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Discussion papers
https://doi.org/10.5194/acp-2019-932
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/acp-2019-932
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: technical note 18 Nov 2019

Submitted as: technical note | 18 Nov 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Atmospheric Chemistry and Physics (ACP).

Technical Note: Equilibrium droplet size distributions in a turbulent cloud chamber with uniform supersaturation

Steven K. Krueger Steven K. Krueger
  • University of Utah, Salt Lake City, USA

Abstract. In a laboratory cloud chamber that is undergoing Rayleigh-Bénard convection, supersaturation is produced by isobaric mixing. When aerosols (cloud condensation nuclei) are injected into the chamber at a constant rate, and the rate of droplet activation is balanced by the rate of droplet loss, an equilibrium droplet size distribution (DSD) can be achieved. We derived analytic equilibrium DSDs and PDFs of droplet radius and squared radius for conditions that could occur in such a turbulent cloud chamber when there is uniform supersaturation. The loss rate due to fall out that we used assumes that (1) the droplets are well-mixed by turbulence, (2) when a droplet becomes sufficiently close to the lower boundary, the droplet’s terminal velocity determines its probability of fall out per unit time, and (3) a droplet’s terminal velocity follows Stokes’ Law (so it is proportional to its radius squared). Given the chamber height, the analytic PDF is determined by the mean supersaturation alone. From the expression for the PDF of the radius, we obtained analytic expressions for the first five moments of the radius, including moments for truncated DSDs. We used statistics from a set of measured DSDs to check for consistency with the analytic PDF. We found consistency between the theoretical and measured moments, but only when the truncation radius of the measured DSDs was taken into account. This consistency allows us to infer the mean supersaturations that would produce the measured PDFs in the absence of supersaturation fluctuations. We found that accounting for the truncation radius of the measured DSDs is particularly important when comparing the theoretical and measured relative dispersions of the droplet radius. We also included some additional quantities derived from the analytic DSD: droplet sedimentation flux, precipitation flux, and condensation rate.

Steven K. Krueger
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Steven K. Krueger
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Latest update: 07 Dec 2019
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Short summary
When CCN are injected into a turbulent cloud chamber at a constant rate, and the rate of droplet activation is balanced by the rate of droplet fall out, a steady-state droplet size distribution (DSD) can be achieved. We derived analytic DSDs and PDFs of droplet radius for such conditions when there is uniform supersaturation. Given the chamber height, the analytic PDF is determined by the supersaturation alone, which allows one to infer the supersaturation that would produce a measured PDF.
When CCN are injected into a turbulent cloud chamber at a constant rate, and the rate of droplet...
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