Generalized surface momentum balances for the analysis of surface dilatational data

Dilatational rheological properties of interfaces are often determined using drop tensiometers, in which the interface of the droplet is subjected to oscillatory area changes. A dynamic surface tension is determined either by image analysis of the droplet profile or by measuring the capillary pressure. Both analysis modes tend to use the Young-Laplace equation for determining the dynamic surface tension. For complex fluid-fluid interfaces there is experimental evidence that this equation does not describe the response of the interface to deformations adequately. Generalizations of this equation are available, and in this comment we will discuss these generalizations, and the conditions for which they reduce to the Young-Laplace equation.     

A fixture for interfacial dilatational rheometry using a rotational rheometer

In characterizing complex fluid-fluid interfaces, interfacial rheometry has become an important tool to indirectly probe the interfacial microstructure and molecular interactions. It can also be useful to obtain the constitutive properties of an interface for calculating the interfacial flows of complex fluid-fluid interfaces. A number of devices for measuring interfacial shear rheology have been designed and have been thoroughly validated. However, although a range of devices for measuring interfacial dilatational rheology exist, they do not always allow for a proper separation of the effects of dynamic surface tension, curvature elasticity, Marangoni stresses, bulk flow effects and the desired dilatational rheological material functions. In the present work it is investigated if a fixture for a standard rotational rheometer can be designed which probes the dilatational viscoelastic properties of a planar complex fluid-fluid interface. A modification of the double wall ring geometry for shear rheometry is proposed, which creates a mixed but analyzable flow field. The use of a mixed flow field inherently limits the sensitivity for the dilatational properties, but some advantages over existing techniques are presented, in particular for insoluble monolayers. More importantly, the analysis illustrate some generic aspects on the use of mixed interfacial flow fields for measuring the surface rheological properties.     

Nonlinear rheological models for structured interfaces

The GENERIC formalism is a formulation of nonequilibrium thermodynamics ideally suited to develop nonlinear constitutive equations for the stress-deformation behavior of complex interfaces. Here we develop a GENERIC model for multiphase systems with interfaces displaying nonlinear viscoelastic stress-deformation behavior. The link of this behavior to the microstructure of the interface is described by including a scalar and a tensorial structural variable in the set of independent surface variables. We derive an expression for the surface stress tensor in terms of these structural variables, and a set of general nonlinear time evolution equations for these variables, coupling them to the deformation field. We use these general equations to develop a number of specific models, valid for application near equilibrium, or valid for application far beyond equilibrium.     

An extended rational thermodynamics model for surface excess fluxes

In this paper, we derive constitutive equations for the surface excess fluxes in multiphase systems, in the context of an extended rational thermodynamics formalism. This formalism allows us to derive Maxwell-Cattaneo type constitutive laws for the surface extra stress tensor, the surface thermal energy flux vector, and the surface mass flux vector, which incorporate a direct coupling to their corresponding bulk fluxes in the adjacent bulk phases. These constitutive laws also incorporate contributions to the time evolution of the surface excess fluxes from spatial inhomogeneities in these flux fields. These phenomenological equations can be used to model the dynamic behavior of complex viscoelastic interfaces in multiphase systems, in the small deformation limit.     

Dynamics of encapsulation and controlled release systems based on water-in-water emulsions: Liposomes and polymersomes

The deformation relaxation behavior of two types of vesicles, liposomes and polymersomes, was investigated using a general nonequilibrium thermodynamics theory based on the interfacial transport phenomena (ITP) formalism. Liposomes and polymersomes are limiting cases of this theory with respect to rheological behavior of the interfaces. They represent respectively viscous, and viscoelastic surface behavior. We have determined the longest relaxation time for a small perturbation of the interfaces for both these limiting cases. Parameter maps were calculated which can be used to determine when surface tension, bending rigidity, spontaneous curvature, interfacial permeability, or surface rheology dominate the response of the vesicles. In these systems up to nine different scaling regimes were identified for the relaxation time of a deformation with droplet size, with scaling exponent n ranging from 0 to 4.     

Dynamic surface tension of complex fluid-fluid interfaces: A useful concept, or not?

Dilatational moduli are typically determined by subjecting interfaces to oscillatory area deformations, and are often defined in terms of the difference between the dynamic or transient surface tension of the interface (the surface tension in its deformed state), and the surface tension of the interface in its non-deformed state. Here we will discuss the usefulness of the dynamic surface tension concept in the characterization of dilatational properties of complex fluid-fluid interfaces. Complex fluid-fluid interfaces are interfaces stabilized by components which form mesophases (two-dimensionional gels, glasses, or (liquid) crystalline phases), as a result of in-plane interactions between the components. We will show that for such interfaces dilatational properties are not exclusively determined by the exchange of surface active components between interface and adjoining bulk phases, but also by in-plane viscoelastic stresses. The separation of these contributions remains a challenging problem which remains to be solved.     

Viscometric characterization of cobalt nanoparticle-based magnetorheological fluids using genetic algorithms

The rheological flow curves (shear stress vs. shear rate) of a nanoparticle cobalt-based magnetorheological fluid can be modeled using Bingham-plastic and Herschel–Bulkley constitutive models. Steady-state rheological flow curves were measured using a parallel disk rheometer for constant shear rates as a function of applied magnetic field. Genetic algorithms were used to identify constitutive model parameters from the flow curve data.     

Computer simulations of critical phenomena and phase behaviour of fluids

Computer simulation techniques such as Monte Carlo (MC) and Molecular Dynamics (MD) methods yield numerically exact information (apart from statistical errors) on model systems of classical statistical mechanics. However, a systematic limitation is the restriction to a finite (and often rather small) particle number N (or box linear dimension L, respectively). This limitation is particularly restrictive near critical points (due to the divergence of the correlation length of the order parameter) and for the study of phase equilibria (possibly involving interfaces, droplets, etc.). Starting out with simple lattice gas (Ising) models, finite size scaling analyses have been developed to overcome this limitation. These techniques work for both simple Lennard-Jones fluids and their mixtures, including generalizations to approximate models for quadrupolar fluids such as carbon dioxide, benzene etc. and various mixtures, whose phase behaviour can be predicted. A combination of MC and MD allows the study of dynamic critical phenomena, and specialised techniques (umbrella sampling plus thermodynamic integration) yield the surface free energy of droplets as function of droplet size. Thus, computer simulation has become a versatile and widely applicable tool for the study of fluids.     

Anomalous transport in disordered dynamical systems

We consider simple extended dynamical systems with quenched disorder. It is shown that these systems exhibit anomalous transport properties such as the total suppression of chaotic diffusion and anomalous drift. The relation to random walks in random environments, in particular to the Sinai model, explains also the occurrence of ageing in such dynamical systems. Anomalous transport is explained by spectral properties of corresponding propagators and by escape rates in these systems. For special cases we provide a connection to quantum mechanical tight-binding models and Anderson localization. New classes of anomalous transport behavior with clear deviations from the behavior of Sinai type are found for generalizations of these models.     

A class of partially solvable two-dimensional quantum models with periodic potentials

The supersymmetric approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the corresponding wave functions (partial solvability) for several models. These models are not amenable to conventional separation of variables, and they can be considered as two-dimensional generalizations of Lamé, associated Lamé, and trigonometric Razavy potentials. All these models have the symmetry operators of fourth order in momenta, and one of them (the Lamé potential) obeys the property of self-isospectrality.     

On the Regression Model for Generalized Normal Distributions

The traditional linear regression model that assumes normal residuals is applied extensively in engineering and science. However, the normality assumption of the model residuals is often ineffective. This drawback can be overcome by using a generalized normal regression model that assumes a non-normal response. In this paper, we propose regression models based on generalizations of the normal distribution. The proposed regression models can be used effectively in modeling data with a highly skewed response. Furthermore, we study in some details the structural properties of the proposed generalizations of the normal distribution. The maximum likelihood method is used for estimating the parameters of the proposed method. The performance of the maximum likelihood estimators in estimating the distributional parameters is assessed through a small simulation study. Applications to two real datasets are given to illustrate the flexibility and the usefulness of the proposed distributions and their regression models.     

Nonperturbative gadget for topological quantum codes

Many-body entangled systems, in particular topologically ordered spin systems proposed as resources for quantum information processing tasks, often involve highly nonlocal interaction terms. While one may approximate such systems through two-body interactions perturbatively, these approaches have a number of drawbacks in practice. In this Letter, we propose a scheme to simulate many-body spin Hamiltonians with two-body Hamiltonians nonperturbatively. Unlike previous approaches, our Hamiltonians are not only exactly solvable with exact ground state degeneracy, but also support completely localized quasiparticle excitations, which are ideal for quantum information processing tasks. Our construction is limited to simulating the toric code and quantum double models, but generalizations to other nonlocal spin Hamiltonians may be possible.     

Protein adsorption and interfacial rheology interfering in dilatational experiment

The static and dilatational response of β-lactoglobulin fibrils and native β-lactoglobulin (monomers) at water-air and water-oil interfaces (pH 2) was measured using the pendant drop method. The resulting adsorption behavior and viscoelasticity is dependent of concentration and adsorption time. The interfacial pressure of the β-lactoglobulin fibrils obtained in static measurements was 16–18?mN/m (against air) and 7?mN/m (against oil) for all concentrations. With higher concentrations, faster adsorption kinetics and slightly higher interfacial and surface pressure is achieved but did not lead to higher viscoelastic moduli. The transient saturation of the interface is similar for both the fibril solution and the monomers, however the fibril solution forms a strong viscoelastic network. To evaluate the superimposed adsorption behavior and rheological properties, the formed interfacial layer was subjected to dilatational experiments, which were performed by oscillating the surface area of the drop in sinusoidal and sawtooth (diagonal) deformation manner. The sinusoidal oscillations (time depended area deformation rate) result in a complex interfacial tension behavior against air and oil interfaces and show remarkable differences during compression and expansion as emphasized by Lissajous figures. For diagonal (constant area deformation rate) experiments, a slight bending of the interfacial tension response was observed at low frequencies emphasizing the influence of protein adsorption during rheological measurements.     

Empirical rheological model for rough or grooved bonded interfaces

In the industrial sector, it is common to use metal/adhesive/metal structural bonds. The cohesion of such structures can be improved by preliminary chemical treatments (degreasing with solvents, alkaline, or acid pickling), electrochemical treatments (anodising), or mechanical treatments (abrasion, sandblasting, grooving) of the metallic plates. All these pretreatments create some asperities, ranging from roughnesses to grooves. On the other hand, in damage solid mechanics and in non-destructive testing, rheological models are used to measure the strength of bonded interfaces. However, these models do not take into account the interlocking of the adhesive in the porosities. Here, an empirical rheological model taking into account the interlocking effects is developed. This model depends on a characteristic parameter representing the average porosity along the interface, which considerably simplifies the corresponding stress and displacement jump conditions. The paper deals with the influence of this interface model on the ultrasonic guided modes of the structure.     

Shearing active gels close to the isotropic-nematic transition

We study numerically the rheological properties of a slab of active gel close to the isotropic-nematic transition. The flow behavior shows a strong dependence on the sample size, boundary conditions, and on the bulk constitutive curve, which, on entering the nematic phase, acquires an activity-induced discontinuity at the origin. The precursor of this within the metastable isotropic phase for contractile systems (e.g., actomyosin gels) gives a viscosity divergence; its counterpart for extensile suspensions admits instead a shear-banded flow with zero apparent viscosity.     

Bubble oscillation and inertial cavitation in viscoelastic fluids

Non-linear acoustic oscillations of gas bubbles immersed in viscoelastic fluids are theoretically studied. The problem is formulated by considering a constitutive equation of differential type with an interpolated time derivative. With the aid of this rheological model, fluid elasticity, shear thinning viscosity and extensional viscosity effects may be taken into account. Bubble radius evolution in time is analyzed and it is found that the amplitude of the bubble oscillations grows drastically as the Deborah number (the ratio between the relaxation time of the fluid and the characteristic time of the flow) increases, so that, even for moderate values of the external pressure amplitude, the behavior may become chaotic. The quantitative influence of the rheological fluid properties on the pressure thresholds for inertial cavitation is investigated. Pressure thresholds values in terms of the Deborah number for systems of interest in ultrasonic biomedical applications, are provided. It is found that these critical pressure amplitudes are clearly reduced as the Deborah number is increased.     

Various kinds of two-dimensional rheological models

Two-dimensional rheological models consisting of two-dimensional elastic, viscous, and plastic elements are introduced in order to represent more closely the real rheological behavior of various isotropic and orthotropic viscoelastic, elastoplastic, viscoplastic, and elastoviscoplastic bodies in the plane-stress or plane-strain state, respectively. These models represent schematically the unit area of a body and consist of plane elastic, viscous, and plastic regions with rectangular straight boundaries lying in the principal direction of orthotropy.

The two-dimensional rheological models may be considered either from the phenomenological or from the structural point of view. They may also represent rheological structures with variously oriented multiphase systems having elastic, viscous, and plastic properties. The configuration of such models may correspond to the rheological nonhomogeneity of bodies and to both kinds of orthotropy arising either from the orthotropic properties of elastic, plastic, and viscous phases or from various configurations of phases. These models may also represent nonsymmetrical shear effects which are analogous to those arising in elastic Cosserat media.

The main differences between the presented two-dimensional models and the usual rheological models, which are one-dimensional, consist of the possibilities of representing directly two-dimensional rheological behavior, the anisotropy of rheological processes, and nonsymmetrical shear effects in rheological bodies.     

Characteristics of defect formation in aluminium oxide reinforced bioactive glass

Composite materials containing a bioactive phase (sol–gel-derived bioglass) and a mechanical strength phase (bubble alumina or sintered corundum) are promising materials for repair of living tissues. The microstructure of the biocomposite material, its mechanical properties and the processing routes used are all very strongly interrelated. SEM was used to investigate the phenomena occurring at the two phase interfaces. Porosity is one of the most common defects in this composite, which negatively affects strength. The systems were irradiated with beta radiation at different doses. Absorption and luminescence of these biocomposites were studied with the main attention paid to trap centres. The measurement results prove a high sensitivity of our experimental method to the effects of the surface glass modifications.     

Slow coarsening in a class of driven systems

The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher dimensions. In particular we study a system of three types of particles that diffuse under local conserving dynamics in two dimensions. Arguments and numerical studies are presented indicating that the coarsening process in any number of dimensions is logarithmically slow in time. A key feature of this behavior is that the interfaces separating the various growing domains are macroscopically smooth (well approximated by a Fermi function). This implies that the coarsening mechanism in one dimension is readily extendible to higher dimensions. Received 3 April 2000