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HCL-acid system
Suppl.I, pp. S133-S134. 1998
J. Aemsol Sci. Vol. 29.
8 1998Publishedby Elsevier
Pergamon
BINARY ESTIMATING
HETEROGENEOUS THE CRITICAL
NUCLEATION SATURATION
INSIDE THE FORMED
IN GAS CLEANING
RATE OF &O-VAPOR
AEROSOL
ABSORPTION
IN A H,O/HCL-ACID
Nucleation,
SYSTEM
Schmidt’**
Duisburg, Process Engineering, Bismarckstr. 90,47048 Duisburg, Germany
‘Institute for Environmental Technology and Chemical Analytics,Bliersheimer
Heterogeneous
PROCESS:
AND ACID CONCENTRATION
Stefan Haep’y2, Michael Luckas’ and Klaus-Gerhard ‘Gerhard-Mercator-University
Science Ltd. All rights reserved Printed in Great Britain 0021~83x/98 $19.00 + 0.00
Condensed
Keywords Phases, Surface Tension
Str. 60,47229Duisburg,Germany
Dependence
on Curvature
Modelling aerosol growth in absorption processes with multicomponent heterogeneous condensation theory, requires an existing aerosol droplet, balancing the gradient of partial pressures necessary for the molecular flux. Getting information about the composition of that ,,basic“ aerosol, the preceding heterogeneous nucleation process has to be considered. Following the classical description of nucleation rate, one can use it’s equation to determine the critical point from which nucleation might occur on spherical substrates:
Required input data are the partial pressures and temperature of the system, the corresponding concentrations inside the formed phase, calculated with a thermodynamic model for the electrolyt solution and the substrate radius. Fig. 1,2,3 and 4 show the characteristic results of some calculations for a binary system (H,O/HCl-vapor, cHC,= 10 mg/m3).
I verify these results especially for aerosols with where the assumption of macroscopic properties like clusters become more and more questionable with tension dependence on curvature, using the modified
v(r)=y, e++(l+&=)] s133
diameters in the far submircron regime, density and surface tension of the formed decreasing size, a model for the surface Tolman-equation, has been implemented.
s134
Abstracts
of the 5th International
Aerosol Conference
1998
The derivation of the Gibbs free energy, leading to the general Kelvin equations, necessary for the determination of the concentrations inside the nucleated embryo at the critical point, gives:
The sec. important on: Z=
effect concerns
the Zeldovich
vb=geom. 4 r” -4y,
factor) derived
R Tin(f)-4y_ V r”
Figure 5.6.7 and 8 show the comnuted
,,non equilibrium“
6:
f, -4y,
Vr”
from
f, -4y_
V r’ 6:
z =
cr”
f, -2
correction
jw
factor. Equatibecomes:
6_ f, + y,
V 84 f,
results:
The incorporation of the curvature dependence of surface tension reduces the crit. energy barrier thus the crit. aerosol radius and the crit. saturation rate, though the deviations are only slightly visible in the figures, except a significant decrease of. crit saturation rate in fig 5. Comparing the computed results in an area of special interest below 40” contact angle, relevant for fly ash substrate particles (rsobY 0.1 - 1urn) in absorption processes, the crit. saturation rate related to H,O vapor and 10 mg HCl/m’ both lie near 1 (0.96-1.18). The mol fraction of the condensed HCl acid lies between 0.013 and 0.018. REFERENCES Lazaridis, M., Kulmala, M., Gorbunov, B. Z., (1992) Binary Heterogeneous Nucleation at a Non-Uniform Surface, J. Aer. Sci., 23 457-466 Kumar, F. J., et. al., (1991) P.Curvature Dependence of Surface Free Energy and Nucleation Kinetics of Ccl, and C,H,Cl, Vapours, J. of Materials Sci. Letters, 10 608-610 Pruppacher, H. R., Klett, J. D., (1980) Microphysics of Clouds and Precipitation, Luckas, M., Eden, D. M., (1995) Improved Representation HCl-H,O, AIChE Journal, 41 (4) 104 1- 1043
of the Vapor-Liquid
Reidel Publ. Equilibrium
of
J. Aemsol Sci. Vol. 29.
8 1998Publishedby Elsevier
Pergamon
BINARY ESTIMATING
HETEROGENEOUS THE CRITICAL
NUCLEATION SATURATION
INSIDE THE FORMED
IN GAS CLEANING
RATE OF &O-VAPOR
AEROSOL
ABSORPTION
IN A H,O/HCL-ACID
Nucleation,
SYSTEM
Schmidt’**
Duisburg, Process Engineering, Bismarckstr. 90,47048 Duisburg, Germany
‘Institute for Environmental Technology and Chemical Analytics,Bliersheimer
Heterogeneous
PROCESS:
AND ACID CONCENTRATION
Stefan Haep’y2, Michael Luckas’ and Klaus-Gerhard ‘Gerhard-Mercator-University
Science Ltd. All rights reserved Printed in Great Britain 0021~83x/98 $19.00 + 0.00
Condensed
Keywords Phases, Surface Tension
Str. 60,47229Duisburg,Germany
Dependence
on Curvature
Modelling aerosol growth in absorption processes with multicomponent heterogeneous condensation theory, requires an existing aerosol droplet, balancing the gradient of partial pressures necessary for the molecular flux. Getting information about the composition of that ,,basic“ aerosol, the preceding heterogeneous nucleation process has to be considered. Following the classical description of nucleation rate, one can use it’s equation to determine the critical point from which nucleation might occur on spherical substrates:
Required input data are the partial pressures and temperature of the system, the corresponding concentrations inside the formed phase, calculated with a thermodynamic model for the electrolyt solution and the substrate radius. Fig. 1,2,3 and 4 show the characteristic results of some calculations for a binary system (H,O/HCl-vapor, cHC,= 10 mg/m3).
I verify these results especially for aerosols with where the assumption of macroscopic properties like clusters become more and more questionable with tension dependence on curvature, using the modified
v(r)=y, e++(l+&=)] s133
diameters in the far submircron regime, density and surface tension of the formed decreasing size, a model for the surface Tolman-equation, has been implemented.
s134
Abstracts
of the 5th International
Aerosol Conference
1998
The derivation of the Gibbs free energy, leading to the general Kelvin equations, necessary for the determination of the concentrations inside the nucleated embryo at the critical point, gives:
The sec. important on: Z=
effect concerns
the Zeldovich
vb=geom. 4 r” -4y,
factor) derived
R Tin(f)-4y_ V r”
Figure 5.6.7 and 8 show the comnuted
,,non equilibrium“
6:
f, -4y,
Vr”
from
f, -4y_
V r’ 6:
z =
cr”
f, -2
correction
jw
factor. Equatibecomes:
6_ f, + y,
V 84 f,
results:
The incorporation of the curvature dependence of surface tension reduces the crit. energy barrier thus the crit. aerosol radius and the crit. saturation rate, though the deviations are only slightly visible in the figures, except a significant decrease of. crit saturation rate in fig 5. Comparing the computed results in an area of special interest below 40” contact angle, relevant for fly ash substrate particles (rsobY 0.1 - 1urn) in absorption processes, the crit. saturation rate related to H,O vapor and 10 mg HCl/m’ both lie near 1 (0.96-1.18). The mol fraction of the condensed HCl acid lies between 0.013 and 0.018. REFERENCES Lazaridis, M., Kulmala, M., Gorbunov, B. Z., (1992) Binary Heterogeneous Nucleation at a Non-Uniform Surface, J. Aer. Sci., 23 457-466 Kumar, F. J., et. al., (1991) P.Curvature Dependence of Surface Free Energy and Nucleation Kinetics of Ccl, and C,H,Cl, Vapours, J. of Materials Sci. Letters, 10 608-610 Pruppacher, H. R., Klett, J. D., (1980) Microphysics of Clouds and Precipitation, Luckas, M., Eden, D. M., (1995) Improved Representation HCl-H,O, AIChE Journal, 41 (4) 104 1- 1043
of the Vapor-Liquid
Reidel Publ. Equilibrium
of