Motility-Induced Phase Separation (MIPS)

Active Brownian particles slow down in dense regions, causing a positive feedback that leads to gas-liquid phase separation without any attractive forces — a purely non-equilibrium phenomenon driven by self-propulsion.

Self-propulsion v₀ v₀ = 2.0 Rotational diff Dᵣ Dᵣ = 0.30 Packing φ φ = 0.35

ṙ = v₀ê(θ) − ∇V | θ̇ = √(2Dᵣ)η(t) | MIPS when Pe = v₀/Dᵣ·σ ≳ 4