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Behavior of aerosols formed by clustering of molecules around gaseous ions
Atmospheric Environment Pergamon Press 1969. Vol. 3, pp. 697-698. Printed in Great Britain
BEHAVIOR
OF AEROSOLS FORMED BY CLUSTERING AROUND GASEOUS IONS*
OF MOLECULES
THEPAPERby VOX-IRA ei al. (1969) contains two serious errors concerning aerosol particle size deter-
mination, The authors believed that diffusion deposition of an aerosol enclosed in a large sphere could be described by the use of the Fick’s law equation. However, convective mass transfer and stirring is neglected and so such an approach is obviously invalid in the case under consideration. Also, particle radii were calculated from diffusion mobilities using the StokesXmmingham formula which is valid only in the slip-flow regime. Calculated particle size values were lo-’ cm in order, i.e. corresponded to near free molecule regime of momentum transfer (Fucw, 1964); HIDY and BROCK,1958). It is well-known that at large Knudsen numbers the EPSTW (1924) or CERCIGNANI
(1968) formulae must be used. In view of the above mentioned errors it is doubtful if even the order of the particle size was determined correctly. Karpov-Indute,
A. G. !%TUGIN
Moscow.
AUTHOR’S
REPLY
Tm MAINobject of the paper is to show the formation of aerosols in the presence of charges and different vapours. The estimation of aerosol size is carried out to find out the initial size and rate of growth for different vapours. The criticism points to the finer details of the method of size estimation, which would not a&t the general concltions of the paper, as explained below. Firstly, it has been pointed out that the *ion coelB&nt based on Fick’s law would be a&ted by convection and stirring. The degree of convection depends on the thermal gradient in the system, and we believe that in our system the effect was negligible. In regard to the second point, we wish to state that the use of gas kinetic equations with Cunningham’s correction, as has been done by us, is based on well accepted approach for the calculation of particle radii from diffusion mobility. For particles whose diameters are approximately equal to or less than the mean free path of the gas in which they are suspended, the particles can be considered to slip between the gas moleculea. It is for this purpose that Cunningham introduced the slip correction factor. Particles in thesize range studied (10m6 to lo-’ cm) are smaller than the mean free path in air at NTP, by factors of 10 and 100, respectively. Therefore, they clearly fall in the slip flow regime. For this size range JUIWB(1963) has shown that both the gas kinetic formula extrapolated to larger sizes and Stoke formula are identical. Therefore, the formula used in the paper should be valid for the size range studied. DAVIE)(1945) and in a private communication has also used the same general formula, but with somewhat higher value of fi for particles below 10q6 cm. It has been further pointed out that EPSON (1924) and CERCIGNANI (1968) formulae should have been used. The above two authors have essentially based their formulae on MUX&S tindings (1923). The formula used by us is in fact very similar to the formula suggested by the above authors. It is well known in particle kinetics that for large Knudsen numbers the resistance offered to the particle is largely due to the inertia of the molecules hit and is proportional to the square of the radius of the particle. From kinetic theory, however, it has been shown that the value of b varies with the Knudsen number. This variation is taken care of in tho approach suggested by Epstein and Cer&ani and the empirical formula of Mill&an. However, it has been found by calculation that for particlea in the size rangeof10-6to10-7Cm(I(nudsQ1numberfrom10to100inthesystemusedbyus)thevariationin the estimated particle size would not be more than 5 to 10 per cent. * VOERAK. O., SUBBARAMUM. C. and VASUDIWAN K. N. (1969) Atmospheric Btvironment 3, 99-10s. 697
BEHAVIOR
OF AEROSOLS FORMED BY CLUSTERING AROUND GASEOUS IONS*
OF MOLECULES
THEPAPERby VOX-IRA ei al. (1969) contains two serious errors concerning aerosol particle size deter-
mination, The authors believed that diffusion deposition of an aerosol enclosed in a large sphere could be described by the use of the Fick’s law equation. However, convective mass transfer and stirring is neglected and so such an approach is obviously invalid in the case under consideration. Also, particle radii were calculated from diffusion mobilities using the StokesXmmingham formula which is valid only in the slip-flow regime. Calculated particle size values were lo-’ cm in order, i.e. corresponded to near free molecule regime of momentum transfer (Fucw, 1964); HIDY and BROCK,1958). It is well-known that at large Knudsen numbers the EPSTW (1924) or CERCIGNANI
(1968) formulae must be used. In view of the above mentioned errors it is doubtful if even the order of the particle size was determined correctly. Karpov-Indute,
A. G. !%TUGIN
Moscow.
AUTHOR’S
REPLY
Tm MAINobject of the paper is to show the formation of aerosols in the presence of charges and different vapours. The estimation of aerosol size is carried out to find out the initial size and rate of growth for different vapours. The criticism points to the finer details of the method of size estimation, which would not a&t the general concltions of the paper, as explained below. Firstly, it has been pointed out that the *ion coelB&nt based on Fick’s law would be a&ted by convection and stirring. The degree of convection depends on the thermal gradient in the system, and we believe that in our system the effect was negligible. In regard to the second point, we wish to state that the use of gas kinetic equations with Cunningham’s correction, as has been done by us, is based on well accepted approach for the calculation of particle radii from diffusion mobility. For particles whose diameters are approximately equal to or less than the mean free path of the gas in which they are suspended, the particles can be considered to slip between the gas moleculea. It is for this purpose that Cunningham introduced the slip correction factor. Particles in thesize range studied (10m6 to lo-’ cm) are smaller than the mean free path in air at NTP, by factors of 10 and 100, respectively. Therefore, they clearly fall in the slip flow regime. For this size range JUIWB(1963) has shown that both the gas kinetic formula extrapolated to larger sizes and Stoke formula are identical. Therefore, the formula used in the paper should be valid for the size range studied. DAVIE)(1945) and in a private communication has also used the same general formula, but with somewhat higher value of fi for particles below 10q6 cm. It has been further pointed out that EPSON (1924) and CERCIGNANI (1968) formulae should have been used. The above two authors have essentially based their formulae on MUX&S tindings (1923). The formula used by us is in fact very similar to the formula suggested by the above authors. It is well known in particle kinetics that for large Knudsen numbers the resistance offered to the particle is largely due to the inertia of the molecules hit and is proportional to the square of the radius of the particle. From kinetic theory, however, it has been shown that the value of b varies with the Knudsen number. This variation is taken care of in tho approach suggested by Epstein and Cer&ani and the empirical formula of Mill&an. However, it has been found by calculation that for particlea in the size rangeof10-6to10-7Cm(I(nudsQ1numberfrom10to100inthesystemusedbyus)thevariationin the estimated particle size would not be more than 5 to 10 per cent. * VOERAK. O., SUBBARAMUM. C. and VASUDIWAN K. N. (1969) Atmospheric Btvironment 3, 99-10s. 697