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PubMed1999

Hydrodynamic fluctuations in the Kolmogorov flow: linear regime.

The Landau-Lifshitz fluctuating hydrodynamics is used to study the statistical properties of the linearized Kolmogorov flow. The relative simplicity of this flow allows a detailed analysis of the fluctuation spectrum from near equilibrium regime up to the vicinity of the first convective instability threshold. It is shown that in the long time limit the flow behaves as an incompressible fluid, regardless of the value of the Reynolds number. This is not the case for the short time behavior where the incompressibility assumption leads in general to a wrong form of the static correlation functions, except near the instability threshold. The theoretical predictions are confirmed by numerical simulations of the full nonlinear fluctuating hydrodynamic equations.

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PubMed1999

Heavy-ion-beam-induced hydrodynamic effects in solid targets.

It is expected that after the completion of a new high current injector, the heavy-ion synchrotron (SIS) at the Gesellschaft für Schwerionforschung (GSI) Darmstadt will accelerate U(+28) ions to energies of the order of 200 MeV/u. The use of a powerful rf buncher will reduce the pulse length to about 50 ns, and employment of a multiturn injection scheme will provide 2 x 10(11) particles in the beam that correspond to a total energy of the order of 1 kJ. This upgrade of the SIS, hopefully, will be completed by the end of the year 2001. These beam parameters lead to a specific power deposition of the order of 1-2 TW/g in solid matter that will provide temperatures of about 10 eV. Such low specific power deposition will induce hydrodynamic effects in solid materials, and one may design appropriate beam-target interaction experiments that could be used to investigate the equation of state of matter under extreme conditions. The purpose of this paper is to propose suitable target designs with optimized parameters for the future GSI experiments with the help of one and two-dimensional hydrodynamic simulations. Cylindrical geometry is the natural geometry for highly focused ion beams, and therefore cylindrical targets are the most appropriate for this type of interaction experiments. The numerical simulations presented in this paper show that one can experimentally measure the characteristic sound speed in beam heated targets which is an important physical parameter. Moreover, one can study the propagation of ion-beam-induced shock waves in the solid materials. Different values for the specific power deposition, namely, 10, 25, 50, and 100 kJ/g, have been used. In some cases the pulse length is assumed to be 40 ns while in others it is considered to be 50 ns. Various materials including lead, aluminum, and solid neon have been used.

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PubMed1999

Dissipation in ferrofluids: mesoscopic versus hydrodynamic theory.

Part of the field dependent dissipation in ferrofluids occurs due to the rotational motion of the ferromagnetic grains relative to the viscous flow of the carrier fluid. The classical theoretical description due to Shliomis (Zh. Eksp. Teor. Fiz. 61, 2411 (1971) [Sov. Phy JETP 34, 1291 (1972)]) uses a mesoscopic treatment of the particle motion to derive a relaxation equation for the nonequilibrium part of the magnetization. Complementary, the hydrodynamic approach of Liu [Phys. Rev. Lett. 70, 3580 (1993)] involves only macroscopic quantities and results in dissipative Maxwell equations for the magnetic fields in the ferrofluid. Different stress tensors and constitutive equations lead to deviating theoretical predictions in those situations, where the magnetic relaxation processes cannot be considered instantaneous on the hydrodynamic time scale. We quantify these differences for two situations of experimental relevance, namely, a resting fluid in an oscillating oblique field and the damping of parametrically excited surface waves. The possibilities of an experimental differentiation between the two theoretical approaches is discussed.

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PubMed2000

Hydrodynamic-flow-driven wetting in thin film polymer blends: growth kinetics and morphology

A thin film of deuterated poly(methyl methacrylate) (A) and poly(styrene-ran-acrylonitrile) at the critical composition is annealed in the two phase region to induce simultaneous phase separation and wetting of the A-rich phase at the surface. Using forward recoil spectrometry, the wetting layer thickness is found to grow linearly with time at 185 degrees C and 190 degrees C. After selective etching of A, atomic force microscopy reveals a depletion layer having a bicontinuous, phase separated morphology. The A-rich tubes in this layer provide a pathway for rapid transport of the wetting phase from the bulk to the surface via hydrodynamic flow. Taken together, fast wetting layer growth t(1) and connectivity between the wetting layer and bulk provide unambiguous support for hydrodynamic-flow-driven wetting in thin film polymer blends.

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PubMed2000

Hamiltonian dynamics of vortex and magnetic lines in hydrodynamic type systems

Vortex line and magnetic line representations are introduced for a description of flows in ideal hydrodynamics and magnetohydrodynamics (MHD), respectively. For incompressible fluids, it is shown with the help of this transformation that the equations of motion for vorticity Omega and magnetic field follow from a variational principle. By means of this representation, it is possible to integrate the hydrodynamic type system with the Hamiltonian H=integral|Omega|dr and some other systems. It is also demonstrated that these representations allow one to remove from the noncanonical Poisson brackets, defined in the space of divergence-free vector fields, the degeneracy connected with the vorticity frozenness for the Euler equation and with magnetic field frozenness for ideal MHD. For MHD, a new Weber-type transformation is found. It is shown how this transformation can be obtained from the two-fluid model when electrons and ions can be considered as two independent fluids. The Weber-type transformation for ideal MHD gives the whole Lagrangian vector invariant. When this invariant is absent, this transformation coincides with the Clebsch representation analog introduced by V.E. Zakharov and E. A. Kuznetsov [Dokl. Ajad. Nauk 194, 1288 (1970) [Sov. Phys. Dokl. 15, 913 (1971)]].

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PubMed2000

Generalized hydrodynamics of binary liquids: transverse collective modes

The parameter-free generalized collective modes approach in eight-variable approximation is applied for investigation of transverse dynamics of Lennard-Jones liquid Kr-Ar beyond the hydrodynamic region. We find four branches of propagating eigenmodes in the spectrum of transverse collective excitations. Different basis sets of dynamical variables are applied to estimate the origin of different branches in the spectrum. It is shown that for large wave numbers the general feature of transverse collective excitations is their "partial" character, while in hydrodynamic limit they are formed by collective behavior of liquid. A detailed analysis of the separated contributions from different collective modes into time correlation functions and spectral functions is performed. The condition of existence of high-frequency mass-concentration waves is derived. It is shown that high-frequency collective excitations, caused by the mass-concentration fluctuations, reflect some properties of optic phonon modes in solids.

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PubMed2000

Hydrodynamic fluctuations in the kolmogorov flow: nonlinear regime

In a previous paper [I. Bena, M. Malek Mansour, and F. Baras, Phys. Rev. E 59, 5503 (1999)] the statistical properties of linearized Kolmogorov flow were studied, using the formalism of fluctuating hydrodynamics. In this paper the nonlinear regime is considered, with emphasis on the statistical properties of the flow near the first instability. The normal form amplitude equation is derived for the case of an incompressible fluid and the velocity field is constructed explicitly above (but close to) the instability. The relative simplicity of this flow allows one to analyze the compressible case as well. Using a perturbative technique, it is shown that close to the instability threshold the stochastic dynamics of the system is governed by two coupled nonlinear Langevin equations in Fourier space. The solution of these equations can be cast into the exponential of a Landau-Ginzburg functional, which proves to be identical to the one obtained for the case of an incompressible fluid. The theoretical predictions are confirmed by numerical simulations of the nonlinear fluctuating hydrodynamic equations.

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PubMed2000

Crossover from the hydrodynamic regime to the thermal fluctuation regime in a two-dimensional phase-separating binary fluid containing surfactants

Extensive simulations were carried out to investigate the crossover between the hydrodynamic regime at intermediate stage and the thermal fluctuation regime at late stage in a phase-separating binary fluid/surfactant system in two dimensions. The existence of the crossover and its dependence on the surfactant concentration were analyzed using Kawasaki and Ohta's interface kinetic equation [Physica A 118, 175 (1983)]. The analysis showed that there should exist a critical surfactant concentration, above which thermal fluctuations dominate phase separation at all times. Simulations suggested that the crossover exists and the hydrodynamic regime shrinks when surfactant concentration increases. Simulations also demonstrated that the trapped surfactants seen in a previous study [Phys. Rev. E 59, 2109 (1999)] can remain trapped for a time much longer than the time needed to form well segregated domains, in spite of the presence of significant thermal fluctuations.

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PubMed2001

Dewetting hydrodynamics in 1+1 dimensions.

A model for the phase transition between partial wetting and dewetting of a substrate has been formulated that explicitly incorporates the hydrodynamic flow during the dewetting process in 1+1 dimensions. The model simulates a fluid layer of finite thickness on a substrate in coexistence with a dry part of the substrate and a gas phase above the substrate. Under nonequilibrium "dewetting" conditions, the front between the dry part and the wet part of the surface moves towards the wet part inducing hydrodynamic flow inside the wet layer. In more general terms, the model handles two immiscible fluids with a freely movable interface in an inhomogeneous external force field. Handling the interface by a new variant of the phase-field model, we obtain an efficient code with well-defined interfacial properties. In particular, the (free) energy can be chosen at will. We demonstrate that our model works well in the viscosity range of creeping flow and we give qualitative results for the higher Reynolds numbers. Connections to experimental realizations are discussed.

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PubMed2001

Necessity of bunch compression for heavy-ion-induced hydrodynamics and studies of beam fragmentation in solid targets at a proposed synchrotron facility.

This paper presents two-dimensional numerical simulations of hydrodynamic response of a solid lead cylindrical target that is irradiated by an intense uranium beam having a particle energy of 1 GeV/u and that consists of 10(12) particles. Different time profiles have been considered for the beam power that include a case where the beam consists of five identical parabolic bunches with equal separation between neighboring bunches as well as a beam that consists of a single bunch. For the single bunch case we consider two different values for pulse length, namely, 1000 and 50 ns, respectively. Moreover we allow for two different values for the beam radius that is 0.5 and 1.0 mm, respectively. These calculations show that in order to achieve a high degree of beam-target coupling, it is absolutely essential to use a single bunched beam that has a reasonably short pulse length, which is 50 ns in this case. Such a large beam-target coupling efficiency is highly desirable for creating high-density strongly coupled plasmas as well as for studies that involve fragmentation of the projectile ions as the beam passes through solid matter. If the pulse length is assumed to be too long, substantial hydrodynamic expansion of the target material occurs during the early stages of irradiation that leads to significant reduction in the energy deposition by the ions that are delivered in the later part of the pulse. In case of the five-bunch configuration, heating caused by the first bunch is so strong that the target is completely distorted. As a result, the ions that are delivered in the later four bunches pass through the target without any interaction.

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PubMed2001

Hydrodynamic characteristics of transient Ni-like x-ray lasers.

A simple similarity model is presented to study the hydrodynamics of transient collisional excitation nickellike x-ray lasers. Scaling laws for the temperature, scale length, and electron density are obtained by analytic derivation. The hydrodynamic characteristics of transient Ni-like Pd x-ray lasers are investigated using this model. The calculations agree well with Dunn's experimental results.

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PubMed2001

Lattice Boltzmann simulations of liquid crystal hydrodynamics.

We describe a lattice Boltzmann algorithm to simulate liquid crystal hydrodynamics. The equations of motion are written in terms of a tensor order parameter. This allows both the isotropic and the nematic phases to be considered. Backflow effects and the hydrodynamics of topological defects are naturally included in the simulations, as are non-Newtonian flow properties such as shear thinning and shear banding.

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PubMed2001

Hydrodynamics of an open vibrated granular system.

Using the hydrodynamic description and molecular dynamics simulations, the steady state of a fluidized granular system in the presence of gravity is studied. For an open system, the density profile exhibits a maximum, while the temperature profile goes through a minimum at high altitude, beyond that the temperature increases with the height. The existence of the minimum is explained by the hydrodynamic equations if the presence of a collisionless boundary layer is taken into account. The energy dissipated by interparticle collisions is also computed. A good agreement is found between theory and simulation. The relationship with previous works is discussed.

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PubMed2001

Screening of hydrodynamic interactions in semidilute polymer solutions: a computer simulation study.

We study single-chain motion in semidilute solutions of polymers of length N=1000 with excluded-volume and hydrodynamic interactions by a novel algorithm. The crossover length of the transition from Zimm (short lengths and times) to Rouse dynamics (larger scales) is proportional to the static screening length. The crossover time is the corresponding Zimm time. Our data indicate Zimm behavior at large lengths but short times. There is no hydrodynamic screening until the chains feel constraints, after which they resist the flow: "Incomplete screening" occurs in the time domain.

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PubMed2001

Plasma hydrodynamics of the intense laser-cluster interaction.

We present a one-dimensional hydrodynamic model of the intense laser-cluster interaction in which the laser field is treated self-consistently. We find that for clusters initially as small as approximately 25 A in radius nonuniform expansion of the heated material results in long-time resonance of the laser field at the critical density plasma layer. A significant result of this is that the ponderomotive force, which is enhanced at the critical density surface, can be large enough to strongly modify the plasma hydrodynamics, even at laser intensities as low as 10(15) W/cm(2) for 800 nm laser pulses. Simulations of our recent experiments in extreme ultraviolet and x-ray generation from clusters explain the dependence of generation efficiency on laser pulse width.

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PubMed2002

Hydrodynamics of thermal granular convection.

A hydrodynamic theory is formulated for buoyancy-driven ("thermal") granular convection, recently predicted in molecular dynamic simulations and observed in experiment. The limit of a dilute flow is considered. The problem is fully described by three scaled parameters. The convection occurs via a supercritical bifurcation, the inelasticity of the collisions being the control parameter. The character of hydrodynamic modes of the system is discussed. The theory is expected to be valid for small Knudsen numbers and nearly elastic grain collisions.

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PubMed2002

Hydrodynamic interactions in ordering process of two-dimensional quenched block copolymers.

The hydrodynamic coarsening of microphase separation in two-dimensional diblock copolymers is studied using numerical simulations. Results for symmetric and asymmetric block copolymers are compared. In contrast to the formation of the hexagonal phase where hydrodynamic flow appears not to be effective in enhancing domain coarsening, the late-time evolution of the lamellar phase proceeds faster, thus leading to a different power-law scaling with the addition of coupling of the velocity field to the order parameter.

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PubMed2002

Hydrodynamics of pair-annihilating disclination lines in nematic liquid crystals.

The pair annihilation of straight line defects with strength +/-1/2 in bulk nematic systems is studied numerically, considering a full coupling of orientational degrees of freedom and hydrodynamics. This work is based on the generalization of the Ericksen-Leslie theory to the tensor order parameter as proposed by Qian and Sheng [T. Qian and P. Sheng, Phys. Rev. E 58, 7475 (1998)]. The approach is particularly suited for the late stages of the annihilation process. It is confirmed that the +1/2 disclination line moves considerably faster than the -1/2 one (e.g., twice as fast) due to the hydrodynamic flow. Symmetries of the important stress tensor terms upon inverting the sign of the winding number and performing a homogeneous in-plane rotation of the Q-tensor eigensystem are discussed. The stress tensor terms that dominantly contribute to the advective flow and to the flow asymmetry are identified.

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