Dynamics of two Interacting Drops in a Microfluidic Confinement under imposed Temperature Gradient

Abstract A tiny drop of one liquid, suspended within another, is known to 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 proximity as well as a nearby solid boundary, setting up a complex interplay between the confinement-mediated interactions and the three-dimensional nature of the drop dynamics. In this study, we present numerical solutions for the migration dynamics of a tightly confined drop couple, incorporating deformable interfaces, and Marangoni effects in the presence of dynamically evolving thermocapillary stresses induced by an imposed uniform temperature gradient. Unlike prior investigations, our work delineates a parameter that highlights the influence of the droplet surface tension forces 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 and imposed external poiseulle flow. The study reveals that the influence of the droplet surface tension forces is more prominent in flows under low confinement and where conductivity ratio between the droplet and carrier phases is low. The droplets in these scenarios deform to orient the Marangoni forces along motion with time thus reducing the influence of the droplet interactions. 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 drop microfluidics to space technology.