Aggregation of particles settling in shear-thinning fluids

We have experimentally studied the coaxial settling of three identical non-Brownian spheres in a shear-thinning fluid at small Reynolds numbers. While settling, the particles create corridors of reduced viscosity in their wake and, if they are initially close enough to one another, they can form stable clusters. By analogy with previous results obtained on two-particle interaction in the first part of this work, we show that the particle velocities can be satisfactorily described using a first-order expression and assuming that the reduced viscosity remains constant. We report systematic experiments performed at different initial separation distances between particles and the use of our simple model allows the prediction of the settling behaviour and in particular the conditions for clusters formation. We thus show that particle aggregation can occur even for large initial distances between particles and within times that are small compared to the time scales in Newtonian fluids.     

Viscosity minimum in bimodal concentrated suspensions under shear

We study a model of concentrated suspensions under shear in two dimensions. Interactions between suspended particles are dominated by direct-contact viscoelastic forces and the particles are neutrally bouyant. The bimodal suspensions consist of a variable proportion between large and small droplets, with a fixed global suspended fraction. Going beyond the assumptions of the classical theory of Farris (R.J. Farris, Trans. Soc. Rheol. 12, 281 (1968)), we discuss a shear viscosity minimum, as a function of the small-to-large-particle ratio, in shear geometries imposed by external body forces and boundaries. Within a linear-response scheme, we find the dependence of the viscosity minimum on the imposed shear and the microscopic drop friction parameters. We also discuss the viscosity minimum under dynamically imposed shear applied by boundaries. We find a reduction of macroscopic viscosity with the increase of the microscopic friction parameters that is understood using a simple two-drop model. Our simulation results are qualitatively consistent with recent experiments in concentrated bimodal emulsions with a highly viscous or rigid suspended component. Received 28 June 2002 RID="a" ID="a"e-mail: ernesto@pion.ivic.ve     

Coherence properties of two trapped particles

We analyse the coherence properties of two particles trapped in a one-dimensional harmonic potential. This simple model allows us to derive analytic expressions for the first and second order coherence functions. We investigate their properties depending on the particle nature and the temperature of the quantum gas. We find that at zero temperature non-interacting bosons and fermions show very different correlations, while they coincide for higher temperatures. We observe atom bunching for bosons and atom anti-bunching for fermions. When the effect of s-wave scattering between bosons is taken into account, we find that the range of coherence is enhanced or reduced for repulsive or attractive potentials, respectively. Strongly repelling bosons become in some way more “fermion-like" and show anti-bunching. Their first order coherence function, however, differs from that for fermions. Received 19 September 2002 Published online 4 February 2003     

Lyapunov exponent, generalized entropies and fractal dimensions of hot drops

We calculate the maximal Lyapunov exponent, the generalized entropies, the asymptotic distance between nearby trajectories and the fractal dimensions for a finite two-dimensional system at different initial excitation energies. We show that these quantities have a maximum at about the same excitation energy. The presence of this maximum indicates the transition from a chaotic regime to a more regular one. In the chaotic regime the system is composed mainly of a liquid drop while the regular one corresponds to almost freely flowing particles and small clusters. At the transitional excitation energy the fractal dimensions are similar to those estimated from the Fisher model for a liquid-gas phase transition at the critical point. Received: 16 March 2001 / Accepted: 12 July 2001     

Noise correlations in shear flows

We consider the effects of a shear on velocity fluctuations in a flow. The shear gives rise to a transient amplification that not only influences the amplitude of perturbations but also their time correlations. We show that, in the presence of white noise, time correlations of transversal velocity components are exponential and that correlations of the longitudinal components are exponential with an algebraic prefactor. Cross correlations between transversal and downstream components are strongly asymmetric and provide a clear indication of non-normal amplification. We suggest experimental tests of our predictions. Received 26 February 2002 / Received in final form 11 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: bruno.eckhardt@physik.uni-marburg.de RID="b" ID="b"Also at: Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India     

Interactions and correlations of particulate inclusions in a columnar phase

We calculate the elastic-field-mediated interaction between macroscopic particles in a columnar hexagonal phase. The interaction is found to be long-ranged and non-central, with both attractive and repulsive parts. We show how the interaction modifies the particle correlations and the column fluctuations. We also calculate the interaction of particles with the topological defects of the columnar phase. The particle-defect interaction reduces the mobility of the defects. Received 14 March 2002 and Received in final form 13 August 2002 RID="a" ID="a"e-mail: rjoy@physics.iisc.ernet.in     

Strange attractor simulated on a quantum computer

We show that dissipative classical dynamics converging to a strange attractor can be simulated on a quantum computer. Such quantum computations allow to investigate efficiently the small scale structure of strange attractors, yielding new information inaccessible to classical computers. This opens new possibilities for quantum simulations of various dissipative processes in nature. Received 10 August 2002 Published online 29 October 2002 RID="a" ID="a"e-mail: dima@irsamc.ups-tlse.fr RID="b" ID="b"UMR 5626 du CNRS     

Hydromagnetic transverse instability of two highly viscous fluid-particle flows with finite ion Larmor radius corrections

A linear analysis of the combined effect of viscosity, finite ion Larmor radius and suspended particles on Kelvin-Helmholtz instability of two superposed incompressible fluids in the presence of a uniform magnetic field is carried out. The magnetic field is assumed to be transverse to the direction of streaming. A general dispersion relation for such a configuration has been obtained using appropriate boundary conditions. The stability analysis is discussed analytically, and the obtained results are numerically confirmed. Some special cases are recovered and corrected. The limiting cases of absence of suspended particles (or fluid velocities) and finite Larmor radius, absence of suspended particles are discussed in detail. In both cases, all other physical parameters are found to have stabilizing as well as destabilizing effects on the considered system. In the former case, the kinematic viscosity is found to has a stabilizing effect, while in the later case, the finite Larmor radius is found to has a stabilizing influence for a vortex sheet. It is shown also that both finite Larmor radius and kinematic viscosity stabilizations for interchange perturbations are similar to the stabilization effect due to a magnetic field for non-interchange perturbations. Received 13 January 2003 Published online 24 April 2003 RID="a" ID="a"Also at: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt. e-mail: m.elsayed@uaeu.ac.ae     

Phase transitions in a cluster molecular field approximation

Cluster molecular field approximations represent a substantial progress over the simple Weiss theory where only one spin is considered in the molecular field resulting from all the other spins. In this work we discuss a systematic way of improving the molecular field approximation by inserting spin clusters of variable sizes into a homogeneously magnetised background. The density of states of these spin clusters is then computed exactly. We show that the true non-classical critical exponents can be extracted from spin clusters treated in such a manner. For this purpose a molecular field finite size scaling theory is discussed and effective critical exponents are analysed. Reliable values of critical quantities of various Ising and Potts models are extracted from very small system sizes. Received 30 September 2002 / Received in final form 25 November 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: pleim@theorie1.physik.uni-erlangen.de     

DFT studies of ionic vibrations in Na clusters

We use time-dependent density functional theory coupled to molecular dynamics for ionic motion to compute the spectra of ionic vibrations in small Na clusters. Comparison with results from the distance dependent tight-binding approach shows good agreement between these two very different methods. We discuss the evolution of the spectra with cluster size and charge and the impact of ionic vibrations on the optical response. Received 23 July 2001 / Received in final form 5 July 2002 Published online 8 October 2002 RID="a" ID="a"e-mail: suraud@irsamc.ups-tlse.fr     

Preparation and characterization of cobalt-based nanostructured materials

Nano-sized cobalt clusters passivated by alkane-thiol molecules were obtained by the action of concentrated thiol solutions on micrometric cobalt particles. Thiol molecules caused an erosive process on the metal grains with the consequent formation of nano-sized metal debris and cobalt thiolate as by-product. The final material microstructure was composed by cobalt clusters embedded into a continuum cobalt thiolate matrix. Depending on the thiol molecule length, the material texture ranged from rubbery to waxy. These new types of nanocomposite materials were found to be crystalline, thermally stable up to ca. 300 ^°C, intensely red colored, and high hydrophobic. In addition, they generated polymeric structures when dissolved in non-polar solvents. Received 27 September 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: giancaro@unina.it     

Flow birefringence,stress optical rule and rheology of four micellar solutions with the same low shear viscosity

The flow birefringence and the rheological properties of four viscoelastic solutions having nearly the same zero shear viscosity and subjected to shear flows are investigated in the linear and non-linear domains. The surfactant used for the samples is the cetyltrimethylammonium chloride in water at the concentration of 100 mmol/l with an organic salt, the sodium salicylate. The low shear viscosity curve versus the salt concentration is non-monotonic and has two maxima separated by a minimum forming four domains in which the salt concentration is chosen. For the two solutions belonging to the inner branch, i.e. between the two maxima, a simple Maxwellian behaviour is observed and shear banding occurs as confirmed by the flow birefringence pictures. Contrary to the results of P. Fisher (1996) where the unstable flow regime is restricted to the first decreasing part of the low shear viscosity curve of a cetylpyridinium chloride solution, we show that shear banding exits in a wider domain of the salt concentration. Received 18 November 2002 / Published online: 1 April 2003 RID="a" ID="a"e-mail: Decruppe@lpli.sciences.univ-metz.fr     

Osmotic force resisting chain insertion in a colloidal suspension

We consider the problem of inserting a stiff chain into a colloidal suspension of particles that interact with it through excluded volume forces. The free energy of insertion is associated with the work of creating a cavity devoid of colloid and sufficiently large to accommodate the chain. The corresponding work per unit length is the force that resists the entry of the chain into the colloidal suspension. In the case of a hard sphere fluid, this work can be calculated straightforwardly within the scaled particle theory; for solutions of flexible polymers, on the other hand, we employ simple scaling arguments. The forces computed in these ways are shown, for nanometer chain and colloid diameters, to be of the order of tens of pN for solution volume fractions of a few tenths. These magnitudes are argued to be important for biophysical processes such as the ejection of DNA from viral capsids into the cell cytoplasm. Received 18 December 2002 Published online: 16 April 2003 RID="a" ID="a"e-mail: castel@chem.ucla.edu RID="b" ID="b"Present address: Courant Institute of Mathematical Sciences, NYU, New York, New York 10012, USA     

Scattering of a sound wave by a vibrating surface

We report an experimental study of the scattering of a sound wave of frequency f by a surface vibrating at frequency F. Both the Doppler shift at the vibrating surface and acoustic nonlinearities in the bulk of the fluid, generate the frequencies f±nF (n integer) in the spectrum of the scattered wave. We show that these two contributions can be separated because they scale differently with respect to the vibration frequency and to the distance between the vibrating scatterer and the detector. We determine the parameter ranges in which one or the other mechanism dominates and present quantitative studies of these two regimes. Received 2 December 2002 / Received in final form 27 March 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: fauve@physique.ens.fr RID="b" ID="b"UMR 8550     

Stability of charged metal clusters in the vicinity of an ionic charge

Stability of highly charged metal clusters in the electric field of an external ion is investigated with the classical liquid drop model. We study the optimum shape of the cluster which has a local minimum of the total energy, taking account of the effects of the surface charge polarization on the Coulomb energy and the cluster deformation on the surface energy. We find that the cluster deformation greatly affects the total energy of the system and that a cluster with a fissility larger than some critical value 0.7-0.8 can become unstable against deformation. We investigate the local competition between the Coulomb force and the surface tension at the cluster surface and show that the surface charge polarization which is induced by the external electric field significantly affects the shape of the cluster and its stability. Received 5 November 2002 / Received in final form 27 January 2003 Published online 11 March 2003 RID="a" ID="a"e-mail: hamada@konan-u.ac.jp     

Flow phase diagrams for concentration-coupled shear banding

After surveying the experimental evidence for concentration coupling in the shear banding of wormlike micellar surfactant systems, we present flow phase diagrams spanned by shear stress Σ (or strain rate ) and concentration, calculated within the two-fluid, non-local Johnson-Segalman (d-JS-φ) model. We also give results for the macroscopic flow curves Σ(ˉ,ˉφ) for a range of (average) concentrations ˉφ. For any concentration that is high enough to give shear banding, the flow curve shows the usual non-analytic kink at the onset of banding, followed by a coexistence “plateau” that slopes upwards, dΣ/dˉ > 0. As the concentration is reduced, the width of the coexistence regime diminishes and eventually terminates at a non-equilibrium critical point [Σ_c,ˉφ_c,ˉ_c]. We outline the way in which the flow phase diagram can be reconstructed from a family of such flow curves, Σ(ˉ,ˉφ), measured for several different values of ˉφ. This reconstruction could be used to check new measurements of concentration differences between the coexisting bands. Our d-JS-φ model contains two different spatial gradient terms that describe the interface between the shear bands. The first is in the viscoelastic constitutive equation, with a characteristic (mesh) length l. The second is in the (generalised) Cahn-Hilliard equation, with the characteristic length ξ for equilibrium concentration-fluctuations. We show that the phase diagrams (and so also the flow curves) depend on the ratio r ≡ l /ξ, with loss of unique state selection at r = 0. We also give results for the full shear-banded profiles, and study the divergence of the interfacial width (relative to l and ξ) at the critical point. Received: 20 December 2002 / Accepted: 24 April 2003 / Published online: 11 June 2003 RID="a" ID="a"e-mail: physf@irc.leeds.ac.uk RID="b" ID="b"e-mail: p.d.olmsted@leeds.ac.uk     

An advected-field method for deformable entities under flow

We study dynamics of a deformable entity (such as a vesicles under hydrodynamical constraints). We show how the problem can be solved by means of Green's functions associated with the Stokes equations. A gauge-field invariant formulation makes the study of dynamics efficient. However, this procedure has its short-coming. For example, if the fluids are not Newtonian, then no Green's function is available in general. We introduce a new approach, the advected field one, which opens a new avenue of applications. For example, non-Newtonian entities can be handled without additional deal. In addition problems like budding, droplet break-up in suspensions, can naturally be treated without additional complication. We exemplify the method on vesicles filled by a fluid having a viscosity contrast with the external fluid, and submitted to a shear flow. We show that beyond a viscosity contrast (the internal fluid being more viscous), the vesicle undergoes a tumbling bifurcation, which has a saddle-node nature. This bifurcation is known for blood cells. Indeed red cells either align in a shear flow or tumble according to whether haematocrit concentration is high or low. Received 19 December 2001 / Received in final form 31 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: chaouqi.misbah@ujf-grenoble.fr     

Distribution of local entropy in the Hilbert space of bi-partite quantum systems: origin of Jaynes' principle

For a closed bi-partite quantum system partitioned into system proper and environment we interpret the microcanonical and the canonical condition as constraints for the interaction between those two subsystems. In both cases the possible pure-state trajectories are confined to certain regions in Hilbert space. We show that in a properly defined thermodynamical limit almost all states within those accessible regions represent states of some maximum local entropy. For the microcanonical condition this dominant state still depends on the initial state; for the canonical condition it coincides with that defined by Jaynes' principle. It is these states which thermodynamical systems should generically evolve into. Received 13 June 2002 / Received in final form 14 November 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: jochen@theol.physik.uni-stuttgart.de     

Self-affine random surfaces

We consider general d-dimensional random surfaces that are characterized by power-law power spectra defined in both infinite and finite spectral regions. The first type of surfaces belongs to the class of ideal fractals, whereas the second possess both the smallest and the largest scales and physically is more realistic. For both types we calculate the structure functions (SF) exactly; in addition for the second type we obtain the SF's asymptotic expansions. On this basis we show that the surfaces are (in statistical sense) self-affine and approximately self-affine, respectively. Depending on the value of the spectral exponent, we find imbalance between the finite size effects which results in systematic discrepancy in the scaling properties between the two types of surfaces. Explicit expressions for the topothesy, and in the case of second type of surfaces for the large correlation length and cross-over distances are also derived. Received 3 October 2001 / Received in final form 5 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: oyordanov@aubg.bg