Longitudinal and bulk viscosities of binary fluid mixtures

Expressions for zeroth, second and fourth sum rules of longitudinal and bulk stress auto correlation functions have been derived for binary fluid mixtures. Longitudinal and bulk viscosities of an Ar–Kr mixture have been calculated using Mori's memory function formalism coupled with the sum rules of longitudinal and bulk stress auto correlation functions. The results obtained are compared with the molecular dynamics simulation. Mass dependence of the longitudinal and bulk viscosities has been studied for different compositions of an isotopic mixture at different densities and temperatures. For very large mass ratio, the longitudinal and bulk viscosities of the isotopic mixture are more dependent on mole fraction than on mass.     

Light scattering by transverse waves in supercooled liquids and application to metatoluidine

We discuss the hydrodynamic equations which describe the shear dynamics of a liquid composed of anisotropic molecules, both in its normal and its supercooled phases. We use these equations to analyze 90 depolarized light scattering experiments performed in the supercooled phase of a glass forming liquid, metatoluidine, and show that the information extracted from this analysis is consistent with independent shear viscosity measurements performed on that liquid in the same temperature range. Received 28 April 1998     

Strong anisotropic nematic order in liquid crystal polymers: [4] a quasi-elastic neutron scattering study

From quasi-elastic neutron scattering experiments performed in glassy, nematic and isotropic phases, the dynamics of oriented samples of strong anisotropic side-on fixed liquid crystal polymers have been analysed. Using the selective deuteration method, we are able to attribute motions to specific parts of the molecule in the parallel and perpendicular orientations. The motions of the whole macromolecule decrease as soon as the temperature decreases below the isotropic-nematic transition. Nevertheless, the motions of the polymer backbone, compared to the whole polymer dynamics, are systematically reduced, even in the isotropic phase. Moreover, an anisotropy of the motions is revealed, with a reduction in the direction parallel to the orientation. An harmonic character of the vibrational processes is also evidenced. We conclude that the anisotropy of the dynamic corroborates the anisotropy of conformation of the macromolecule (so-called jacketed structure). Received: 29 October 1997 / Revised: 22 January 1998/ Accepted: 11 May 1998     

Minimum description of the onset of pipe turbulence

To demonstrate essentials of the mechanism for the onset of turbulence in a pipe at Re=2000, 48 degrees of freedom are enough. The derivation from the Navier-Stokes equation uses a novel type of modes which guarantee linear stability. For the reduction of the nonlinear interactions, the modes are grouped in 3 blocks. Facilitated by these simplifications the interdependence between linear and nonlinear processes is analysed, however, just for a special example. A phenomenon resembling backflow is identified. Received 20 October 1997     

Settling and fluidization of non Brownian hard spheres in a viscous liquid

A mean field approach is used to estimate the energy dissipation during the homogeneous sedimentation or the particulate fluidization of non Brownian hard spheres in a concentrated suspension of infinite extent. Depending on inertial screening and the range of the hydrodynamic interactions, the effective buoyancy force is determined either from the average suspension density in a Stokes flow or from the fluid density in the turbulent flow regime. An energy balance then yields a settling or fluidization law depending on the particle Reynolds number in reasonable agreement with the Richardson and Zaki correlation and recent experimental results for particle settling or fluidization. We further estimate the energy dissipation in the turbulent boundary layers around the particles to precise the Reynolds number dependence of the hindered settling function in the intermediate flow regime. Received 22 February 1999 and Received in final form 14 June 1999     

Hydrodynamic screening of star polymers in shear flow

The mutual effects of the conformations of a star polymer in simple shear flow and the deformation of the solvent flow field are investigated by a hybrid mesoscale simulation technique. We characterize the flow field near the star polymer as a function of its functionality (arm number) f . A strong screening of the imposed flow is found inside the star polymer, which increases with increasing f . To elucidate the importance of hydrodynamic screening, we compare results for hydrodynamic and random solvents. The dependence of the polymer orientation angle on the Weissenberg number shows a power law behavior with super-universal exponent --independent of hydrodynamic and excluded-volume interactions. In contrast, the polymer rotation frequency changes qualitatively when hydrodynamic interactions are switched on.     

Rotational viscosity enhancement in nematic liquid crystal near a charged surface

The effective rotational viscosity coefficient and flow alignment angle are investigated for polar liquid crystals (LCs), such as 4-n-octyloxy- 4^′-cyanobiphenyl (8OCB), in the vicinity of a charged bounding surface. is calculated using the Ericksen-Leslie theory, both for stationary and nonstationary regimes. Calculations of , both for homeotropic and planar alignment of 8OCB molecules, at a charged indium tin oxide(ITO)-coated glass plate show an additional contribution to up to 7.8%. The nonequilibrium flow alignment angle (τ) is also calculated for the surface region bounded by 0.1≤y≤3.0 μm. Transition from a tumbling situation to a flow aligning regime can occur near the charged boundary surface. Received 22 November 2001 and Received in final form 31 January 2002     

Free cooling and inelastic collapse of granular gases in high dimensions

The connection between granular gases and sticky gases has recently been considered, leading to the conjecture that inelastic collapse is avoided for space dimensions higher than 4. We report Molecular Dynamics simulations of hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular medium is monitored throughout the cooling process. The behaviour is found to be very similar to that of a two-dimensional system, with a shearing-like instability of the velocity field and inelastic collapse when collisions are inelastic enough, showing that the connection with sticky gases needs to be revised. Received 17 April 2000 and Received in final form 7 June 2000     

Correlation between the viscoelastic properties of a soft crystal and its microstructure

We investigate the rheological properties of a cubic fcc phase of micelles obtained by aggregation of a triblock copolymer (PEO)₁₂₇(PPO)₄₈(PEO)₁₂₇ in water as selective solvent. The resulting soft solid is submitted to a range of stresses varying from 20 to 800Pa in Couette geometry. Creep and flow behaviour can be distinguished and interpreted in terms of structural changes previously observed by SAXS under flow. Contrasting with other systems, no discontinuity in the flow behaviour is associated with the structural changes. The strong shear thinning is interpreted from the scattering data, as resulting from the nucleation of a new structure of hexagonal compact planes parallel to the Couette walls. This creates a lubricating domain in the gap, whose size grows with the applied shear rate. We argue moreover that the very existence of flow (as a steady state opposed to creep) is associated with this so-called layer-sliding structure in a fraction, however small, of the sample. Received on 4 June 1999 and Received in final form 6 September 1999     

Hydrodynamic interactions in self similar structures, such as polymers

We study the hydrodynamic properties of polymers and more generally self-similar structures using a new recursion model. The hydrodynamic interaction between monomers is modeled by the standard Green's function of Stokes flow in which an ultrametric distance is substituted for the usual Euclidean distance. This leads to a model where the long-range hydrodynamic interactions and the long-range correlations of the polymer conformation can both be accounted for and yet allow for analytical solutions. We explore the asymptotic as well as the finite size corrections to the scaling behavior with this model. In order to compare the results of the present scheme with more conventional techniques a generalized version of the existing mean field results by Kirkwood and Riseman for the hydrodynamic drag is introduced. Received 26 August 1998 and Received in final form 7 December 1998     

Hydrodynamic vector potentials

Solving the Navier-Stokes equation for incompressible fluids is greatly simplified by the solution of the vorticity equation. To accomplish this for three-dimensional flows requires vector potentials. These potentials are not only useful to take care of the incompressibility. Their modes are suitable also as test functions since the familiar Galerkin procedure does not work. The new method is checked by examples with known results and its relation to the classical approach with the stream function is clarified. The principle demonstration, however, concerns the transition to turbulence in plane shear flows. A simple layer of long rolls with axes parallel to the basic flow incites the transition. Received 20 August 2001     

Transition to chaos via the quasi-periodicity and characterization of attractors in confined Bénard-Marangoni convection

A study of dynamic regimes in Bénard-Marangoni convection was carried out for various Prandtl and Marangoni numbers in small aspect ratio geometries (Γ = 2.2 and 2.8). Experiments in a small hexagonal vessel, for a large range of the Marangoni number (from 148 to 3636), were carried out. Fourier spectra and an auto-correlation function were used to recognize the various dynamic regimes. For given values of the Prandtl number (Pr = 440) and aspect ratio (Γ = 2.2), mono-periodic, bi-periodic and chaotic states were successively observed as the Marangoni number was increased. The correlation dimensions of strange attractors corresponding to the chaotic regimes were calculated. The dimensions were found to be larger than those obtained by other authors for Rayleigh-Bénard convection in aspect ratio geometries of the same order. The transition from temporal chaos to spatio-temporal chaos was also observed. For Γ = 2.2, when larger values of the Marangoni number were imposed (Ma = 1581 for Pr = 160 and Ma = 740 for Pr = 440), spatial modes were involved through the convective pattern dynamics.     

Capillary filling with pseudo-potential binary Lattice-Boltzmann model

We present a systematic study of capillary filling for a binary fluid by using a mesoscopic lattice Boltzmann model for immiscible fluids describing a diffusive interface moving at a given contact angle with respect to the walls. The phenomenological way to impose a given contact angle is analysed. Particular attention is given to the case of complete wetting, that is contact angle equal to zero. Numerical results yield quantitative agreement with the theoretical Washburn’s law, provided that the correct ratio of the dynamic viscosities between the two fluids is used. Finally, the presence of precursor films is experienced and it is shown that these films advance in time with a square-root law but with a different prefactor with respect to the bulk interface.     

Structure and rheology of the defect-gel states of pure and particle-dispersed lyotropic lamellar phases

We present important new results from light-microscopy and rheometry on a moderately concentrated lyotropic smectic, with and without particulate additives. Shear-treatment aligns the phase rapidly, except for a striking network of oily-streak defects, which anneals out much more slowly. If spherical particles several microns in diameter are dispersed in the lamellar medium, part of the defect network persists under shear-treatment, its nodes anchored on the particles. The sample as prepared has substantial storage and loss moduli, both of which decrease steadily under shear-treatment. Adding particles enhances the moduli and retards their decay under shear. The data for the frequency-dependent storage modulus after various durations of shear-treatment can be scaled to collapse onto a single curve. The elasticity and dissipation in these samples thus arises mainly from the defect network, not directly from the smectic elasticity and hydrodynamics. Received 19 April 1999 and Received in final form 20 May 1999     

Resonant quantum coherence of magnetization at excited states in nanospin systems with different crystal symmetries

The quantum interference effects induced by the Wess-Zumino term, or Berry phase are studied theoretically in resonant quantum coherence of the magnetization vector between degenerate states in nanometer-scale single-domain ferromagnets in the absence of an external magnetic field. We consider the magnetocrystalline anisotropy with trigonal, tetragonal and hexagonal crystal symmetry, respectively. By applying the periodic instanton method in the spin-coherent-state path integral, we evaluate the low-lying tunnel splittings between degenerate excited states of neighboring wells. And the low-lying energy level spectrum of mth excited state are obtained with the help of the Bloch theorem in one-dimensional periodic potential. The energy level spectrum and the thermodynamic properties of magnetic tunneling states are found to depend significantly on the total spins of ferromagnets at sufficiently low temperatures. Possible relevance to experiments is also discussed. Received 15 December 1999     

Soft Dynamics simulation. 1. Normal approach of two deformable particles in a viscous fluid and optimal-approach strategy

Discrete simulation methods are efficient tools to investigate the behaviors of complex fluids such as dry granular materials or dilute suspensions of hard particles. By contrast, materials made of soft and/or concentrated units (emulsions, foams, vesicles, dense suspensions) can exhibit both significant elastic particle deflections (Hertz-like response) and strong viscous forces (squeezed liquid). We point out that the gap between two particles is then not determined solely by the positions of their centers, but rather exhibits its own dynamics. We provide the first ingredients of a new discrete numerical method, named Soft Dynamics, to simulate the combined dynamics of particles and contacts. As an illustration, we present the results for the approach of two particles. We recover the scaling behaviors expected in three limits: the Stokes limit for very large gaps, the Poiseuille-lubricated limit for small gaps and even smaller surface deflections, and the Hertz limit for significant surface deflections. We find that for each gap value, an optimal force achieves the fastest approach velocity. The principle of larger-scale simulations with this new method is provided. They will consitute a promising tool for investigating the collective behaviors of many complex materials.