Dynamics of Complex Fluid-Fluid Interfaces

This chapter presents an overview of recent progress in modelling the behaviour of complex fluid–fluid interfaces with non-equilibrium thermodynamics. We will limit ourselves to frameworks employing the Gibbs dividing surface model, and start with a general discussion of the surface excess variables, introduced in this model. We then discuss conservation principles for multiphase systems with excess mass, momentum, energy, and entropy associated with the dividing surfaces. The inclusion of surface excesses in the conservation principles leads to a set of time-evolution equations for these excesses: the jump balances. The jump momentum balance is a generalised form of the Young–Laplace equation, often used for analysing surface dilatational rheology experiments. We conclude this chapter with an overview of methods to derive (nonlinear) constitutive equations for the fluxes that appear in the jump balances. In particular, we will focus on surface constitutive modelling using classical irreversible thermodynamics (combined with internal variables theory), extended irreversible thermodynamics, and the General Equation for Non-Equilibrium Reversible–Irreversible Coupling (GENERIC) framework. With these frameworks we can construct a wide range of constitutive models, which include surface generalizations of the Maxwell and Giesekus models for the surface-stress tensor, or Maxwell–Cattaneo model for the surface energy flux vector.