Entropy-Regulated Dynamics of Surface Tension: Coupling Langmuir Kinetics with High-Precision Tensiometry

Dynamic surface tension γ(t) is widely measured but often interpreted with system-specific models that obscure general design rules. We develop a minimal kinetic-thermodynamic framework that couples two-rate adsorption-desorption with the Gibbs adsorption relation and Arrhenius temperature dependence, and validate it on ionic (SDS, CTAB) and nonionic (Tween 80) surfactants by force tensiometry from 10-80 °C (10, 20, 30, 40, 60, and 80 °C) across sub- to supra-CMC concentrations, with full uncertainty propagation. A single closed-form expression reproduces γ(t, T, C_b) with R² ≥ 0.99. A Damköhler group, Da_γ = k_a C_b/k_d, partitions regimes (desorption-limited <1; balanced ≈ 1; adsorption-dominated >10). Extracted trends show k_a increases approximately linearly with C_b up to the CMC, while k_d ≈ 10^-2-10^-3 s^-1 remains nearly constant; Arrhenius fits yield consistent activation energies, and the entropy-generation rate Ṡ_gen = -T^-1dγ/dt peaks early then relaxes toward zero, confirming thermodynamic consistency. The framework maps raw γ(t) to rate constants, energy barriers, and regime labels, enabling rational selection of surfactant chemistry, concentration, and temperature to achieve rapid interfacial equilibration in sprays, coatings, emulsification, and related processes.