of three concentrations of NaCl solutions with fixed volume 2mL 11 Table Results of densities of NaCl solutions of the three methods 13 Table Measured mass and calculated density of human saliva 13 Table Mass concentration of inorganic components of human saliva 14 Table Mole number in 1mL and density information of salts in human saliva 15 Table 10 Major components of proteins in human saliva 16 Table 11 Substances used in the calculation of density of mL human saliva 16 Table 12 The measurement data and calculation of density of solid part of human saliva 19 Table 13 Calculation of density of human saliva 20 Table 14 Difference of human saliva density of the two methods 20 Table 15 Results of surface tension of each kind of liquid 23 Table Composition of human saliva in the mathematical solution…………………………40 Table Comparison of numerical results: Matlab vs experiments 47 Table Evaporation rate of human saliva droplet: experiment vs numerical results 48 Table Evaporation rate of other kinds droplets: experiment vs numerical results 48 Table The concentration of components of artificial human saliva…………………………55 vi List of Figure Figure Surface Tension Measurement: Red Tube I.D = 1.12mm, O.D = 1.47mm Figure 2 Surface Tension Measurement: Yellow Tube I.D = 0.96mm, O.D = 1.38mm Figure Density changing with concentration of NaCl 12 Figure Samples of the human saliva solid part on glasses 18 Figure The sample of image analysis of surface area of the solid part 19 Figure Height of the liquid level system 21 Figure Contact angle by Matlab: (a) Actual photo of the boundary, (b) Maniscus boundary obtained from Matlab 22 Figure Surface tension of each liquid 24 Figure Scales on microinjector 26 Figure Photo studio used in the experiment of evaporation rate 27 Figure 3 Pictures of droplet on the needle: (a) Photo of droplet on the needle, (b) Binary photo obtained from program 28 Figure Pictures of droplet on the surface: (a) Photo of droplet on the needle, (b) Binary photo obtained from program 28 Figure The experimental result of evaporation rate distilled water droplet: Surface area vs Time 29 Figure Experimental results: saline water and human saliva droplets evaporation: Surface area vs Time 30 Figure The experimental result of evaporation of NaCl water solution droplets: Surface area [mm2] vs Time [s] 31 Figure The experimental result of evaporation of human saliva droplets: Surface area [mm2] vs Time [s] 31 Figure Experimental results of semi-sphere Human saliva Droplets evaporation under different environmental temperature and relative humidity: Surface area [mm2] vs Time [s] 32 Figure Water droplet evaporation: Surface area vs Time 41 Figure 0.3% NaCl water droplet evaporation: Surface area [mm2] vs Time [s} 42 Figure Results of Evaporation of different droplets under various environmental temperatures: Surface area [mm2] vs Time [s] 44 vii Figure The evaporation results of human saliva droplets at different temperature and relative humidity; Surface area [mm2] vs Time [s] 45 Figure 5 Evaporation of human saliva droplets under different environmental temperature, similar relative humidity 46 Figure Evaporation of coffee and 0.9% NaCl water solution droplet: Temp=22°C, RH=33% 47 Figure Numerical results of human saliva droplets under different temperature, same relative humidity 49 Figure Numerical results of human saliva droplets under different relative humidity, same temperature 50 Figure Numerical results of evaporation of different droplets 51 Figure 10 Numerical solution of evaporation of artificial human saliva evaporation vs Human saliva 52 Figure 11 Human saliva droplet evaporation: temperature [˚C] vs time [s] 52 viii Nomenclature A surface area cp specific heat at constant pressure Dv diffusivity of water vapor in air D0 Initial Diameter d droplet diameter e pressure esat saturation vapor pressure over a pure, flat water surface ev partial vapor pressure ev,0 initial vapor pressure of jet ev,∞ vapor pressure of the ambient g acceleration due to gravity h height of the liquids in a capillary tube ka' modified thermal conductivity of air Lv latent heat of vaporization of water M molecular weight Ms molecular weight of solute mN mass of the solid components ms mass of solute R universal gas constant Rer RH Reynolds number based on the relative speed between the droplet and the carrier gas relative humidity r droplet radius rN diameter of the nuclei after evaporation Sc Schmidt number Sh Sherwood number T instantaneous droplet temperature T∞ ambient air temperature Td droplet temperature t droplet evaporation time ix Chapter 6: Conclusions The surface tension and evaporation rate of different droplets has been measured and analyzed in this study Employing Matlab techniques and software, the surface tension and evaporation rate of different kinds of droplet have been calculated or simulated It can be calculated that for water, if the temperature increases 20˚C, the surface tension of water will decrease 4.33% When the salt concentration increases, the surface tension of the water solution will increase; contrarily, when the glucose concentration increases, the surface tension of the water solution will decrease Furthermore, salt decreases the evaporation rate of water droplet It is reasonable that the intermolecular forces of atoms and molecules may repel or attract all elements In the case of a soluble salt when dissolved into water it forms hydrogen bonds with the water through the dipole ends of the water molecule and the salt These bonds make it necessary to apply more kinetic energy to create enough movement to break the bonds and the attraction between water molecules to change of state, in this case liquid to gas If the temperature increases, the evaporation rate will be faster, and if the relative humidity increases, the evaporation rate will be slower, which can be concluded that when the temperature increases, the kinetic energy of the molecules of water will increase, and when the relative humidity increases, the concentration of water vapor in the ambient environment will increase which can restrain the water molecules evaporate Under various temperature and constant relative humidity, the evaporation rate varies When the temperature is increasing, the evaporation rate will increase, and contrarily, the evaporation rate will decrease On the other hand, under constant temperature and various relative humidity, the 54 evaporation rate also varies When the relative humidity of the ambient environment is increasing, the evaporation rate will decrease, and when it is decreasing, the evaporation rate will increase When the salinity increases, the evaporation rate will decrease, that is to say the pure water droplet has the largest evaporation rate among these kinds of droplets: 0.3% NaCl water solution droplet, 0.6% NaCl water solution droplet, 0.9% NaCl water solution, 1.2% NaCl water solution droplet, and 1.2% NaCl water solution droplet has the slowest evaporation rate In order to make artificial human saliva, numerical solution is used and environmental conditions are: temperature=23˚C; relative humidity=38% The components of the artificial human saliva are shown in Table 6.1 It has the same evaporation time as human saliva droplet Table The concentration of components of artificial human saliva Concentration [mg/mL] Salt Protein 30 Carbohydrate 35 Lipid DNA 55 References (CDC), C.f.D.C.a.P., 2009 CDC-Key Facts About Avian Influenza (Bird Flu) and Avian Influenza A (H5N1) Virus [Online] Available at: http://www.cdc.gov/flu/avian/gen- info/facts.htm [Accessed 17 Nov 2010] Andreas, E.L., 2005 Hndbook of Physical Constants and FUnctions for Use in Atmospheric Boundary Layer Studies ENGINEER RESEARCH AND DEVELOPMENT CENTER HANOVER NH COLD REGIONS RESEARCH AND ENGINEERING LAB Batchelor, G.K., 2000 An Introduction to Fluid Dynamics Cambridge University Press Boretti, A., 2010 Comparative Emissions from Diesel and Biodiesel Fueled Buses from 2002 to 2008 Model Years SAE International, 1683(01) Bull, H.B., 1941 Osmotic pressure of egg albumin solutions 137, pp.143-51 CDC, 2010 H1N1 Flu | Interim Guidance on Infection Control Measures for 2009 H1N1 Influenza in Healthcare Settings, Including Protection of Healthcare Personnel [Online] Available at: http://www.cdc.gov/h1n1flu/guidelines_infection_control.htm [Accessed 17 Nov 2010] Chiappin, S., Antonelli, G., Gatti, R & Palo, E.F.D., 2007 Saliva specimen: A new laboratory tool for diagnostic and basic investigation 383(1-2), pp.30-40 Clark, N et al., 2010 Improvements of Vehicle Fuel Economy Using Mechanical Regenerative Braking SAE International, 1967(01) Crowe, C.T., Sommerfeld, M & Tsuji, Y., 1997 Multiphase flows with droplets and particles CRC Press Duguid, J.P., 1946 The size and duration of air-carriage of respiratory droplets and droplet nuclei 44(6), pp.471-79 56 Efunda, 2011 Properties of Distilled Water [Online] Available at: http://www.efunda.com/materials/common_matl/show_liquid.cfm?matlname=waterdistilled4c [Accessed 2011] EngineeringToolBox, n.d Sodium Chloride - Water [Online] Available at: http://www.engineeringtoolbox.com/sodium-chloride-water-d_1187.html [Accessed 17 Nov 2010] Esser, A.F., Bartholomew, R.M., Jensen, F.C & Muller-Eberhard, H.J., 1979 Disassembly of viral membranes by complement independent of channel formation Proc Natl Acad Sci USA, 76(11), pp.5843-47 Fuks, N.A., 1959 Evaporation and droplet growth in gaseous media London: Pergamon Press Gururaja, T.L & Levine, M.J., 1996 Solid-phase synthesis and characterization of human salivary statherin: a tyrosine-rich phosphoprotein inhibitor of calcium phosphate precipitation 9(6), pp.283-89 Hegde, R., Mastrianni, J & Scott, M., 2010 A transmembrane form of the prion protein in neurodegenerative disease Science, 279(5352), pp.827-34 Hinds, W.C., 1999 Aerosol technology: properties, behavior, and measurement of airborne particles Wiley-Interscience Jones, A.N., 2002 Density of Milk [Online] Available at: http://hypertextbook.com/facts/2002/AliciaNoelleJones.shtml [Accessed 17 Nov 2010] Lindfore, K.R., 1924 Surface Tension of Sugar Factory Products 16(8) Makkar, H.P.S., Siddhuraju, P & Becker, K., 2007 Plant Secondary Metabolites Methods in Molecular Biology Moyle, A.M., Smidansky, P.M & Lamb, D., 2006 Laboratory studies of water droplet evaporation kinetics In 12th Conference on Cloud Physics Madison, 2006 American Meteorological Society 57 Muson, B.R., Young, D.F & Okiishi, T.H., 1994 Fundamentals of Fluid Mechanics John Wiley & Sons, Inc Nicas, M., Nazaroff, W & A, H., 2005 Toward understanding the risk of secondary airborne infection: emission of respirable pathogens Journal of Occupational and Environmental Hygiene, 2, pp.143-54 [Accessed March 2011] NOAA, 2010 Water Density Calculator [Online] Available at: http://www.csgnetwork.com/h2odenscalc.html [Accessed 17 Nov 2010] Pierre, P., 1998 A to Z of Thermodynamics Oxford University Press Pruppacher, H.R & Klett, J.D., 1978 Microphysics of Clouds and Precipitations London: D Reidel Publishing Company Racaniello, V., 2009 Influenza virus transmission [Online] Available at: http://www.virology.ws/2009/04/29/influenza-virus-transmission/ [Accessed 27 Feb 2011] Ranz, W.E & Marchall, W.R., 1952a Evaporation From Drops Part 48(3), pp.141-46 Ranz, W.E & Marshall, W.R., 1952b Evaporation from drops part Chemical Engineering Progress, 48(4), pp.173-80 Redmond, N.E., 2007 MET4 and MET4A Calculation of Dew Point Paroscientific, Inc Redrow, J.B., 2009 An investigation into the theoretical and analytical basis for the spread of airborne influenza Morgantown: West Virginia University Roberts, R.C., Makey, D.G & Seal, U.S., 1966 Human Transferrin MOLECULAR WEIGHT AND SEDIMENTATION PROPERTIES The Journal of Biological Chemistry, 24, pp.4907-13 Roger, R.R & Yau, M.K., 1989 A Short Course in Cloud Physics Butterworth-Heinemann Ro, P.S., Hahlen, T.S & Bryant, H.C., 1968 Precision Measurements of Water Droplet Evaporation Rates 7(5) Rxlist, 2008 nystop (nystatin topical) drug [Online] Available at: http://www.rxlist.com/nystopdrug.htm [Accessed 17 Nov 2010] 58 Schipper, R.G., Silletti, E & Vingerhoeds, M.H., 2007 Saliva as research material: Biochemical, physicochemical and practical aspects 52(12) SImetric, 2010 Summary: Mass, Weight, Density or Specific Gravity of water at various temperatures C and thermal coefficient of expansion of water [Online] Available at: http://www.simetric.co.uk/si_water.htm [Accessed 2010] Smolik, J., Dzumbova, L., Schwarz, J & Kulmala, M., 2001 Evaporation of ventilated water droplet: connection between heat and mass transfer Aerosol Science, 32, pp.739-48 Spicer, S.S & Martinez, J.R., 1984 Mucin Biosynthesis and Secretion in the Respiratory Tract Env Health Perspectives, 55, pp.193-204 Tartakoff, A.M., 1982 The Role of Subcompartments of the Golgi Complex in Protein Intracellular Transport 300(1099), pp.173-84 Trefethen, L., 1969 Film Notes for Surface Tension in Fluid Mechanics Tufts University WBC, 2010 Amylase, Alpha [Online] Available at: http://www.worthington- biochem.com/aa/default.html [Accessed 17 Nov 2010] Weast, R.C., 1990 CRC handbook of chemistry and physics 70th ed Boca Raton: CRC Press Weber, T & Stilianakis, N., 2008 Inactivation of influenza A viruses in the environment and modes of transmission: a critical review J Infect, 57(5), pp.361-73 Weissenborn, P.K., 2006 Surface Tension of Aqueous Electrolytes Encyclopedia of Surface and Colloid Science 59 Appendix I This appendix shows the calculation of how long the tap water takes to obtain the same temperature with the environment The initial temperature is not a factor that can influence the result The solution is contained in a beaker and the shape of water can be considered as a cylinder, which has a volume of 1105 m3 ; the height and the diameter of the section of the cylinder are 0.08m There is no obvious convection factor Characteristic Length: Lc  Biot number: Bi  V 1 105 m3   2.5  104 m As   0.08m 2   0.08  103    hLc 15W m2 K  2.5 104   6.45 103  0.1 0.58W mK K Lumped system analysis is valid to solve this problem: b hAs 15  0.041   0.0146s 1 Vc p 1000 105  4200 0.00001  e  bt  e 0.0146 t t  13.14min 60 Appendix II // clear all;close all;clc fns = dir('*.jpg'); fnames = char(fns.name); fdates = datevec(char(fns.date)); [j,k]=size(fnames); ini_crop=[1150 1880 180 410]; vol(j)=0.4664; %Needle Volume for i=1:j I=imread(fnames(i,:)); I2=imrotate(I,90); I3=imcrop(I2,ini_crop); %BW = im2bw(I3,0.5);%graythresh(I3+10)); %to be fixed BW=(1-bwmorph((1-im2bw(I3,0.56)),'clean')); % 'bwmorph, clean'removes isolated pixels BW3=double(BW); box = regionprops(BW3,'BoundingBox','centroid'); if i == xw1 = box.BoundingBox(3); yw1 = box.BoundingBox(4); end ctr_x = box.Centroid(1); ctr_y = box.Centroid(2); % I4=imcrop(I3,[ctr_x-xw1/2-15 ctr_y-yw1/2+120 xw1+60 yw1-150]); I5=imresize(I3,1.2); %to be fixed imshow(I5) [m,n] = size(BW3); verlin_x(1:m) = ctr_x; verlin_y = 1:m; BWT_1=1-BW3;% inverse: turns 1-0, 0-1 BWT_1=BWT_1(:,1:round(size(BW3,2)/2)+20); % Cut the shadow in the right part % r_t=round(size(BW3,1)/2)-2:round(size(BW3,1)/2)+2; % the row of the water center (5 length) % c_t=[round(size(BW3,2)/2)-20 round(size(BW3,2)/2)-20 round(size(BW3,2)/2)-20 round(size(BW3,2)/2)-20 round(size(BW3,2)/2)-20]; % the col of the water center (approximately) c_t=1:size(BWT_1,2); % the column of the water center (approximately) r_t=round(size(BW3,1)/2)*ones(size(c_t)); % the row of the water center (5 length) BWT_2=bwselect(BWT_1,c_t,r_t); % select the main body of the water [r_t c_t]=find(BWT_2==1); % select the coordinates of water r_t_max=max(r_t); % find the lowest point's row number i_t=find(r_t==r_t_max); % find the index of that point 61 i_t=i_t(ceil(length(i_t)/2)); % in case there are more than point, select the middle one ctr_x=c_t(i_t); % then find the column number of that point SBW = BW3(:,1:round(ctr_x)); [m,q]=size(SBW); n=ctr_x; SBW1 = edge(SBW,'canny'); for ii = 1:m ind = find(SBW1(ii,:),1,'first'); if (isempty(ind)); ind = n; end; zero_pix(ii) = ind; end zero_pix2 = n - zero_pix+15; pixlen = 0.406/81; %pixlen = 0.28702/47.13; Blue needle drop_y = [1:length(zero_pix2)]*pixlen; drop_r = zero_pix2*pixlen; ppx = polyfit(drop_y,drop_r,6); fy = @(y) pi.*(ppx(1)*y.^6+ ppx(2)*y.^5+ppx(3)*y.^4+ppx(4)*y.^3+ppx(5)*y.^2+ppx(6)*y.^1+ppx(7)*y.^0); miny=min(drop_y); maxy=max(drop_y); sur(i)= quad(fy,miny,maxy);%just droplet without nylon thread et(i)=etime(fdates(i,:),fdates(1,:)); timtxt = num2str(et(i)); ttlstr = strcat('Time: ',timtxt,' s'); text(10,20,ttlstr,'FontSize',12,'Color','k'); surtxt = num2str(sur(i),'%1.2f'); ttlsur = strcat('Surface Area: ',surtxt,' mm^2'); text(10,40,ttlsur,'FontSize',12,'Color','k'); if i==1; evap_rate(1)=0; else evap_rate(i)=(sur(i)-sur(i-1))/(et(i)-et(i-1)); end; evaptxt = num2str(evap_rate(i),'%1.4f'); ttlevap=strcat('Evap.rate: ',evaptxt,' mm^2/s'); text(10,65,ttlevap,'FontSize',12,'Color','k'); F(i) = getframe; end movie2avi(F,'example.avi','compression','None','quality',100,'fps',2); for i=2:j lambda_e(i-1) = (sur(i)-sur(i-1))*1e-6/(et(i)-et(i-1))/pi lambda_e_mean = mean(lambda_e) end % evaporation of a pure water droplet 62 Dv = 2.4*10^-5;% water diffusivity m2/sec M = 18.02;% molecular weight of water R = 8.314;%universal gas constant den=998.2;%water density kg/m3 RH=0.33; % Relative humidity of the environment Pd=2.744;% droplet pressure Pi=RH*Pd;%pressure of the environment T=273.15+23; % Temperature 22 celsius %vol_0=vol(1)*1E-9;% in m^3 %d_0=(6*vol_0/pi)^(1/3);% in meters lamda=4*Dv*M*(Pd-Pi)/(R*den*T);%evaporation constant %t_evap=d_0^2/lamda;%lifetime or evaporation time sur_0 = sur(1)*1e-6; t_evap=sur_0/lamda/pi; %n = length(sur); t = 0:t_evap; sur_t = sur_0 - pi*lamda*t; d_0 = (sur_0/pi)^0.5; figure(1) title('Semi-sphere Droplet evaporation'); %plot(et/t_evap,(sur-sur(54))/(sur(1)-sur(54)),'^b',t/t_evap,sur_t/sur_0,'r') % plot(et/t_evap,(sur-sur(29))/(sur(1)-sur(29)),'^b',t/t_evap,sur_t/sur_0,'r') plot(et/t_evap,((sur-0.01)/(sur(1)-0.01)),'^b',t/t_evap,sur_t/sur_0,'r') legend('Experiment of Distilled Water','Numerical Solution for pure water'); xlabel('Time / Analytical Pure Water Evaporation Time') ylabel('Droplet Surface Area / Initial Droplet Surface Area') grid on ylim([0 1]) figure(2) plot(et,sur,'^b',t,sur_t/(1e-6),'r') legend('Experiment of Distilled Water','Numerical Solution for pure water'); xlabel('Time[s]') ylabel('Surface Area [mm^2]') // 63 Appendix III // clear all clc T_d=273.15+23; % droplet temperature [K] T_inf=T_d; % Ambient Temperature [K] % T = 273.15+50; T_0 = 273.15; %reference temperature TC = T_inf-T_0; % Ambient Temperature [C] T_dC=T_inf-T_0; P=1013.25; %reference pressure [hpa] P_a=1013.25; R=8.314472; %J/K mol RH = 0.38; d = (1)*1e-3; %m r=d/2; vol=(1*pi*r^3)/6; vol_semi = vol; %Calculate Sherwood Number V=0; %wind velocity den_air = 1.1839; % [m3/kg] @25C rho_a = den_air; miu_air = 18.3*1e-6; %[kg/m.s]@25C %Constituents in droplet kg/m^3 salt=9.00; % If this is the water, it should be 0, pro=19.9; lip=18.1; carb=12.3; dna=0.820; % % % % % % % % % % salt=9.00; % If this is the water, it should be 0, pro=30; lip=0; carb=35; dna=0; salt=0.001; % If this is the water, it should be 0, pro=0; lip=0; carb=0; dna=0; m_pro=pro*vol; m_lip=lip*vol; m_carb=carb*vol; 64 m_dna=dna*vol; m_salt=salt*vol; % Density of water rho_w=999.842594 + 6.793952e-2*TC - 9.095290e-3*TC^2 + 1.001685e-4*TC^3 - 1.120083e-6*TC^4 + 6.536332e-9*TC^5; m_w = rho_w * vol; % droplet total mass m_tot=m_pro+m_lip+m_carb+m_dna+m_salt+m_w; % mass fractions x_pro=m_pro/m_tot; x_lip=m_lip/m_tot; x_carb=m_carb/m_tot; x_dna=m_dna/m_tot; x_salt=m_salt/m_tot; x_water=m_w/m_tot; %densities of each component [kg/m3] rho_salt=2160; rho_pro=1362; rho_lip=1100; rho_carb=1562; rho_dna=1650; %Molecular weight of each component M_w=18.02; M_s=58.4; M_a=29; M_pro=66500; M_lip=255; M_carb=180.16; M_dna=700; D_v_original=2.11e-5*(T_d/T_0)^1.94*(P/P_a); D_v=D_v_original/((r/(r+(5e8))+(D_v_original/(r*0.0020))*((2*pi*M_w)/(1000*R*T_d))^0.5)); %D_v = 2.04e-5; % specific heat of dry air, const press, T_inf = -40 to 40 C for press near 1atm c_p_d=1005.60 + 0.017211*T_dC + 0.000392*T_dC^2; % thermal conductivity of air (W/mC) k_a_O=2.411e-2*(1 + 3.309e-3*T_dC - 1.441e-6*T_dC^2); % sherwood number Sh = 2+0.6*(miu_air/den_air/D_v)^(1/3)*(d*V*den_air/miu_air)^0.5; % saturation vapor pressure e_sat=6.1121*(1.0007+(3.46e-6)*P)*exp((17.502*T_dC)/(240.97+T_dC)); % total density of droplet rho_s=(x_pro/rho_pro+x_lip/rho_lip+x_salt/rho_salt+x_dna/rho_dna+ 65 x_carb/rho_carb+x_water/rho_w)^(-1); % mass of water in the droplet m_w=rho_w*(vol-(m_salt/rho_salt+m_pro/rho_pro+m_lip/rho_lip+ m_dna/rho_dna+m_carb/rho_carb)); delta=T_d/T_inf-1; % volume of solid part vol_sol=((m_salt/rho_salt + m_pro/rho_pro + m_lip/rho_lip + m_dna/rho_dna + m_carb/rho_carb)); % the radius of the solid part r_sol=(6*vol_sol/pi)^(1/3); %% Latent heat L_v=(25.00-0.02274*TC)*10^5; % Surface tension of water sig_w=0.2358*((374.00-TC)/647.15)^1.256*(1-0.625*((374.00-TC)/647.15)); % Surface tension sig_s=sig_w*0.01; % the number of ions into which a salt molecule dissociates nu_ion = 2; mf_salt = m_salt/m_w; mf_carb = m_carb/m_w;%m_carb/(m_tot-m_w); mf_pro = m_pro /m_w;%m_pro/(m_tot-m_w); rho_sol=(m_pro+m_lip+m_carb+m_dna+m_salt)/vol_sol; %% molalities (of binary solution) molal_s=(m_salt/M_s)*1000/m_w; molal_c=(m_carb/M_carb)*1000/m_w; molal_p=(m_pro/M_pro)*1000/m_w; % practical osmotic coefficients phi_s=0.0055*molal_s^2+0.028*molal_s+0.9128; % high concentration limiting condition if phi_s > 1.5 phi_s=1.5; end phi_c=0.0233*molal_c+1; % high concentration limiting condition if phi_c > 1.2 phi_c=1.2; end phi_p=22.0357*2099560^molal_p-21.718; % efflorescence conditions (for BSA protein) if RH