The effect of an electric force on the fall speed of a particle has been considered using a simple model of a spherical particle of radius r in a vertical electric field E, with weight W, an Archimedean upthrust U, an electric force FE, and a drag force FD. If the particle is moving downward but experiencing an upward electric force (due to carrying a negative charge in a downward-directed field, such as that in fair weather), then the balance of forces in equilibrium can be represented asEmbedded Image(4)

The ratio of U to W is given by the ratio of the densities of air ρa and the particle ρp, which is ~1:1000; hence, U<<W and U can be neglected. The drag force depends on the particle’s projected area A (= πr2), its fluid-relative speed v, and the drag coefficient CD. Assuming a spherical particle carrying a charge q, the electric force can be written as qE, the drag force parameterized as Embedded Image; hence, the equilibrium description of Eq. 4 becomesEmbedded Image(5)

For calculation of v, CD depends on the flow and the associated Reynolds number and typically varies from 0.5 to 1.5 for a smooth sphere.

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