  A numerical study of the homo-interactions between two falling droplets and
between two rising bubbles in a strongly coupled dusty plasma medium is
presented in this article. This strongly coupled dusty plasma is considered as
a viscoelastic fluid using the generalized hydrodynamic fluid model formalism.
Two factors that affect homo-interactions are taken into account: the initial
spacing and the coupling strength of the medium. Three different spacings
between two droplets are simulated: widely, medium, and closely. In each case,
the coupling strength has been given as mild-strong and strong. It is shown
that the overall dynamic is governed by the competition between the
acceleration of two droplets/bubbles due to gravity and the interaction due to
the closeness of the droplets/bubbles. Especially in viscoelastic fluids, the
closeness between two droplets/bubbles, aside from their initial separation, at
a later time may result from shear waves that emerge from rotating vorticies.
For widely-spaced, unlike classical hydrodynamic fluids, we find that shear
waves in viscoelastic fluids facilitate the pairing between two
bubbles/droplets. In the case of medium-spaced, the two new dipoles of unequal
strength blobs exhibit a circular motion and exchange their partners. For
closely-spaced, the droplet/bubble fall/rise is suppressed as the coupling
strength of the medium increases. Numerous two-dimensional simulations have
been carried out. This work is a continuation of the work done in parts I (V.
S. Dharodi and A. Das, J. Plasma Phys. 87 (02), 905870216 (2021)) and II (V. S.
Dharodi, J. Plasma Phys. 87 (04), 905870402 (2021)).
