Modeling the Relationship Between the Transition Time and Energy Barrier in Films from Nanofluid Stepwise Thinning

Abstract

Liquid films formed from nanofluids exhibit a ubiquitous, multiple stepwise thinning phenomenon, where the film thins layer by layer. Under film confinement, the nanoparticles experience a significant reduction in their degrees of freedom, inducing entropy-driven structural transitions. The primary goal of this research is to model this oscillatory stepwise thinning behavior and predict the associated film thickness transition time. To achieve this, the oscillatory structural film free energy was quantified from the macroscopic contact angle of the film meniscus, providing a physically grounded measure of the energy barrier. As film thickness reduces, 2D in-layer structural ordering enhances, resulting in larger energy barriers and prolonged transition times. We present a power-law model relating the transition time to the corresponding free energy barrier. The fitted scaling exponent indicates a super-linear dependence, demonstrating that progressively thinner films resist thinning disproportionately due to confinement-induced cooperative ordering. This framework establishes a quantitative, predictive basis for understanding stepwise thinning (stratification) dynamics while offering practical insights for designing stable colloidal and interfacial assemblies.