What is liquid-liquid equilibrium (LLE) and how is it modeled?

LLE occurs when a liquid mixture separates into two liquid phases with different compositions. Condition: component fugacities equal in both phases: x_i^alpha*gamma_i^alpha = x_i^beta*gamma_i^beta. Requires strongly non-ideal behavior (gamma >> 1). Modeled using activity coefficient models (NRTL, UNIQUAC) with parameters fitted to LLE data - these may differ from VLE parameters. Type I systems have one pair of partially miscible components; Type II have two pairs. Important for extraction, product purification, and understanding mixture stability.