Dancing Droplets *

Droplet motion and collisional processes are important in many applications including cloud growth and fuel spray combustion. Unlike rigid particles, whose surfaces, by definition are invariant to fluid stresses and neighbor impacts, droplets can experience large surface deformations and break up when subjected to external loads. In particular, surface deformation can couple to droplet migration whereby changes in a droplet’s projected area and moment of inertia changes the forces and torques it experiences. To study some of these effects, we introduce a Lagrangian droplet deformation model inspired by Taylor’s experiments in 1934 whereby a four-roll apparatus deforms a spherical droplet into an ellipsoid. The proposed model takes into account the dynamic evolution of the droplet’s principal axes allowing changes in shape to feed into the equations of linear and angular momentum.  The model is formally valid in the limit of low Capillary number to ensure the assumption of ellipsoid deformation remains valid. We apply the Lagrangian model to a cellular flow considered by Maxey in 1987 for rigid particles to understand how the basic clustering mechanisms of strain-rate versus vorticity effect droplet clustering whose surface evolution and hence clustering are dependent on local fluid properties.