Pastes: lubricated and cohesive granular media

We analyze, in the light of experiments, a few typical aspects of the rheological or mechanical behavior of pastes, defined as dense and liquid-saturated assemblies of grains, with or without physical–chemical interactions. Emphasis is placed on the consequences of jamming, which distinguishes pastes from concentrated suspensions, contact lubrication, which distinguishes pastes from dry granular media, and cohesion. The points addressed are the following: the onset of flow, the contribution of friction in the yield stress, solid–liquid segregation and compaction, adhesion (tackiness) and cohesive rupture. To cite this article: H. Van Damme et al., C. R. Physique 3 (2002) 229–238.     

Vesicles and red blood cells in flow: From individual dynamics to rheology

The rheology of suspensions of soft particles, such as red blood cells, is a long-standing problem in science and engineering due to the complex interplay between deformable microstructure and the macroscale flow. The major challenge stems from the free-boundary nature of the particle interface. Lipid bilayer membranes that envelop cells and vesicles are particularly complex interfaces because of their unusual mechanics: the molecularly thin membrane is a highly-flexible incompressible fluid sheet. As a result, particles made of closed lipid bilayers (red cells and vesicles) can exhibit richer dynamics than would capsules and drops. We overview the key experimental observations and recent advances in the theoretical modeling of the vesicles and red blood cells in flow. To cite this article: P.M. Vlahovska et al., C. R. Physique 10 (2009).     

Rheological characterization of aging in a concentrated colloidal suspension

Suspensions of soft particles display a rheological transition when their concentration is increased: above a critical concentration, they become pasty and display a yield-stress. We report experiments on silica suspensions in the pasty phase that show how the response of the system to the application of mechanical perturbations depends on its history. Stress relaxation experiments performed after different waiting times clearly show aging taking place in the pasty phase, characterized by an aging exponent of order μ∼0.5–0.7.     

Compactification of d = 11 supergravity on S4 (or 11 = 7 + 4, too)

Eleven-dimensional supergravity can compactify spontaneously on either S⁷ or S⁴. We study the latter case, with attention to its connection with a possible gauged N = 4 supergravity in d = 7. We derive the linearized field equations and supersymmetry transformation rules for the effective d = 7 supergravity multiplet. There are five third rank antisymmetric tensors in this multiplet which are in the 5 representation of the gauge group USp(4) and they are propagated with a self-duality condition in 7 dimensions. There is also a 14 of scalar fields and they are found to propagate with a non-conformal wave operator.     

Theory of light scattering from a system of interacting Brownian particles

Starting from a N-particle diffusion equation for a system of N interacting spherical Brownian particles, a non-linear transport equation for concentration fluctuations δc(r, t) of the particles is derived. This dynamic equation is transformed into a hierarchy of equations for retarded propagators of increasing numbers of concentration fluctuations. A cluster expansion to lowest order in the average concentration results in a set of two coupled equations. The spectrum of light scattered by the interacting particles is in general not a Lorentzian, due to the non-linear term in the transport equation. For small scattering wave vectors k the width is D(ω)k², where ω is the transferred frequency. It is shown that D(0) = D_e, the effective diffusion coefficient. For a hardcore interaction potential the spectrum is Lorentzian and it is found that D_e = D₀(1 + φ), where D₀ is the diffusion constant for independent particles and φ the volume concentration of Brownian particles.     

Rheological approaches to food systems

Foods, consumer products and cosmetics belong to a wide range of colloidal and non-colloidal materials. Often, they are composite materials comprising several classes of fluid and solid constituents, including biopolymer gels, particulate suspensions, emulsions and foams. Length scales relevant for such materials may be anywhere between those associated with the molecular conformation of the ingredients up to long-scale dimensions of processing flows. The corresponding time scales may be in the sub-millisecond regime during aggregation of the ingredients or up to years during the shelf life of the final product. Rheological research of food material focuses on both the interaction between its ingredients, which might exhibit a complex rheological response function themselves and the influence of processing on the food structure and its properties. This brief overview summarizes suitable food rheology approaches and is grouped by the degree of abstraction of length scales and interactions. To cite this article: P. Fischer et al., C. R. Physique 10 (2009).     

Electronically driven phonon anomalies in transition metal carbides

Large maxima in the generalized susceptibility of χ(q) of TaC calculated from its APW band structure are found to correlate very well with observed soft phonon modes. Such maxima are not found for HfC where phonon anomalies are not observed.     

Charge displaced by a one-body potential in a Fermion assembly in terms of the highest occupied state

For (i) a slowly varying potential V(r) in a Fermi gas and (ii) N particles moving in a linear harmonic-oscillator potential, the total displaced charge and the particle density are respectively written in terms of the highest occupied state.     

The influence of surface forces on shear-induced tracer diffusion in mono and bidisperse suspensions

The shear-induced self-diffusivity of tracer particles of radius a _t = λa in a suspension of particles having a radius, a , is calculated by Stokesian dynamics for different values of the size ratio, λ , both in 2 and 3 dimensions in the binary-collision regime. The self-diffusion is found to decrease strongly when the size ratio becomes quite different from unity. On the other hand, for the same average distance of contact between two spheres, the presence of a soft force always increases greatly the diffusion compared to the effect of a hard shell which is used to model the roughness. This is particularly true for tracer particles smaller than the bath particles, where the shear-induced diffusion can be increased by many order of magnitudes in the presence of a soft force. For suspensions of monodisperse particles we show that, for low volume fraction, the diffusion coefficient is much smaller than the one predicted by the binary collision model, due to the existence of a layered structure. On the contrary at higher volume fraction, many-body collisions strongly enhance the diffusion and it appears that the value of the diffusion is quite sensitive to the presence of clusters of particles which are themselves determined by the range of interparticle forces.     

Structural and optical properties of solid-phase singlet oxygen photosensitizers based on fullerene aqueous suspensions

The relationship between the structural and photosensitizing properties of solid-phase particles of fullerene C₆₀ in aqueous suspensions is studied using the methods of absorption spectroscopy, electron spin resonance spectroscopy (ESR), X-ray diffraction, and spectrophotometry of solutions of singlet oxygen chemical traps—histidine in combination with p-nitrosodimethylaniline. Two new variants are proposed for obtaining aqueous suspensions of particles of solid-phase fullerene whose structures are disordered and whose degrees of amorphization are 67 and 40%, respectively. It is shown that an increase in the disorder of the structure of particles in suspensions and a decrease in their average size facilitate an increase in the formation efficiency of singlet oxygen by solid-phase fullerene presumably due to an in increase in the concentration of surface localized excitons.     

Dynamical properties of colloidal systems: III. Collective and self-diffusion of interacting charged particles

The formalism, developed in two earlier papers, for the dynamics of interacting Brownian particles is applied to a system of charged spherical particles in solution. Memory-type transport equations are derived for the propagators of collective and self-diffusion. The memory function for collective diffusion can be related, in the hydrodynamic limit, to the viscosity of the “fluid” of Brownian particles. The memory functions are calculated for a Debye-Hückel system, from an experimentally determined static structure factor S(k), and for an overdamped one-component plasma (OCP). In the two latter cases satisfactory agreement is found with dynamical light scattering results on solutions of polystyrene spheres; in particular, the deviation of the dynamical structure factor from a simple exponential decay can be related to memory effects. With regard to self-diffusion the velocity autocorrelation function, the mean square displacement of one particle and from it the self-diffusion coefficient D_s are calculated. Using S(k) for an actual system, $\text{D}{}_{\mathrm{s}}\text{≈}\text{1}\text{3}\text{D}{}_0$ is obtained, where D₀ is the free diffusion constant. The calculations on the basis of the overdamped OCP-model show that the dynamical properties of the experimentally investigated systems of charged polystyrene spheres can be described by this model for a wide range of scattering angles.     

Influence of the kinematical constraints on the transverse momentum correlation features

The influence of the kinematical constraints on the transverse momentum correlation features in multiparticle processes is studied by means of thedN/(d r ₁ d r ₂) distribution,r ₁ andr ₂ being the transverse momenta of the particles entering in each pair. Using a limited transverse momentum phase space we obtain for high energy reactions a simple analytical expression fordN/(d r ₁ d r ₂). This expression, similar to a phenomenological parametrization proposed for analyzing¯pp annihilation data, served to define a correlation parameter, the non vanishing value of which is due to the energy-momentum conservation constraints.     

Features of the magnetic and dielectric behavior of mesophases of chromium (III) complexes with azacyclic ligands

Two paramagnetic (1, 2) chromium metallomesogens were studied by the EPR, magnetic-susceptibility, and dielectric-spectroscopy methods. These mesogens possess columnar liquid-crystal phase polymorphism. For mesogen 1 in the columnar Col_xd phase, an irreversible structural phase transition was detected by the EPR method. An anomalous nonlinear temperature dependence of the resonance fields of the EPR line positions and of the fine-structure parameter D in the mesophases of compound 1 was observed. It was shown that this anomaly is associated with the soft mode of crystal lattice. The dielectric spectroscopy data provide support for the existence of the soft mode, which is probably due to the transition of the system from a paraelectric to a dipole-ordered state. The structure of the hexagonal columnar plastic phase of mesogen 2 is formed by a single type of paramagnetic monomer chromium center and does not exhibit any specific features.     

Comments on the use of loop reactors in sonochemical processes

For sonochemical processing on an industrial scale the traditional choice is either a batch or flow system. The former is straightforward in concept but it requires large scale powerful ultrasonic transducers capable of delivering high intensity ultrasound to large volumes of liquid. Unfortunately at the moment the cost and problems involved in building very large sonication devices for batch processes cannot justify the replacement of existing industrial processes. For this reason most sonochemists prefer some form of flow system where small quantities of reagents can be treated as they are pumped from a large vat of reagents through a smaller sonochemical reactor where high intensity ultrasound can be applied. In this short paper we draw attention to a problem which seems common in a number of papers dealing with such flow systems – a confusion between the terms continuous reactor and loop reactor. Further we emphasise the importance of calculating the actual amount of ultrasonic processing experienced by the reaction mixture within the sonication zone of a loop reactor during its operation. The parameters required for such a calculation are: ultrasonic processor volume (R_v in L), pump flow rate (F_r in L/min), stock solution volume in the reservoir (S_v in L) and the overall system operating time (S_o in min).     

Spin angular momentum of a field interacting with a plane interface

The quantization of the spin angular momentum S of a field interacting with a plane boundary is investigated. When a good set of modes is chosen, the component of S along the momentum P is formally the same as that for a free field. In the case of the presence of an evanescent wave the good modes are the same ones that appear in the filtering of the polarisation states by total reflection. But terms due to the discontinuity appear in the expressions. Although they are clearly related to the interaction field-interface, their interpretation is not obvious.     

Surface polaritons on semi-infinite anisotropic media

We have investigated the nature of polaritons which propagate on the surface of semi-infinite anisotropic dielectric and magnetic media and find that the surface polaritons are regular surface waves [i.e., the penetration constant α (ω) is real] only for special orientations of the wave vector k and of the normal to the surface n relative to the principal axes. In the case of biaxial crystals, regular surface polaritons occur when k and/or n is along a principal axis of the dielectric tensor ε(ω) for dielectric media [or the magnetic permeability tensor μ(ω) for magnetic media]. When k and n are both directed along principal axes, the surface polaritons are TM with E in the saggital plane for dielectric media. One finds that surface polaritons which are coupled photon-virtual surface dipole excitation modes can exist on “surface active” anisotropic media in addition to the familiar coupled photon-real surface dipole excitation modes. When neither k nor n are along principal axes, the surface polaritons that occur are, with the exception of special orientations, “generalized” surface waves [i.e., α(ω) is complex]. The Poynting vectors of the propagating surface polaritons are always in the plane of the surface but not, in general, along k. These results, which hold for uniaxial crystals, are also applicable to gyromagnetic media and to gyrodielectric media. This theory is also applicable to surface polaritons which propagate along the interface between two media, one or both of which is anisotropic, and with one or the other serving as the “surface active” medium.     

Interference effects in the electrical conductivity tensors of doped polar semiconductors

In this paper, we develop a general procedure, based on the Kubo formula, for finding the frequency- and wavevector-dependent electrical conductivity tensor for arbitrary polarizations of the applied electric field. This procedure gives careful consideration to both the electron and the ion contributions to the current density. We find that, in addition to the standard electron and ion contributions to the conductivity tensor, there are contributions arising from the quantum interference between the electrons and the ions. These interference effects, which will affect the infrared absorption of a material, are similar to the interference effects observed by Cerdeira, Fjeldly, and Cardona (Solid State Commun.13 (1973), 325–328; Phys. Rev. B8 (1973), 4734–4745; 9 (1974), 4344–4350) in Raman scattering from p-type Si. We then evaluate these cross terms for simple models of a variety of semiconductors. We find that these interference effects are finite-q effects, with the actual dependence of the cross terms on the wavevector q being sensitive to the symmetry of the crystal. We also find that, in principle, these cross terms may be quite large near the TO-phonon frequency ω_TO. The cross terms are evaluated for both n-type and p-type semiconductors, and it is suggested that they are probably most important for p-type materials. However, we also find that the basic structure of these terms is very similar in the two cases.