Motility-Induced Phase Separation (MIPS)

MIPS arises purely from motility — no attractive forces needed. Fast self-propelled particles accumulate where they slow down (dense regions), creating a positive feedback: dense → slow → denser. The effective swim pressure P_swim = ρv₀²τ/d decreases with density (anomalous EOS), triggering a mechanical instability analogous to van der Waals. The critical Péclet number Pe = v₀/(λσ) must exceed ~5–10 depending on φ. Above the binodal, the system phase-separates into a dense solid-like cluster and a dilute gas of fast swimmers.