Influence of vapor depletion on nucleation rate

Abstract

During condensation in finite systems part of molecules is transformed from supersaturated mother phase to a new one and depletion of the mother phase occurs. Kinetic equations describing homogeneous nucleation process including decrease of supersaturation are solved numerically. It is shown that dependency of nucleation rate on nucleus size reaches some maximum, which decreases with time and moves to higher nucleus sizes. Nucleation rate is negative for undercritical size of nuclei.

Size distribution of nuclei formed by homogeneous nucleation in closed systems

“…Unfortunately, typical transient time of nucleation process for condensation is too short (in order of 10 −7 s) and thus direct comparison with experimental data is not possible due to lack of experimental data. Similarly as in our previous works (Koíšek & Demo, 2005;Koíšek et al, 2006;Koíšek & Demo, 2007) we have chosen as a model system condensation of ethanol vapor at T = 260 K, P 0 = 598.26 Pa, = 0.025 J m −2 , and = 817.5 kg m −3 . Condensation of ethanol vapor was measured to determine the stationary nucleation rate (Kacker & Heist, 1985;Peters & Paikert, 1989;Schmitt, Adams, & Zalabsky, 1982;Strey & Viisanen, 1993) or critical supersaturation (Katz & Ostermier, 1967).…”

“…In a closed system and at higher initial supersaturations, the nucleation rate does not reach its stationary limit, as in the standard theory. After reaching some extremal value the nucleation rate falls to zero and system tends to equilibrium state (Chesnokov & Krasnoperov, 2002;Koíšek & Demo, 2007).…”

“…It was shown (Koíšek & Demo, 2005) that in a closed system the initial size distribution of clusters influences formation of nuclei much more than in standard theory of nucleation with constant supersaturation does. At low initial supersaturation, depletion of the mother phase (decrease in supersaturation) is low and the standard model describes satisfactorily the formation of nuclei (Koíšek & Demo, 2007). In this case (constant supersaturation) various analytical approaches to nucleation rate (the number of critical nuclei formed in unit volume per unit time) have been derived-see e.g.…”

Homogeneous nucleation rate at various initial supersaturations in a closed system

“…In the standard model with a constant supersaturation under the same conditions, one gets for the time delay (corresponding to an appropriate critical size) = 0.42 s at S = 3 and = 0.087 s at S = 5 (time delay decreases with increasing supersaturation). If one takes into account a decrease in the supersaturation for the high initial supersaturation, the nucleation rate does not necessarily reach its stationary value and for sufficiently long times approaches zero (Koíšek & Demo, 2007). If one compares a dimensionless nucleation rate (nucleation rate normalized to its stationary value) for various initial supersaturations (see Figs.…”

“…Negative nucleation rates mean a decrease of the number density of nuclei for subcritical sizes. Detailed discussion about negative nucleation rates in closed systems can be found in Koíšek and Demo (2007). At t = 6 s ( Fig.…”