Collision Enhancement for Droplet Pairs with Electrically Reduced Approach Speed

E. Freire Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7

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Roland List Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7

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Abstract

The collision efficiency of two droplet pairs, (10;9) µm and (10;2) µm in radius, was computed as a function of background field strength for the following conditions: uniform background field pointed vertically downward, varying in strength from 300 V to 600 kV m−1; and 10 µm droplet charge of −3.34×10−17C or −3.34×10−16C for the (10;9) pair, and of −3.34×10−16C or −6.68×10−16C for the (10;2) pair. The smaller droplet had a positive charge of magnitude equal to the big droplet's in the (10;9) pair, and 25 times smaller in the, (10;2) pair. These moderate charges allowed reasonably strong critical back-ground fields E0 at which the droplets, when far apart, would fall with the same terminal speed.

With varying background field E0, the collision efficiency rises steeply on either side of the critical value E0, toward an asymptotic value of infinity. The maximum collision efficiencies computed were 19.0 for the (10;9) µm pair in a field of only 9 kV m−1, and 11.2 for the (10;2) µm pair in a field of 45 kV m−1. Both values are three orders of magnitude greater than the respective collision efficiencies obtained in the absence of electrical forces, namely, 0.013 and 0.0044, and also substantially larger than hitherto assumed possible electrical effects.

The physics behind this electrical configuration suggests a considerable enhancement of the collision efficiency far beyond the investigated droplet sizes and into a range where electrical effects have hitherto been assumed unimportant.

Abstract

The collision efficiency of two droplet pairs, (10;9) µm and (10;2) µm in radius, was computed as a function of background field strength for the following conditions: uniform background field pointed vertically downward, varying in strength from 300 V to 600 kV m−1; and 10 µm droplet charge of −3.34×10−17C or −3.34×10−16C for the (10;9) pair, and of −3.34×10−16C or −6.68×10−16C for the (10;2) pair. The smaller droplet had a positive charge of magnitude equal to the big droplet's in the (10;9) pair, and 25 times smaller in the, (10;2) pair. These moderate charges allowed reasonably strong critical back-ground fields E0 at which the droplets, when far apart, would fall with the same terminal speed.

With varying background field E0, the collision efficiency rises steeply on either side of the critical value E0, toward an asymptotic value of infinity. The maximum collision efficiencies computed were 19.0 for the (10;9) µm pair in a field of only 9 kV m−1, and 11.2 for the (10;2) µm pair in a field of 45 kV m−1. Both values are three orders of magnitude greater than the respective collision efficiencies obtained in the absence of electrical forces, namely, 0.013 and 0.0044, and also substantially larger than hitherto assumed possible electrical effects.

The physics behind this electrical configuration suggests a considerable enhancement of the collision efficiency far beyond the investigated droplet sizes and into a range where electrical effects have hitherto been assumed unimportant.

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