Particles at fluid-fluid interfaces: A new Navier-Stokes-Cahn-Hilliard surface- phase-field-crystal model

Active smectics on a sphere

The dynamics of active smectic liquid crystals confined on a spherical surface is explored through an active phase field crystal model. Starting from an initially randomly perturbed isotropic phase, several types of topological defects are spontaneously formed, and then annihilate during a coarsening process until a steady state is achieved. The coarsening process is highly complex involving several scaling laws of defect densities as a function of time where different dynamical exponents can be identified. In general the exponent for the final stage towards the steady state is significantly larger than that in the passive and in the planar case, i.e. the coarsening is getting accelerated both by activity and by the topological and geometrical properties of the sphere. A defect type characteristic for this active system is a rotating spiral of evolving smectic layering lines. On a sphere this defect type also determines the steady state. Our results can in principle be confirmed by dense systems of synthetic or biological active particles.

Nonlinear Viscoelasticity of Highly Ordered, Two-Dimensional Assemblies of Metal Nanoparticles Confined at the Air/Water Interface

In this study, we investigated the viscoelastic properties of metal nanoparticle monolayers at the air/water interface by dilational rheology under periodic oscillation of surface area. Au nanoparticles capped with oleylamine form a stable, dense monolayer on a Langmuir film balance. The stress response function of a nanoparticle monolayer was first analyzed using the classical Kelvin-Voigt model, yielding the spring constant and viscosity. The obtained results suggest that the monolayer of nanoparticles is predominantly elastic, forming a two-dimensional physical gel. As the global shape of the signal exhibited a clear nonlinearity, we further analyzed the data with the higher modes in the Fourier series expansion. The imaginary part of the higher mode signal was stronger than the real part, suggesting that the dissipative term mainly causes the nonlinearity. Intriguingly, the response function measured at larger strain amplitude became asymmetric, accompanied by the emergence of even modes. The significance of interactions between nanoparticles was quantitatively assessed by calculating the potential of mean force, indicating that the lateral correlation could reach up to the distance much larger than the particle diameter. The influence of surface chemical functions and core metal has also been examined by using Au nanoparticles capped with partially fluorinated alkanethiolate and Ag nanoparticles capped with myristic acid. The combination of dilational rheology and correlation analyses can help us precisely control two-dimensional colloidal assembly of metal nanoparticles with fine-adjustable localized surface plasmon resonance.

Interfacial rheology of model particles at liquid interfaces and its relation to (bicontinuous) Pickering emulsions

Interface-dominated materials are commonly encountered in both science and technology, and typical examples include foams and emulsions. Conventionally stabilised by surfactants, emulsions can also be stabilised by micron-sized particles. These so-called Pickering-Ramsden (PR) emulsions have received substantial interest, as they are model arrested systems, rather ubiquitous in industry and promising templates for advanced materials. The mechanical properties of the particle-laden liquid-liquid interface, probed via interfacial rheology, have been shown to play an important role in the formation and stability of PR emulsions. However, the morphological processes which control the formation of emulsions and foams in mixing devices, such as deformation, break-up, and coalescence, are complex and diverse, making it difficult to identify the precise role of the interfacial rheological properties. Interestingly, the role of interfacial rheology in the stability of bicontinuous PR emulsions (bijels) has been virtually unexplored, even though the phase separation process which leads to the formation of these systems is relatively simple and the interfacial deformation processes can be better conceptualised. Hence, the aims of this topical review are twofold. First, we review the existing literature on the interfacial rheology of particle-laden liquid interfaces in rheometrical flows, focussing mainly on model latex suspensions consisting of polystyrene particles carrying sulfate groups, which have been most extensively studied to date. The goal of this part of the review is to identify the generic features of the rheology of such systems. Secondly, we will discuss the relevance of these results to the formation and stability of PR emulsions and bijels.

Mesoscale models of dispersions stabilized by surfactants and colloids

In this paper we discuss and give an outlook on numerical models describing dispersions, stabilized by surfactants and colloidal particles. Examples of these dispersions are foams and emulsions. In particular, we focus on the potential of the diffuse interface models based on a free energy approach, which describe dispersions with the surface-active agent soluble in one of the bulk phases. The free energy approach renders thermodynamic consistent models with realistic sorption isotherms and adsorption kinetics. The free energy approach is attractive because of its ability to describe highly complex dispersions, such as emulsions stabilized by ionic surfactants, or surfactant mixtures and dispersions with surfactant micelles. We have classified existing numerical methods into classes, using either a Eulerian or a Lagrangian representation for fluid and for the surfactant/colloid. A Eulerian representation gives a more coarse-grained, mean field description of the surface-active agent, while a Lagrangian representation can deal with steric effects and larger complexity concerning geometry and (amphiphilic) wetting properties of colloids and surfactants. However, the similarity between the description of wetting properties of both Eulerian and Lagrangian models allows for the development of hybrid Eulerian/Lagrangian models having advantages of both representations.

Crystalline order and topological charges on capillary bridges

We numerically investigate crystalline order on negative Gaussian curvature capillary bridges. In agreement with the experimental results in [W. Irvine et al., Nature, Pleats in crystals on curved surfaces, 2010, 468, 947] we observe for decreasing integrated Gaussian curvature, a sequence of transitions, from no defects to isolated dislocations, pleats, scars and isolated sevenfold disclinations. We especially focus on the dependency of topological charge on the integrated Gaussian curvature, for which we observe, again in agreement with the experimental results, no net disclination for an integrated curvature down to -10, and an approximately linear behavior from there on until the disclinations match the integrated curvature of -12. In contrast to previous studies in which ground states for each geometry are searched for, we here show that the experimental results, which are likely to be in a metastable state, can be best resembled by mimicking the experimental settings and continuously changing the geometry. The obtained configurations are only low energy local minima. The results are computed using a phase field crystal approach on catenoid-like surfaces and are highly sensitive to the initialization.

Nonlinear hydrodynamic theory of crystallization

We present an isothermal fluctuating nonlinear hydrodynamic theory of crystallization in molecular liquids. A dynamic coarse-graining technique is used to derive the velocity field, a phenomenology which allows a direct coupling between the free energy functional of the classical density functional theory and the Navier-Stokes equation. In contrast to the Ginzburg-Landau type amplitude theories, the dynamic response to elastic deformations is described by parameter-free kinetic equations. Employing our approach to the free energy functional of the phase-field crystal model, we recover the classical spectrum for the phonons and the steady-state growth fronts. The capillary wave spectrum of the equilibrium crystal-liquid interface is in good qualitative agreement with the molecular dynamics simulations.