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

Dynamic surface tension γ(<i>t</i>) 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(<i>t</i>, <i>T</i>, <i>C</i>_b) with <i>R</i>² ≥ 0.99. A Damköhler group, Da_γ = <i>k</i>_a <i>C</i>_b/<i>k</i>_d, partitions regimes (desorption-limited <1; balanced ≈ 1; adsorption-dominated >10). Extracted trends show <i>k</i>_a increases approximately linearly with <i>C</i>_b up to the CMC, while <i>k</i>_d ≈ 10^-2-10^-3 s^-1 remains nearly constant; Arrhenius fits yield consistent activation energies, and the entropy-generation rate <i>S</i>̇_gen = -<i>T</i>^-1<i>d</i>γ/<i>dt</i> peaks early then relaxes toward zero, confirming thermodynamic consistency. The framework maps raw γ(<i>t</i>) 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.