Lattice Boltzmann simulation of a binary fluid with different phase viscosities and its application to fingering in two dimensions

A thermodynamically consistent lattice Boltzmann scheme for simulating the flow of a binary fluid is extended to allow the fluid components to have different viscosities. The approach is tested for the shear and Poiseuille flow of layered immiscible fluids and for the dispersion relation and the damping of a capillary wave. We then consider the fingering that results when a fluid is displaced by a less viscous fluid in a two-dimensional channel. The finger widths obtained match the results of Reinelt and Saffman [#!Reinelt85!#], but differ somewhat from those of Halpern and Gaver [#!Halpern94!#] for capillary numbers above 2. A limiting finger width close to 1/2 is obtained for high capillary numbers and high viscosity ratios. Received 25 May 1999 and Received in final form 19 November 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.     

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     

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     

Thermodynamic and transport properties in equilibrium air plasmas in a wide pressure and temperature range

Thermodynamic and transport properties of high temperature equilibrium air plasmas have been calculated in a wide pressure ( atm) and temperature range ( K). The results have been obtained by using a self-consistent approach for the thermodynamic properties and higher order approximation of the Chapman-Enskog method for the transport coefficients. Debye-Hükel corrections have been considered in the thermodynamic properties while collision integrals of charge-charge interactions have been obtained by using a screened Coulomb potential. Calculated values have been fitted by closed forms ready to be inserted in fluid dynamic codes.     

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     

Structural and dynamical properties of aqueous suspensions of NaPSS (HPSS) at very low ionic strength

Results on the structural and dynamical properties of aqueous solutions of NaPSS (HPSS) are reported. Most samples of previous measurements, including our own, are contaminated by the presence of (temporal) aggregates. The emphasis of this paper lies on investigations of well purified samples at very low ionic strength where interacting effects are maximum. As previously reported, this can be achieved by pumping the suspension through ion exchange resin by means of a tube-pump, using filters of pore size. Information has been extracted from static and dynamic light scattering and viscosity measurements. A second maximum is observed in the scattering curves versus wavenumber for the first time. It is discussed on the basis of two current models describing the structure of charged macromolecules. The short time dynamics reflects the measured intensity. Detailed viscosity data in comparison of those of rodlike (TMV), slightly flexible so-called fd virus particles (length 880 nm) are used to confirm the interpretation of the light scattering results. The recently observed maximum in the reduced viscosity could be confirmed. Received: 5 May 1997 / Revised: 1 September 1997 / Accepted: 10 November 1997     

Transport properties of high temperature air in local thermodynamic equilibrium

In the paper new calculated transport coefficients of air in the temperature range 50-100 000 K are presented. The results have been obtained by means of the perturbative Chapman-Enskog method, assuming that the plasma is in local thermodynamic equilibrium (LTE). The calculations include viscosity, thermal conductivity, electric conductivity and multicomponent diffusion coefficients. For the calculation, a recent compilation of collision integrals obtained by Capitelli et al. [1] has been utilized. Analytical expression for all transport coefficients and thermodynamic parameters of the air plasma are also reported. Received 17 November 1999     

Free precession and transverse relaxation of hyperpolarized <Superscript>129</Superscript>Xe gas detected by SQUIDs in ultra-low magnetic fields

We studied the free precession of the nuclear magnetization of hyperpolarized ¹²⁹Xe gas in external magnetic fields as low as B₀ = 4.5 nT, using SQUIDs as magnetic flux detectors. The transverse relaxation was mainly caused by the restricted diffusion of ¹²⁹Xe in the presence of ambient magnetic field gradients. Its pressure dependence was measured in the range from 30 mbar to 850 mbar and compared quantitatively to theory. Motional narrowing was observed at low pressure, yielding transverse relaxation times of up to 8000 s.     

Molecular flow and wall collision age distributions

The use of storage cells has become a standard technique for internal gas targets in conjunction with high energy storage rings. In case of spin-polarized hydrogen and deuterium gas targets the interaction of the injected atoms with the walls of the storage cell can lead to depolarization and recombination. Thus the number of wall collisions of the atoms in the target gas is important for modeling the processes of spin relaxation and recombination. It is shown in this article that the diffusion process of rarefied gases in long tubes or storage cells can be described with the help of the one-dimensional diffusion equation. Mathematical methods are presented that allow one to calculate collision age distributions (CAD) and their moments analytically. These methods provide a better understanding of the different aspects of diffusion than Monte Carlo calculations. Additionally it is shown that measurements of the atomic density or polarization of a gas sample taken from the center of the tube allow one to determine the possible range of the corresponding density weighted average values along the tube. The calculations are applied to the storage cell geometry of the HERMES internal polarized hydrogen and deuterium gas target. Received 9 July 2001 and Received in final form 18 September 2001     

Electron swarm coefficients in 1,1,1,2 tetrafluoroethane (R134a) and its mixtures with Ar

Using a pulsed Townsend technique, we have measured the drift velocity, the longitudinal diffusion coefficient and the effective ionisation coefficient of electrons in R134a and R134a-Ar over a wide range of the density-reduced electric field intensity, E/N. Regarding the measurement of the electron drift velocities and of the effective ionization coefficients, we have covered a wider range than that hitherto achieved for pure R134a. Both the electron drift velocity and the effective ionisation coefficient have been found in very good agreement with those published in the literature, covering a shorter range of E/N. On the other hand, the swarm coefficients on R134a-Ar are, to the best of our knowledge, the first to be published. It is hoped that these data will be of interest for the test/derivation of electron collision cross sections for this important hydrofluorocarbon gas, which is nowadays of great use in gaseous detectors.     

Microscopic quantities in discharge in air obtained from an electro-mechanical experiment

The results of an experiment of impulsive electrodynamics [Eur. Phys. J. D 15, 87 (2001)] are shown to be due to electrons and ions in run-aways. By fitting the theoretical values with the experimental data, the values of microscopic quantities, at present unknown, can be derived, thus opening a new field of research. The obtained quantities are three, namely: (i) the contribution to air ionization due to the current (mainly of run-aways) and characterized by a parameter ρ; (ii) the product ζ=n_ein_ie (where n_ei is the number of ions extracted by one electron in run-away and n_ie the number of electrons extracted by one run-away ion colliding on the electrodes in electrical discharges with temperatures (for non run-aways) of ≃4×10⁴ K); (iii) the reconstruction time constant of the high-energy tail of the distribution function, from which we can derive the concentration per unit time of electrons and ions which become run-aways. The value is useful for the theoretical explanation of the electronic noise with power spectral density inversely proportional to the frequency.     

Enskog’s kinetic theory of dense gases for chemically reacting binary mixtures, II: Light scattering and sound propagation

Enskog’s kinetic theory for a symmetric moderately dense reaction A+A?B+B is used to determine Fick’s and Fourier’s law. The transport coefficients of diffusion, thermal-diffusion rate and thermal conductivity are represented graphically for endothermic and exothermic reactions and are analyzed as a function of the activation energy and of the density of the mixture. The Onsager reciprocity relations are numerically investigated and verified. The problems related to sound propagation and light scattering are investigated for such a mixture and it is shown that the influence of chemical reactions on phase velocity, attenuation coefficient and light scattering spectra is more pronounced for rarefied gases although there is a considerable change in these quantities as the mixture becomes denser.     

Shear viscosity and entropy of quark matter

We consider the shear viscosity of a system of quarks and its ratio to the entropy density above the critical temperature for deconfinement. Expressions for both quantities are derived in the quasi-particle approximation and calculations are carried out for different modeling of the quark self-energy, also allowing for a temperature dependence of the effective mass and width. Beyond the temperature dependence, the behaviour of the viscosity and the entropy density is discussed in terms of the strength of the coupling and of the main characteristics of the quark self-energy. A comparison with existing approaches is also discussed.     

Universality in diffusion front growth dynamics

We have studied the scaling properties of diffusion fronts by numerical calculations based on the mean field approach in the context of a lattice gas model, performed in a triangular lattice. We find that the height-height correlation function scales with time t and length l as C(l, t) ≈l ^α f (t/l ^α/β) with α = 0.62±0.01 and β = 0.39±0.02. These exponent values are identical to those characterising the roughness of the diffusion fronts evolving through a square lattice [1,2], thus confirming their universality. Received 14 November 2001 / Received in final form 20 April 2002 Published online 31 July 2002     

Directed transport of an asymmetric particle pair induced by non-equilibrium conditions

The hopping motion of a classical bounded pair of two particles along a chain is investigated. It is shown that in the asymmetric case of the system dynamics including excited states which differ from the respective ground states by the barrier to be overcome by one of the two particles, the over- and underpopulation of these excited states leads to a directed motion of the particle pair. Thereby, overpopulation results in one direction of motion, whereas underpopulation results in the opposite direction, and the mean velocity is determined by the amount of over-resp. underpopulation. For small deviations from equilibrium, the system exhibits linear response well known from other ratchet-type models. Possible generalizations and applications are discussed. Received 17 August 2001 and Received in final form 11 October 2001     

Segregation by thermal diffusion in moderately dense granular mixtures

A theory based on a solution of the inelastic Enskog equation that goes beyond the weak dissipation limit is used to determine the thermal diffusion factor of a binary granular mixture under gravity. The Enskog equation that aims to describe moderate densities neglects velocity correlations but retains spatial correlations arising from volume exclusion effects. As expected, the thermal diffusion factor provides a segregation criterion that shows the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the system (masses, sizes, composition, density and coefficients of restitution). The form of the phase diagrams for the BNE/RBNE transition is illustrated in detail in the tracer limit case, showing that the phase diagrams depend sensitively on the value of gravity relative to the thermal gradient. Two specific situations are considered: i) absence of gravity, and ii) homogeneous temperature. In the latter case, after some approximations, our results are consistent with previous theoretical results derived from the Enskog equation. Our results also indicate that the influence of dissipation on thermal diffusion is more important in the absence of gravity than in the opposite limit. The present analysis, which is based on a preliminary short report of the author (Phys. Rev. E 78, 020301(R) (2008)), extends previous theoretical results derived in the dilute limit case.     

Slowly rocking symmetric, spatially periodic Hamiltonians: The role of escape and the emergence of giant transient directed transport

The nonintegrable Hamiltonian dynamics of particles placed in a symmetric, spatially periodic potential and subjected to a periodically varying field is explored. Such systems can exhibit a rich diversity of unusual transport features. In particular, depending on the setting of the initial phase of the drive, the possibility of a giant transient directed transport in a symmetric, space-periodic potential when driven with an adiabatically varying field arises. Here, we study the escape scenario and corresponding mean escape times of particles from a trapping region with the subsequent generation of a transient directed flow of an ensemble of particles. It is shown that for adiabatically slow inclination modulations the unidirectional flow proceeds over giant distances. The direction of escape and, hence, of the flow is entirely governed whether the periodic force, modulating the inclination of the potential, starts out initially positive or negative. In the phase space, this transient directed flow is associated with a long-lasting motion taking place within ballistic channels contained in the non-uniform chaotic layer. We demonstrate that for adiabatic modulations all escaping particles move ballistically into the same direction, leading to a giant directed current.     

Growth kinetics of polymer crystals in bulk

Temperature-dependent measurements of spherulite growth rates carried out for i-polystyrene, poly(ε -caprolactone) and linear polyethylene show that the controlling activation barrier diverges at a temperature which is 14K, 22K and 12K, respectively, below the equilibrium melting points. We discuss the existence of such a “zero growth temperature” T _zg in the framework of a recently introduced thermodynamic multiphase scheme and identify T _zg with the temperature of a (hidden) transition between the melt and a mesomorphic phase which mediates the crystal growth. The rate-determining step in our model of crystal growth is the attachment of chain sequences from the melt onto the lateral face of a mesomorphic layer at the growth front. The necessary straightening of the sequence prior to an attachment is the cause of the activation barrier. A theory based on this view describes correctly the observations. With a knowledge of T _zg it is possible to fully establish the nanophase diagram describing the stability ranges of crystalline and mesomorphic layers in a melt. An evaluation of data from small-angle X-ray scattering, calorimetry and optical growth rate measurements yields heats of transition and surface free energies of crystals and mesophase layers, as well as the activation barrier per monomer associated with the chain stretching. According to the theory, the temperature dependence of the crystallization rate is determined by both the activation energy per monomer and the surface free energy of the preceding mesomorphic layer. Data indicate that the easiness of crystallization in polyethylene is first of all due to a particularly low surface free energy of the mesomorphic layer.     

Dumbbell transport and deflection in a spatially periodic potential

We present theoretical results on the deterministic and stochastic motion of a dumbbell carried by a uniform flow through a three-dimensional spatially periodic potential. Depending on parameters like the flow velocity, there are two different kinds of movement: transport along a potential valley and a stair-like motion oblique to the potential trenches. The crossover between these two regimes, as well as the deflection angle, depend on the size of the dumbbell. Moreover, thermal fluctuations cause a resonance-like variation in the deflection angle as a function of the dumbbell extension.