  Drop deformation in fluid flows is investigated here as an exchange between
the kinetic energy of the fluid and the surface energy of the drop. We show
analytically that this energetic exchange is controlled only by the stretching
(or compression) of the drop surface by the rate-of-strain tensor. This
mechanism is analogous to the stretching of the vorticity field in turbulence.
Leveraging the non-local nature of turbulence dynamics, we introduce a new
decomposition that isolates the energetic exchange due to local drop-induced
surface effects, from the non-local action of turbulent fluctuations. We
perform direct numerical simulations of single inertial drops in isotropic
turbulence and show that an important contribution to the increments of the
surface energy arises from the non-local stretching of the fluid-fluid
interface by eddies far from the drop surface (outer eddies). We report that
this mechanism is dominant and independent of surface dynamics in a range of
Weber numbers in which drop breakup occurs. These findings shed new light on
drop deformation and breakup in turbulent flows, and open the venue for the
improvement and simplification of breakup models.
