Droplet Reaction and Evaporation of Agents Model (DREAM)

Transcription

1 Droplet Reaction and Evaporation of Agents Model (DREAM) Applied to HD on glass, DEM on glass and MS on glass A.R.T. Hin - TNO, The Netherlands (visiting scientist at AFRL) 26 October 2005

2 Outline Introduction Model Sessile drop model Data Dutch wind tunnel (HD, DEM and MS on Glass) Czech wind tunnel (HD on Glass) ECBC wind tunnel (HD on Glass) Fitting the model to the data

3 4 Transport rates F 1 Droplet F 2 F 3 Absorbed liquid F 4 Substrate

4 Develop in steps Droplet F 1 F 3 F 2 HD on Glass MS on Glass DEM on Glass Sessile Drop Absorbed liquid F 4 Absorbed Drop Substrate Neat Agent Drops spread fast (seconds) Drops absorb fast (minutes) Thickened Agent Drops spread slow (ten minutes) Drops absorb slow (hours) Add reactivity when significant chemical reactions are found

5 Turbulent layer Sessile drop (F1) Drop mass over time T m(t) = m(0) 0 (t) d t Fick s law d m(t) / d t = D A(t) (C skin -C bulk ) / L m& L Transition layer Laminar layer drop Raoult s law (ideal mixtures) P agent in mixture = Mol fraction agent in drop x P pure agent C agent = P agent Mol weight agent / (RT) Reactivity (implemented but not yet tested) d[x]/d[t] = A e e (-E/RT) [X] x [Y] y

6 Diffusivity, D in air How mobile are the molecules in air? Depends on temperature, pressure, molecular mass, molecular volume, and air properties Two estimation methods found Fuller,Schettler,Giddings method (Lyman et al. 1982) All above dependencies Not suitable for phosphor components: no molecular volume data Simple method (Danish EPA) Eliminates molecular volume dependence

7 Diffusivity Data and Estimations Difusivity - cm2/s Diffusivity data at 1 atm for DEM, MS, HD MS MS,2) MS,3) MS,4) DEM,2) DEM,3) DEM,4) HD HD,2) HD,3) HD,4) Temperature - C

8 Vapor Concentration at skin, C skin Get vapor concentration from vapor pressure Get volatility using ideal gas law: C = P Mw / (R T) Antoine equation Depends on Agent from data (if available) or estimation methods P = *10 a-b/(t+c) Clausius-Clapperon Ideal gas Temperature Antoine equation (used for model) three constants a,b,c fitted to data

9 Vapor Pressures DEM Vapor Pressure - Pa [1] [2] [3] [4] [4] [10] [11] Temperature - C

10 Vapor Pressures MS Vapor Pressure - Pa [1] [2] [3] [5] [6] [10] [11] Temperature - C

11 Vapor Pressures HD Vapor Pressure - Pa [7] 100 [8] [9] 10 [10] Temperature - C

12 Diffusion layer thickness, L Depends on wind speed temperature (viscosity air) pressure on turbulence drop size L Turbulent layer Transition layer Laminar layer drop Empirical in semi-empirical model Constant diffusion layer thickness for an experiment ~ laminar layer thickness order of magnitude: 1 millimeter Fitted to data

13 Wind speed vs Height 3 u*'s to be used for comparative testing and matrix, giving 3 wind speed vs height -curves turbulent layer speed (m/s) transition layer 2 laminar layer height (m)

14 Area of evaporation, A(t) Volume from initial drop mass Liquid density a function of agent and of drop temperature Shape over time From observed shape and time behavior of sessile drops: One shape (spherical cap), but two modes needed Constant base area mode Constant contact angle mode

15 Densities of HD, DEM, MS 1.35 HD,0) HD,1) 1.3 HD,2) MS,0) HD,3) MS,1) 1.25 MS,2) DEM,0) Denisity - g/ml DEM,1) DEM,2) Temperature - C

16 Area of evaporation over time evaporating surface area [ mm2 ] Sessile drop - constant angle Sessile drop - constant base area Sessile drop - base switches to angle Drop weight initial drop mg agent HD Drop-Surface L Initial contact angle 35 degree Minimum Contact Angle 10 degree Drop-Air temperature 30 C diffusion layer 0.5 mm Air pressure 1 atm CAP, Constant Angle CAP, Constant Base 0:00 6:00 12:00 18:00 time [ h:mm ]

17 Volume of drop over time Sessile drop - constant angle Sessile drop - constant base area Sessile drop - base switches to angle liquid volume [ µl ] Drop weight initial drop mg agent HD Drop-Surface L Initial contact angle 35 degree Minimum Contact Angle 10 degree Drop-Air temperature 30 C diffusion layer 0.5 mm Air pressure 1 atm 0:00 6:00 12:00 18:00 time [ h:mm ]

18 DATA Czech data 30 mass over time curves HD on Glass Dutch data (neat and thick) 42 mass over time curves DEM on Glass 46 mass over time curves MS on Glass 11 mass over time curves HD on Glass ECBC data 5 mass over time curves HD on Glass Much more data on the way UK, Czech, Dutch and ECBC Establish proper tunnels performance Compare effects tunnel size (and turbulence intensity)

19 Dutch DEM data, 42 curves Mass [fraction] DEM on Glass - uncorrected - Neat & Thick ~ Celsius, ~ m/s Time [Hours]

20 Dutch MS data, 46 curves Mass [fraction] MS on Glass - uncorrected - Neat & Thick ~ Celsius, ~ m/s Time [Hours]

21 Dutch HD data, 11 curves Mass [fraction] HD on Glass - Uncorrected - Neat & Thick ~ Celsius, ~ m/s Time [Hours]

22 Fitting the model to the data used empirical fit functions for contact angles and effective average diffusion layer thickness Initial angle Minimum angle Effective average diffusion layer thickness assumed to depend on temperature relative humidity assumed to depend on wind speed drop size

23 MS fit functions Angle - Degrees %Rh, Initial angle 60%Rh, Initial angle 69%Rh, Initial angle 48%Rh, Minimum angle 60%Rh, Minimum angle 69%Rh, Minimum angle Layer Thickness - mm µl drop size 6 µl drop size 9 µl drop size Temperature - oc Wind speed at 2 cm - m/s Temperature Exponential Relative Humidity Exponential Wind Speed Inverse with offset Drop Size Exponential

24 volume - [ - µl [ µl ] ] ] MS data fitted to model Experiment compared with Single Sessile Drop models fx ,n,10.2 C,2.15m/s volume agent model 0.9 volume drop model d(agent)/dt model d(agent)/dt experiment :00 1:12 2:24 3:36 4:48 6:00 7:122 0:00 1:12 2:24 2:24 4:48 3:36 7:12 4:48 9:36 6:00 12:00 7: :00 2:24 1:12 4:48 4:482:24 7:12 7:12 9:36 3:36 9:3612:00 4:48 12:00 14:24 6:00 14:24 16:48 19:12 16:48 7:12 0 time - [ hh:mm ] evaporation rate rate - [ - µl [ µl / h / h ] ]

25 1.5 MS on Glass Over / Under model over/under prediction predicts times (by a of factor time of X) by model % over / under prediction of time % 100% 66% % 90% 80% fx ,n,10.2 C,2.15m/s fx ,n,1 C,2.15m/s fx ,n,10.2 C,1.44m/s fx ,n,10.4 C,1.44m/s fx ,n,10.9 C,0.77m/s fx ,n,10.6 C,0.77m/s ex ,n,19.5 C,2.08m/s ex ,n,20.7 C,2.08m/s ex ,n,20.2 C,1.44m/s ex ,n,21.4 C,1.44m/s ex ,n,19.7 C,0.72m/s ex ,n,20.2 C,0.72m/s fx ,n,29.0 C,2.13m/s fx ,n,31.3 C,2.13m/s fx20108b-1,n,29.0 C,2.04m/s fx20108b-2,n,31.1 C,2.04m/s ex ,n,30.2 C,1.36m/s ex ,n,29.9 C,1.36m/s ex ,n,29.9 C,0.71m/s ex ,n,29.9 C,0.71m/s fx ,t,10.1 C,2.19m/s fx ,t,9.9 C,2.19m/s fx ,t,10.6 C,1.42m/s fx ,t,10.4 C,1.42m/s fx ,t,11.0 C,0.78m/s fx ,t,10.5 C,0.78m/s ex16038b-1,t,19.5 C,2.03m/s ex16038b-2,t,20.7 C,2.03m/s ex24038b-1,t,20.2 C,1.44m/s ex24038b-2,t,21.4 C,1.44m/s ex ,t,20.1 C,0.71m/s ex ,t,20.5 C,0.71m/s fx23108b-1,t,29.2 C,2.04m/s fx23108b-2,t,31.3 C,2.04m/s fx ,t,29.2 C,2.05m/s fx ,t,31.2 C,2.05m/s fx ,t,31.8 C,1.35m/s fx ,t,32.7 C,1.35m/s fx ,t,31.1 C,1.43m/s fx ,t,32.1 C,1.43m/s fx ,t,30.9 C,1.42m/s fx ,t,31.8 C,1.42m/s ex ,t,31.8 C,0.74m/s ex ,t,31.2 C,0.74m/s ex ,t,29.6 C,0.71m/s ex ,t,29.8 C,0.71m/s 70% 60% 50% mass fraction 40% 30% 20% 10% 0%

26 1.5 DEM on Glass Over / Under model over/under prediction predicts times (by of a factor time of X) by model % over / under prediction of time % 100% 66% % 90% 80% ex ,n,19.3 C,2.07m/s ex ,n,20.5 C,2.07m/s ex ,n,19.9 C,1.45m/s ex ,n,21.3 C,1.45m/s ex ,n,19.6 C,0.72m/s ex ,n,20.1 C,0.72m/s ex ,n,30.2 C,0.73m/s ex ,n,30.4 C,0.73m/s ex ,n,31.2 C,0.71m/s ex ,n,30.8 C,0.71m/s ex ,n,30.1 C,1.37m/s ex ,n,30.2 C,1.37m/s ex ,n,30.2 C,1.32m/s ex ,n,30.1 C,1.32m/s fx ,n,29.1 C,2.03m/s fx ,n,31.3 C,2.03m/s fx ,n,29.1 C,1.93m/s fx ,n,31.1 C,1.93m/s fx ,n,9.9 C,2.14m/s fx ,n,10.1 C,2.14m/s fx ,n,10.7 C,1.45m/s fx ,n,10.4 C,1.45m/s fx ,n,11.0 C,0.78m/s fx ,n,10.8 C,0.78m/s fx ,t,9.6 C,2.19m/s fx ,t,9.9 C,2.19m/s fx ,t,10.8 C,1.43m/s fx ,t,10.5 C,1.43m/s fx ,t,10.9 C,0.77m/s fx ,t,10.5 C,0.77m/s ex ,t,19.8 C,2.05m/s ex ,t,20.8 C,2.05m/s ex ,t,20.3 C,1.45m/s ex ,t,21.4 C,1.45m/s ex ,t,19.8 C,0.70m/s ex ,t,20.4 C,0.70m/s fx21108c-1,t,29.1 C,2.04m/s fx21108c-2,t,31.2 C,2.04m/s ex ,t,3 C,1.42m/s ex ,t,29.9 C,1.42m/s ex ,t,30.2 C,0.72m/s ex ,t,30.2 C,0.72m/s 70% 60% 50% mass fraction 40% 30% 20% 10% 0%

27 1.5 HD on Glass Over / Under model over/under prediction predicts times (by a of factor time of X) by model % over / under prediction of time % 100% 66% % 90% 80% HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls HD-Glass_ xls Neat HD on glass fx s1 Neat HD on glass fx s2 Neat HD on glass fx s1 Neat HD on glass fx s2 Thickened HD on glass fx s1 Thickened HD on glass fx s2 Thickened HD on glass fx s1 Thickened HD on glass fx s2 Thickened HD on glass fx s1 Thickened HD on glass fx s2 6/14/2005 ECBC 3a31.xls ECBC 3a32.xls ECBC 3a33.xls ECBC 3a34.xls ECBC 3a35.xls 70% 60% 50% mass fraction 40% 30% 20% 10% 0%

28 Data space and Fit Quality's HD on Glass wind speed at 2 cm - m/s CZ ~9 µl, 4 exp CZ ~6 µl, 13 exp CZ ~1 µl, 13 exp TNO ~6 µl, 6 exp ECBC ~6 µl, 5 exp TNO ~1 µl, 2 exp TNO ~12µl, 2exp temperature - oc the normalized square root of the summed square error

29 Conclusion Semi Empirical Sessile Drop model Fits existing data fairly well Persistence times typically within 66% to 150% of experiment Work in progress More sessile drop data Experimental Contact angle functions Reactivity not tested yet Semi Empirical Absorbed drop model Prototype exists, Awaiting data

30 MS data fitted to model Experiment compared with Single Sessile Drop models volume - [ - µl [ µl ] ] :00 1:12 1:12 2:24 2:24 3:36 4:48 3:36 6:00 4:48 7:12 0:00 1:12 2:24 2:24 4:48 3:36 7:12 4:48 9:36 6:00 12:00 7: :00 1:12 1:12 2:24 2:24 3:36 3:36 4:48 4:48 6: :00 2:24 0:28 1:12 2:24 1:12 4:48 4:48 0:572:24 7:12 4:48 2:24 7:12 1:26 9:36 3:36 9:36 1:55 7:12 3:36 12:00 4:48 12:00 2:24 14:24 9:36 4:48 6:00 14:24 2:52 16:48 19:12 16:48 12:00 3:21 6:00 7:12 0 time - [ hh:mm ] evaporation rate rate - [ - [ µl [ µl / / h / h ] ]