A simple mathematical model of time-dependent interfacial tension

Erwin A. Vogler

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


A mathematical model of time-dependent interfacial tension γ(t) is described which couples empirical relationships for concentration-dependent interfacial tension γ(Cs) with theoretical expressions for time-dependent surfactant surface concentration Cs(t). Method is illustrated with four different diffusion theories and a single γ(Cs) model. The applied γ(Cs) relationship was different from the Szyszkowski equation and used steady-state interfacial tension as a reference state. Resultant γ(t) formulations were in closed analytical form with a single adjustable kinetic parameter, simple to use in data-fitting applications or computational experiments. Utility was demonstrated by application to dynamic measurements of liquid-vapor interfacial tension for aqueous solutions of a nonionic detergent (Tween-80), three food proteins, and a system of polyvinyl alcohols. Concentration-dependence of fitted kinetic parameters provided adsorption kinetic constants. Distinct kinetic-control regimes were separated and quantified.

Original languageEnglish (US)
Pages (from-to)228-236
Number of pages9
JournalJournal of Colloid And Interface Science
Issue number1
StatePublished - Jan 1 1989

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Surfaces, Coatings and Films
  • Colloid and Surface Chemistry


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