Breaking the Logarithmic Barrier: Activity-Induced Recovery of Phase Separation Dynamics in Confined Geometry

Phase separation in confined environments is a fundamental process underlying geological flows, porous filtration, emulsions, and intracellular organization. Yet, how confinement and activity jointly govern coarsening kinetics and interfacial morphology remains poorly understood. Here, we use large-scale molecular dynamics simulations to investigate vapor-liquid phase separation of passive and active fluids embedded in complex porous media. By generating porous host structures via a freeze-quench protocol, we systematically control the average pore size and demonstrate that confinement induces a crossover from the Lifshitz-Slyozov power-law growth to logarithmically slowed coarsening, ultimately arresting domain evolution. Analysis of correlation functions and structure factors reveals that confined passive systems exhibit fractal interfaces, violating Porod’s law and indicating rough morphological arrest. In contrast, introducing self-propulsion dramatically changes the coarsening pathway: activity restores smooth interfaces, breaks the confinement-induced scaling laws, and drives a transition from logarithmic to ballistic domain growth at high activity levels. Our findings reveal an activity-controlled mechanism to overcome geometric restrictions and unlock coarsening in structurally heterogeneous environments. These insights establish a unifying framework for nonequilibrium phase transitions in porous settings, with broad relevance to active colloids, catalytic media, and biologically crowded systems, where living matter routinely reorganizes within geometric constraints to sustain function.

💡 Research Summary

This paper investigates how geometric confinement and nonequilibrium activity jointly influence vapor‑liquid phase separation using large‑scale molecular dynamics (MD) simulations. The authors first generate porous host structures by a freeze‑quench protocol: a 50:50 binary Lennard‑Jones mixture is equilibrated at high temperature, quenched below its critical temperature to form bicontinuous A‑rich/B‑rich domains, and then the A‑type particles are frozen after a waiting time τ. By varying τ (800, 1000, 1600 MD time units) the average pore size dₚ is systematically tuned. The frozen A particles constitute a static, tortuous scaffold; the remaining B‑type particles constitute the fluid that will undergo phase separation within this scaffold.

For the fluid dynamics, the authors employ a Vicsek‑type alignment activity. Each particle experiences a self‑propelling force F_S = f_A v̂_rc, where v̂_rc is the normalized average velocity of neighbors within a cutoff radius r_c. To avoid heating, the speed magnitude is constrained to the passive value, so activity only reorients particle motion. A Langevin thermostat maintains the target temperature (T = 0.8 ε/k_B) and a velocity‑Verlet integrator with Δt = 0.001 is used. Thirty independent runs are averaged for statistical reliability.

Domain growth is quantified by the characteristic length ℓ(t) obtained from the first zero of the two‑point equal‑time correlation function C(r,t). The static structure factor S(k,t) provides complementary information on interfacial morphology. In bulk (unconfined) passive systems, the classic Lifshitz‑Slyozov (LS) diffusion‑limited coarsening ℓ∝t^{1/3} is observed, and S(k) follows Porod’s law S(k)∼k^{-(d+1)} indicating sharp interfaces.

When the same passive fluid is confined within the porous matrices, the dynamics change dramatically. ℓ(t) grows only logarithmically, ℓ∝ln t, and eventually saturates at a value comparable to the pore size, reflecting kinetic arrest imposed by the geometry. The correlation function shows a pronounced cusp at short distances, and S(k) exhibits a non‑Porod power law S(k)∼k^{-(d+θ)} with θ≈0.2, corresponding to a fractal interfacial dimension d_f≈2.8. Thus confinement produces rough, fractal interfaces and breaks the usual scaling universality.

Introducing Vicsek activity fundamentally alters this picture. At low activity strengths f_A the logarithmic slowdown is mitigated, while at sufficiently high f_A the growth law crosses over to ballistic (or “elastic”) scaling ℓ∝t^{β} with β≈1. Simultaneously, the structure factor regains the Porod tail, indicating that interfaces become smooth again. The activity therefore restores the classical power‑law coarsening and even accelerates it beyond the passive diffusion limit. The transition from logarithmic to ballistic growth depends on both pore size and activity: smaller pores require larger f_A to overcome geometric constraints, whereas larger pores are unlocked by relatively modest activity.

The authors interpret these findings as evidence that self‑propelled alignment generates an effective “active fluidity” that allows domains to bypass energy barriers created by the porous scaffold. Activity aligns particle motion over distances larger than the pore throat, effectively reducing the resistance to mass transport and enabling coalescence that would otherwise be prohibited. Consequently, activity acts as a tunable knob that can “unlock” arrested phase separation in heterogeneous environments.

The paper concludes by highlighting the broader relevance of the results. In engineered porous catalysts, filtration membranes, or oil‑recovery media, introducing active agents could enhance mixing and phase separation efficiency. In biological contexts, the work provides a mechanistic framework for how motor‑driven processes and cytoskeletal activity may sustain the dynamics of membraneless organelles within crowded, geometrically complex cytoplasm. Overall, the study establishes a unified perspective on nonequilibrium phase transitions in confined geometries, demonstrating that activity can overcome geometric restrictions and restore—or even accelerate—coarsening dynamics.