Channel instability in binary mixtures with differential diffusivity

Abstract

Rupture dynamics and pinch-off phenomena are essential to understanding instabilities in both fluid dynamics and biological systems. In this thesis, I study the rupture behavior of two-dimensional, channel-like structures formed in a binary mixture of particles with differential diffusivities. Using computational simulations, I explore the evolution of these instabilities under a variety of conditions, focusing on the roles of key parameters such as aspect ratio, particle density, and external drift. Although the observed behavior bears similarities to the Plateau-Rayleigh instability (PRI), the underlying mechanism is fundamentally different, as PRI is inherently three-dimensional. Instead, the instability investigated here emerges from non-equilibrium interactions unique to two-dimensional systems. Notably, comparable behaviors have been reported in chiral fluids, supporting the idea that this is a genuinely new type of instability. The results presented in this work indicate that the instability is not a finite-size effect but an intrinsic feature of systems driven by differential diffusivity. In the latter part of the thesis, I extend the analysis to study the surface dynamics of the active interface. By applying tools from capillary wave theory, I show that the interface roughening follows equilibrium-like scaling laws, even though the system is inherently out of equilibrium. This surprising result allows for the definition of an effective surface tension, whose evolution reveals a gradual weakening of interfacial cohesion leading up to rupture. These findings provide a deeper understanding of how non-equilibrium forces shape interface behavior and suggest new avenues for investigating instability and pattern formation in active matter.