The unsteady motion of a drop moving vertically under gravity

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Abstract
The unsteady flow field pertaining to a drop moving vertically under gravity is obtained from the Stokes equations applicable to low-Reynolds-number flow. A proof is given that there is no variation in the normal stress over the drop surface. In consequence unsteadily moving drops remain spherical, subject only to the criterion of low Reynolds number. Numerical results are presented for a water drop moving through air. A small-time analysis of the motion provides a comparison between the motion of any drop, or bubble, with that of the presented water-drop solution.

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