A study on the method of short-time approximation – Criteria for applicability. (November 2015) - Casandra, Alvin
Highlights: General criteria for the short-time approximation technique were proposed. The error in diffusivity generated by the short-time approximation was evaluated. A nearly zero deviation of the D estimate was observed for surfactants at C0 / a = ∼2. Conditions ( π and t ∗ ) for applying the short-time approximation technique were explored. Abstract: Despite its widespread use in the determination of adsorption mechanisms and the estimation of surfactant diffusivity, the short-time approximation method, used for linearly fitting experimental dynamic surface tension data, should be validly applied only over a very specific range of time intervals or surface pressures. Therefore, the definition of general criteria for the applicability of this method and for error evaluation in diffusivity estimations is fundamental. In this work, a theoretical numerical simulation of the short-time approximation method was conducted, and general benchmarks for its accurate utilization were investigated. Specifically, for systems assuming planar gas–liquid surfaces, diffusion-controlled kinetics and a Langmuir adsorption isotherm, simple rules were developed in terms of limiting surface pressure ( π max ) and dimensionless time ( t ∗ max ) as a function of dimensionless surfactant concentration ( C 0 / a ). For values greater than the limiting ( maximal ) conditions, the dynamic surface tension curve deviates from the short-time approximation straight line, and thus, the corresponding linear fitting could lead to significant errors in evaluating the diffusivity. The simple criteria proposed in this study thus precisely define the range of applicability for the short-time approximation method.