Thermodynamically consistent description of the hydrodynamics of free surfaces covered by insoluble surfactants of high concentration

Abstract

In this paper we propose several models that describe the dynamics of liquid films which are covered by a high concentration layer of insoluble surfactant. First, we briefly review the 'classical' hydrodynamic form of the coupled evolution equations for the film height and surfactant concentration that are well established for small concentrations. Then we re-formulate the basic model as a gradient dynamics based on an underlying free energy functional that accounts for wettability and capillarity. Based on this re-formulation in the framework of nonequilibrium thermodynamics, we propose extensions of the basic hydrodynamic model that account for (i) nonlinear equations of state, (ii) surfactant-dependent wettability, (iii) surfactant phase transitions, and (iv) substrate-mediated condensation. In passing, we discuss important differences to most of the models found in the literature.

Modelling the formation of structured deposits at receding contact lines of evaporating solutions and suspensions

“…A related thin film model for a layer of a decomposing non-volatile binary mixture has recently been derived by Náraigh and Thiffeault 104 as a long-wave approximation to model-H. [105][106][107] A general approach of deriving such thin film evolution equations in the context of nonequilibrium thermodynamics (taking the form of a gradient dynamics based on a free energy functional), was recently proposed. 108,109 This then naturally allows one to incorporate effects like solute-dependent wettability and capillarity (including solutal Marangoni effects), and the dependence of evaporation on the osmotic pressure. In this way, the present model can readily be extended and may be employed to assess the influence of additional effects on the basic mechanism that we have describe here.…”

Swimming active droplet: A theoretical analysis

“…It increases with |φ| and diverges at |φ| = 1. An alternative approach of deriving diffusion currents in mixtures is presented in [33,34].…”

Mathematical model for self-propelled droplets driven by interfacial tension

“…17,18,[20][21][22][23][24][25] Several studies have already been made for the modeling of a deformable self-propelled droplet. [26][27][28][29][30][31][32][33] However, in the case of multiple droplets, the individual volumes are not precisely maintained in these models; hence the droplets exchange mass. Since the experimental system we consider here is macroscopic, such volume changes are usually very slow when compared a) Author to whom correspondence should be addressed.…”