The Influence of a Horizontal Wall on the Motion of a Falling Oil Drop

Abstract

A study has been made of the effect of a horizontal wall on the motion of oil drops of radii ranging from 5 µ to 15 µ falling in air. The following conclusions were reached.

Provided that z/a, the ratio of the distance z of the oil drop from the wall to its radius a, is greater than 20, the resistance W to its motion is satisfied by the formula given by Lorentz, namely :

W = 6πηav (1 + 9/8 a/z).

For z/a ranging from 2 to 500, the coefficient of a/z may be expressed empirically in the form

f(z/a) = k₁ + k₂ a/z

where k₁ = 1.08 ± 0.05 and k₂ = 1.4 ± 1.0.