  The off-center collision of binary bouncing droplets of equal size was
studied numerically by a volume-of-fluid (VOF) method with two marker
functions, which has been validated by comparing with available experimental
results. A non-monotonic kinetic energy recovery with varying impact parameters
was found based on the energy budget analysis. This can be explained by the
prolonged entanglement time and the enhanced internal-flow-induced viscous
dissipation for bouncing droplets at intermediate impact parameters, compared
with those at smaller or larger impact parameters. The universality of this
non-monotonicity was numerically verified, and thereby an approximate fitting
formula was proposed to correlate the kinetic energy dissipation factor with
the impact parameter for various Weber numbers and Ohnesorge numbers. From the
vortex dynamics perspective, a helicity analysis of droplet internal flow
identifies a strong three-dimensional interaction between the "ring-shaped"
vortices and the "line-shaped" shear layers for off-center collisions.
Furthermore, we demonstrated theoretically and verified numerically that the
equivalence between the total enstrophy and the total viscous dissipation,
which holds for a single-phase flow system confined by stationary boundaries,
is not generally satisfied for the two-phase flow system containing gas-liquid
interfaces. This is attributed to the work done by the unbalanced viscous
stresses, which results from the interfacial flow and the vorticity associated
with the movement of the oscillating interface.
