Active Matter: Run-Tumble Phase Separation

MIPS — motility-induced phase separation • self-propelled particles • steric interactions

Particle Parameters

ṙᵢ = v₀ êᵢ + Σ Fᵢⱼ
θᵢ: Poisson tumbles (rate λ)

MIPS criterion:
∂μ/∂ρ < 0 ↔ v₀/λ large

Péclet: Pe = v₀²/(Dλ)
Pe = | φ_dense ≈
Run-and-tumble bacteria (E. coli) spontaneously phase-separate at high speed/density: dense clusters form because fast particles pile up behind slow/stalled ones. No attractive interactions needed — purely kinetic.