  A tiny drop of one liquid, suspended within another, may be set into motion
aligned with an imposed thermal gradient, as influenced by thermocapillary
action stemming from the gradients in interfacial tension due to the local
variations in temperature. In real-world situations, however, such drops do not
remain in isolation, as they interact with their neighbouring entities
including other drops in the proximity as well as a nearby solid boundary,
setting up a complex interplay between the confinement-mediated interactions
and three-dimensional nature of the droplet dynamics. In this study, we present
numerical solutions for the migration dynamics of a tightly-confined
drop-couple, incorporating deformable interfaces, film flow, and Marangoni
effects in the presence of dynamically evolving thermocapillary stresses
induced by an imposed uniform temperature gradient. Unlike prior
investigations, our work highlights the influence of the confinement towards
orchestrating non-trivial features of drop migration, as dictated by an
intricate coupling of the thermal and flow fields amidst the interferences of
the domain boundaries. The study reveals that hydrodynamic interactions
resulting from a juxtaposition of these influences deform the drops in a unique
manner as compared to the characteristics evidenced from previously reported
studies, causing a distortion of the local thermal fields around them. The
consequent alteration in the drop velocities is shown to govern their migration
in a distinctive manner, presenting unique signatures as compared to more
restrictive scenarios studied previously. These findings hold significance in
designing thermocapillary-driven micro-confined systems for controlling drop
trajectories under an imposed thermal field, bearing far-reaching implications
in a plethora of overarching applications ranging from droplet microfluidics to
space technology.
