Gradient dynamics models for liquid films with soluble surfactant

Thiele U, Archer A, Pismen L

Research article (journal) | Peer reviewed

Abstract

In this paper we propose equations of motion for the dynamics of liquid films of surfactant suspensions that consist of a general gradient dynamics framework based on an underlying energy functional. This extends the gradient dynamics approach to dissipative nonequilibrium thin-film systems with several variables and casts their dynamic equations into a form that reproduces Onsager's reciprocity relations. We first discuss the general form of gradient dynamics models for an arbitrary number of fields and discuss simple well-known examples with one or two fields. Next we develop the three-field gradient dynamics model for a thin liquid film covered by soluble surfactant and discuss how it automatically results in consistent convective (driven by pressure gradients, Marangoni forces, and Korteweg stresses), diffusive, adsorption or desorption, and evaporation fluxes. We then show that in the dilute limit, the model reduces to the well-known hydrodynamic form that includes Marangoni fluxes due to a linear equation of state. In this case the energy functional incorporates wetting energy, surface energy of the free interface (constant contribution plus an entropic term), and bulk mixing entropy. Subsequently, as an example, we show how various extensions of the energy functional result in consistent dynamical models that account for nonlinear equations of state, concentration-dependent wettability, and surfactant and film bulk decomposition phase transitions. We conclude with a discussion of further possible extensions towards systems with micelles, surfactant adsorption at the solid substrate, and bioactive behavior.

Details about the publication

Volume1
StatusPublished
Release year2016
Language in which the publication is writtenEnglish
DOI10.1103/PhysRevFluids.1.083903

Authors from the University of Münster

Thiele, Uwe
Professur für Theoretische Physik (Prof. Thiele)
Center for Nonlinear Science
Center for Multiscale Theory and Computation