Second-order theory for the deformation of a Newtonian drop in a stationary flow field

The classical perturbative theory for a single drop immersed in a flowing immiscible fluid is revisited, with the well-known capillary number Ca, ratio of viscous to interfacial stresses, as the expansion parameter. Although the analysis is here limited to the Newtonian case under steady-state conditions, the perturbation method is innovative, as it makes use of rotational invariance to obtain workable tensorial representations of the pressure and velocity fields, and of the drop shape, at any order in Ca. The method is much less cumbersome than the classical one, based on an expansion in spherical harmonics. The analytical second-order solution thus obtained differs somewhat from previously reported results. (C) 2002 American Institute of Physics.