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Precision measurement of supersaturation and temperature in adiabatically expanded gases from the observation of drop growth rates
d. A e r o s o l Sci. Vol. 30, Suppl. 1, pp. $65-$66, 1999 © 1999 Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0021-8502/99/$ - s e e front matter
Pergamon
PRECISION M E A S U R E M E N T OF S U P E R S A T U R A T I O N AND T E M P E R A T U R E IN ADIABATICALLY E X P A N D E D GASES F R O M THE OBSERVATION OF DROP G R O W T H RATES S. Zach, A. Vrtala, G. P. Reischl and P. E. Wagner Institut Mr Experimentalphysik, Universit~t Wien Boltzmanngasse 5, A-1090 Wien, Austria
KEYWORDS adiabatic expansion, vapor supersaturation, nucleation, condensational particle growth, Poisson law INTRODUCTION For experimental studies of nucleation and condensation processes in the gas phase it is essential to obtain condensable vapors with well-defined supersaturations. Supersaturated vapors with uniform partial pressures and temperatures can be reproducibly achieved by adiabatic expansion and corresponding cooling of initially nearly saturated vapor - carrier gas mixtures. Direct experimental determination of the gas temperature during and after the expansion is difficult, however, as vapor condensation will generally occur on the surface of a temperature sensor and thus the temperature of the condensing liquid rather than the gas temperature is measured. Accordingly, the temperature drop during adiabatic cooling is often calculated using the Poisson equations, the adiabatic index for the vapor - carrier gas mixture being determined according to Richarz (1906). Recent nucleation experiments (Viisanen et al., 1993), however, seem to indicate systematic deviations from these calculated temperatures and an empirical correction has been suggested. In the present study the thermodynamic conditions at the end of adiabatic expansions have been experimentally determined from measurement of drop growth rate, which can be used as a sensitive indicator for vapor supersaturation and temperature. The results are compared to corresponding predictions. EXPERIMENTAL METHOD We studied adiabatic expansions of vapor - carrier gas mixtures in an expansion cloud chamber. The expansion times did not exceed 10 ms. The subsequently occuring condensational drop growth was measured by means of the Constant-Angle Mie Scattering (CAMS) method (Wagner, 1985). Comparatively small supersaturations were chosen as the correspondingly slow drop growth is most sensitive to changes of supersaturation and temperature. While keeping the vapor fraction constant, we performed series of different expansions starting from different initial total gas pressures in the expansion chamber and leading to the identical final total gas pressure and thus the identical vapor pressure. The initial (chamber) temperatures were chosen so that the final temperature after expansion, calculated according to the Poisson equations, was kept constant. Thus, according to the Poisson equations, the identical thermodynamic conditions at the end of the different expansions and correspondingly the same drop growth rates can be expected. In first measurement series comparatively small expansion ratios were considered. Within experimental scatter actually the same drop growth rates were found indicating that the Poisson equations are consistent with experiment at small expansion ratios. Accordingly, at small expansion ratios the actual temperature after expansion is known thus allowing calibration of the observed drop growth rates with respect to the gas temperature for the considered conditions at the end of the expansion. Subsequently, measurements were performed over an extended range of expansion ratios and from the measured drop growth rates the actual temperatures after expansion can be determined. It should be emphasized that the temperature measurement method applied in this study does not involve drop growth calculations and thus the results obtained are independent of drop growth theory.
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Abstracts of the 1999 EuropeanAerosol Conference theoret. Poisson
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Fig. 2. Final temperatures after expansion for n-propanol - air mixtures
RESULTS AND CONCLUSIONS Temperature and supersaturation at the end of adiabatic expansions were experimentally determined from drop growth measurements. Water - air and n-propanol - air mixtures were considered. First measurement series have shown that the accuracy of the results is critically dependent on the adsorption equilibrium at the walls of the measuring system. In order to establish adsorption equilibrium, extensive flushing of the measuring system at the selected initial thermodynamic conditions before expansion was performed previous to all measurements. Expansion ratios between about 1.1 and 1.9 and corresponding temperature drops ranging from 10 to 55 K were considered. The constant final vapor saturation ratio at the end of expansion was chosen to be close to 1.1 resulting in comparatively slow drop growth rates. The corresponding initial vapor saturation ratios before expansion were varied between about 0.65 and 0.1. As mentioned above, during each series of experiments the final temperature and supersaturation after expansion, calculated according to the Poisson equations, were kept constant. In Figs. 1 and 2 the experimental final temperatures after expansion, as obtained in the present study, are shown vs. the expansion ratio (crosses). It can be seen that the Poisson equations (solid lines) are consistent with the experimental final temperatures except for the highest expansion ratio considered. The deviation observed at the highest expansion ratio may be connected with the extreme temperature gradients in the measuring chamber and with turbulence. The trend predicted by the empirical relation according to Viisanen et al. (1993) (broken lines) has not been observed. ACKNOWLEDGMENTS This work has been supported by the Fonds zur F6rderung der Wissenschaftlichen Forschung, Projekt Nr. P 9421 - GEO, and by the Hochschuljubil~iumsstiftung der Stadt Wien. REFERENCES Richarz, F. (1906) Ann. Phys. 19, 639. Viisanen, Y., Strey, R., Reiss, H. (1993)J. Chem. Phys. 99, 4680. Wagner, P. E. (1985) J. Colloidlnterface Sci. 105, 456.
Pergamon
PRECISION M E A S U R E M E N T OF S U P E R S A T U R A T I O N AND T E M P E R A T U R E IN ADIABATICALLY E X P A N D E D GASES F R O M THE OBSERVATION OF DROP G R O W T H RATES S. Zach, A. Vrtala, G. P. Reischl and P. E. Wagner Institut Mr Experimentalphysik, Universit~t Wien Boltzmanngasse 5, A-1090 Wien, Austria
KEYWORDS adiabatic expansion, vapor supersaturation, nucleation, condensational particle growth, Poisson law INTRODUCTION For experimental studies of nucleation and condensation processes in the gas phase it is essential to obtain condensable vapors with well-defined supersaturations. Supersaturated vapors with uniform partial pressures and temperatures can be reproducibly achieved by adiabatic expansion and corresponding cooling of initially nearly saturated vapor - carrier gas mixtures. Direct experimental determination of the gas temperature during and after the expansion is difficult, however, as vapor condensation will generally occur on the surface of a temperature sensor and thus the temperature of the condensing liquid rather than the gas temperature is measured. Accordingly, the temperature drop during adiabatic cooling is often calculated using the Poisson equations, the adiabatic index for the vapor - carrier gas mixture being determined according to Richarz (1906). Recent nucleation experiments (Viisanen et al., 1993), however, seem to indicate systematic deviations from these calculated temperatures and an empirical correction has been suggested. In the present study the thermodynamic conditions at the end of adiabatic expansions have been experimentally determined from measurement of drop growth rate, which can be used as a sensitive indicator for vapor supersaturation and temperature. The results are compared to corresponding predictions. EXPERIMENTAL METHOD We studied adiabatic expansions of vapor - carrier gas mixtures in an expansion cloud chamber. The expansion times did not exceed 10 ms. The subsequently occuring condensational drop growth was measured by means of the Constant-Angle Mie Scattering (CAMS) method (Wagner, 1985). Comparatively small supersaturations were chosen as the correspondingly slow drop growth is most sensitive to changes of supersaturation and temperature. While keeping the vapor fraction constant, we performed series of different expansions starting from different initial total gas pressures in the expansion chamber and leading to the identical final total gas pressure and thus the identical vapor pressure. The initial (chamber) temperatures were chosen so that the final temperature after expansion, calculated according to the Poisson equations, was kept constant. Thus, according to the Poisson equations, the identical thermodynamic conditions at the end of the different expansions and correspondingly the same drop growth rates can be expected. In first measurement series comparatively small expansion ratios were considered. Within experimental scatter actually the same drop growth rates were found indicating that the Poisson equations are consistent with experiment at small expansion ratios. Accordingly, at small expansion ratios the actual temperature after expansion is known thus allowing calibration of the observed drop growth rates with respect to the gas temperature for the considered conditions at the end of the expansion. Subsequently, measurements were performed over an extended range of expansion ratios and from the measured drop growth rates the actual temperatures after expansion can be determined. It should be emphasized that the temperature measurement method applied in this study does not involve drop growth calculations and thus the results obtained are independent of drop growth theory.
$65
$66
Abstracts of the 1999 EuropeanAerosol Conference theoret. Poisson
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present study
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Fig. 1. Final temperatures after expansion for water - air mixtures
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Fig. 2. Final temperatures after expansion for n-propanol - air mixtures
RESULTS AND CONCLUSIONS Temperature and supersaturation at the end of adiabatic expansions were experimentally determined from drop growth measurements. Water - air and n-propanol - air mixtures were considered. First measurement series have shown that the accuracy of the results is critically dependent on the adsorption equilibrium at the walls of the measuring system. In order to establish adsorption equilibrium, extensive flushing of the measuring system at the selected initial thermodynamic conditions before expansion was performed previous to all measurements. Expansion ratios between about 1.1 and 1.9 and corresponding temperature drops ranging from 10 to 55 K were considered. The constant final vapor saturation ratio at the end of expansion was chosen to be close to 1.1 resulting in comparatively slow drop growth rates. The corresponding initial vapor saturation ratios before expansion were varied between about 0.65 and 0.1. As mentioned above, during each series of experiments the final temperature and supersaturation after expansion, calculated according to the Poisson equations, were kept constant. In Figs. 1 and 2 the experimental final temperatures after expansion, as obtained in the present study, are shown vs. the expansion ratio (crosses). It can be seen that the Poisson equations (solid lines) are consistent with the experimental final temperatures except for the highest expansion ratio considered. The deviation observed at the highest expansion ratio may be connected with the extreme temperature gradients in the measuring chamber and with turbulence. The trend predicted by the empirical relation according to Viisanen et al. (1993) (broken lines) has not been observed. ACKNOWLEDGMENTS This work has been supported by the Fonds zur F6rderung der Wissenschaftlichen Forschung, Projekt Nr. P 9421 - GEO, and by the Hochschuljubil~iumsstiftung der Stadt Wien. REFERENCES Richarz, F. (1906) Ann. Phys. 19, 639. Viisanen, Y., Strey, R., Reiss, H. (1993)J. Chem. Phys. 99, 4680. Wagner, P. E. (1985) J. Colloidlnterface Sci. 105, 456.