The role of inertia in extensional fall of a viscous drop

Abstract

In flows of very viscous fluids, it is often justifiable to neglect inertia and solve the resulting creeping-flow or Stokes equations. For drops hanging beneath a fixed wall and extending under gravity from an initial rest state, an inevitable consequence of neglect of inertia and surface tension is that the drop formally becomes infinite in length at a finite crisis time, at which time the acceleration of the drop, which has been assumed small relative to gravity , which quickly decreases as viscous forces in the drop become dominant during the early stages of fall.