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In fluid dynamics, Epstein drag is a theoretical result, for the drag force exerted on spheres in high Knudsen number flow (i.e., rarefied gas flow).[1] This may apply, for example, to sub-micron droplets in air, or to larger spherical objects moving in gases more rarefied than air at standard temperature and pressure. Note that while they may be small by some criteria, the spheres must nevertheless be much more massive than the species (molecules, atoms) in the gas that are colliding with the sphere, in order for Epstein drag to apply. The reason for this is to ensure that the change in the sphere's momentum due to individual collisions with gas species is not large enough to substantially alter the sphere's motion, such as occurs in Brownian motion.
The result was obtained by Paul Sophus Epstein in 1924. His result was used for. high-precision measurements of the charge on the electron in the oil drop experiment performed by Robert A. Millikan, as cited by Millikan in his 1930 review paper on the subject.[2] For the early work on that experiment, the drag was assumed to follow Stokes' law. However, for droplets substantially below the submicron scale, the drag approaches Epstein drag instead of Stokes drag, since the mean free path of air species (atoms and molecules) is roughly of order of a tenth of a micron.