P1.23 Evaluating assumptions that impact calculation of collision efficiencies

Monday, 28 June 2010
Exhibit Hall (DoubleTree by Hilton Portland)
Jørgen B. Jensen, NCAR, Broomfield, CO; and W. A. Cooper

Recent work on collision efficiencies has focused on the enhancement due to turbulent motions. While this has led to significant progress toward understanding an important effect, commensurate attention has not been directed toward a number of equally important factors that affect the collision efficiency. Some work is prominent in chemical engineering, but the results from that literature have not been incorporated in common cloud physics calculations.

In this presentation, various methods for calculating the collision efficiencies between small cloud droplets are reviewed. The factors considered are body (rigid sphere, viscous drop, surfactant covered viscous drop), drag (Stokes, Oseen), force interactions (van der Walls, lubrication, electric charges, turbulence), and numerical methods and boundary conditions (no slip, slip). By comparing calculations with and without each of the above effects, it is possible to calculate the importance of inclusion of each of the above effects as

E{with effect} / E{without effect} = f(r,R)

which describes the increase in collision efficiency, E, by including a specific effect; i.e. an enhancement effect, E = O(n.n). An enhancement effect of E = O(1.0) would imply that the effect makes no difference to the collision efficiencies, whereas an enhancement effect of E = O(2.0) implies a doubling of the calculated collision efficiency by including a specific factor.

Some surprising results become apparent when calculating E by examining published papers in the cloud physics and chemical engineering literature. This has been done for r/R = 0.5 and 0.9, to cover drops of similar and dissimilar sizes, and for R < 30 μm. In the absence of electric fields, droplet charges, and turbulence levels characteristic of very vigorous cumulus and thunderstorms (ε > 100 cm2 s-3), current estimates of effects support these conclusions:

For similar sized drops and, r/R = 0.9, van der Waals forces are more important than turbulent enhancements of collision rates.

For dissimilar sized drops, r/R = 0.5, and R < 20, van der Waals forces [E = O(1.58) to E = O(1.29)] and the assumption of boundary conditions with slip [E = O(1.52) to E = O(1.29)] are both more important than turbulent enhancements [E = O(1.19) to E = O(1.03)].

The clear conclusion from evaluating these and many other enhancement ratios is that current theoretical knowledge of collision efficiencies is inadequate to support reliable modeling of the warm-rain process. This statement applies equally to the experimental evidence, where the situation remains as summarized by Beard and Ochs in their 1993 review article: There is essentially no experimental evidence to support estimates of collision efficiencies for the sizes most important in warm-rain calculations. It is hard to understand why this topic has not received appropriate attention from cloud physicists in recent years.

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