Dynamics of multiphase systems with complex microstructure. II. Particle-stabilized interfaces.

In this paper we use the GENERIC (general equation for nonequilibrium reversible-irreversible coupling) nonequilibrium thermodynamics framework to derive constitutive equations for the surface extra stress tensor of an interface stabilized by a two-dimensional suspension of anisotropic colloidal particles. The dependence of the surface stress tensor on the microstructure of the interface is incorporated through a dependence on a single tensorial structural variable, characterizing the average orientation of the particles. The constitutive equation for the stress tensor is combined with a time-evolution equation describing the changes in the orientation tensor as a result of the applied deformation field. We examine the predictions of the model in in-plane steady shear flow, in-plane oscillatory shear flow, and oscillatory dilatational flow. The model is able to predict the experimentally observed shear thinning behavior in surface shear flow, and also the experimentally observed emergence of even harmonics in the frequency spectrum of the surface stress in oscillatory dilatational flow. Our results show that the highly nonlinear stress-deformation behavior of interfaces with a complex microstructure can be modeled well using simple structural models like the one presented here.