Thermodynamic reconciliation of stable nanobubbles: pressure, surface tension, and chemical potential

Bulk nanobubbles exhibit exceptionally long lifetimes in solution, fundamentally contradicting classical thermodynamic predictions, which suggest rapid dissolution due to immense internal pressure. In this review we first discuss the theoretical challenges underlying this contradiction: (i) when system characteristic scales shrink to the nanometer range, traditional thermodynamic quantities like pressure and interfacial tension are no longer well-defined intensive properties because they exhibit a strong dependence on size and curvature; (ii) the interfacial phase of nanobubbles remains essentially a black box, with its microscopic structure and composition either unknown or difficult to measure, rendering prediction of surface tension and internal pressure from the interfacial phase often misleading. Then we discuss the fundamental advantage of chemical potential for nanoscale systems: equality of chemical potential remains valid regardless of changes in system size or interfacial characteristics, providing a more reliable foundation for predicting nanobubble properties from known environmental characteristics.