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PubMed2002

Variational formulation of nonequilibrium thermodynamics for hydrodynamic pattern formations.

It is shown that a direct extension of the variational principle of near-equilibrium states due to Onsager leads to the analogous principle in hydrodynamic flows; the entropy production rate of an isolated system is maximized both near and far from equilibrium. It possesses as its extremal paths the solutions to the hydrodynamic equation of motion, and provides a general pattern selection criterion far from equilibrium.

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PubMed2002

Hydrodynamic flow of ions and atoms in partially ionized plasmas.

We have derived the hydrodynamic equations of motion for a partially ionized plasma, when the ionized component and the neutral components have different flow velocities and kinetic temperatures. Starting from the kinetic equations for a gas of ions and a gas of atoms we have considered various processes of encounters between the two species: self-collisions, interspecies collisions, ionization, recombination, and charge exchange. Our results were obtained by developing a general approach for the hydrodynamics of a gas in a binary mixture, in particular when the components drift with respect to each other. This was applied to a partially ionized plasma, when the neutral-species gas and the charged-species gas have separate velocities. We have further suggested a generalized version of the relaxation time approximation and obtained the contributions of the interspecies encounters to the transport equations.

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PubMed2003

Stabilization of hydrodynamic flows by small viscosity variations.

Motivated by the large effect of turbulent drag reduction by minute concentrations of polymers, we study the effects of a weakly space-dependent viscosity on the stability of hydrodynamic flows. In a recent paper [Phys. Rev. Lett. 87, 174501, (2001)], we exposed the crucial role played by a localized region where the energy of fluctuations is produced by interactions with the mean flow (the "critical layer"). We showed that a layer of a weakly space-dependent viscosity placed near the critical layer can have a very large stabilizing effect on hydrodynamic fluctuations, retarding significantly the onset of turbulence. In this paper we extend these observations in two directions: first we show that the strong stabilization of the primary instability is also obtained when the viscosity profile is realistic (inferred from simulations of turbulent flows with a small concentration of polymers). Second, we analyze the secondary instability (around the time-dependent primary instability) and find similar strong stabilization. Since the secondary instability develops around a time-dependent solution and is three dimensional, this brings us closer to the turbulent case. We reiterate that the large effect is not due to a modified dissipation (as is assumed in some theories of drag reduction), but due to reduced energy intake from the mean flow to the fluctuations. We propose that similar physics act in turbulent drag reduction.

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PubMed2003

Effect of rotation on a developed turbulent stratified convection: the hydrodynamic helicity, the alpha effect, and the effective drift velocity.

An effect of rotation on a developed turbulent stratified convection is studied. Dependences of the hydrodynamic helicity, the alpha tensor, and the effective drift velocity of the mean magnetic field on the rate of rotation and an anisotropy of turbulent convection are found. It is shown that in an anisotropic turbulent convection the alpha effect can change its sign depending on the rate of rotation. The evolution of the alpha effect is much more complicated than that of the hydrodynamic helicity in an anisotropic turbulent convection of a rotating fluid. Different properties of the effective drift velocity of the mean magnetic field in a rotating turbulent convection are found: (i) a poloidal effective drift velocity can be diamagnetic or paramagnetic depending on the rate of rotation; (ii) there is a difference in the effective drift velocities for the toroidal and poloidal magnetic fields; (iii) a toroidal effective drift velocity can play a role of an additional differential rotation. The above effects and an effect of a nonzero divergence of the effective drift velocity of the toroidal magnetic field on a magnetic dynamo in a developed turbulent stratified convection of a rotating fluid are studied. Astrophysical applications of the obtained results are discussed.

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PubMed2003

Gaussian factorization of hydrodynamic correlation functions and mode-coupling memory kernels.

A simple method to determine mode-coupling memory functions in generalized Langevin equations is obtained by explicitly expressing the random force of the slow hydrodynamic modes in terms of pair interactions in liquids and by Gaussian factoring the resulting multiple-point time correlation functions into products of linear correlation functions. The approach is used to derive the mode-coupling memory kernels for the velocity autocorrelation function, four-point bilinear density correlation function, and density correlation function of linear molecular liquids. These generalized Langevin equations and their associated memory kernels are useful for calculating relaxation processes and spectroscopic measurements in liquids and solvents. As a central result of our analysis, the non-Gaussian behavior of the bilinear density correlation function is quantitatively related to the nonexponential nature of linear hydrodynamic modes. This relation aids in the understanding of recent simulation results of non-Gaussian indicators in supercooled liquids.

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PubMed2003

Fast heat transfer calculations in supercritical fluids versus hydrodynamic approach.

This study investigates the heat transfer in a simple pure fluid whose temperature is slightly above its critical temperature. We propose an efficient numerical method to predict the heat transfer in such fluids when the gravity can be neglected. The method, based on a simplified thermodynamic approach, is compared with direct numerical simulations of the Navier-Stokes and energy equations performed for CO2 and SF6. A realistic equation of state is used to describe both fluids. The proposed method agrees with the full hydrodynamic solution and provides a huge gain in computation time. The connection between the purely thermodynamic and hydrodynamic descriptions is also discussed.

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PubMed2003

Hydrodynamics and transport coefficients for dilute granular gases.

The hydrodynamics of granular gases of viscoelastic particles, whose collision is described by an impact-velocity dependent coefficient of restitution, which is developed using the Chapman-Enskog approach. We derive the hydrodynamic equations and the according transport coefficients with the assumption that the shape of the velocity distribution function follows adiabatically the decaying temperature. We show numerically that this approximation is justified up to intermediate dissipation. The transport coefficients and the coefficient of cooling are expressed in terms of the elastic and dissipative parameters of the particle material and by the gas parameters. The dependence of these coefficients on temperature differs qualitatively from that obtained with the simplifying assumption of a constant coefficient of restitution which was used in previous studies. The approach formulated for gases of viscoelastic particles may be applied also for other impact-velocity dependencies of the restitution coefficient.

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PubMed2003

Molecular scale contact line hydrodynamics of immiscible flows.

From extensive molecular dynamics simulations on immiscible two-phase flows, we find the relative slipping between the fluids and the solid wall everywhere to follow the generalized Navier boundary condition, in which the amount of slipping is proportional to the sum of tangential viscous stress and the uncompensated Young stress. The latter arises from the deviation of the fluid-fluid interface from its static configuration. We give a continuum formulation of the immiscible flow hydrodynamics, comprising the generalized Navier boundary condition, the Navier-Stokes equation, and the Cahn-Hilliard interfacial free energy. Our hydrodynamic model yields interfacial and velocity profiles matching those from the molecular dynamics simulations at the molecular-scale vicinity of the contact line. In particular, the behavior at high capillary numbers, leading to the breakup of the fluid-fluid interface, is accurately predicted.

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PubMed2003

Metachronal waves for deterministic switching two-state oscillators with hydrodynamic interaction.

We employ a model system, called rowers, as a generic physical framework to define the problem of the coordinated motion of cilia (the metachronal wave) as a far from equilibrium process. Rowers are active (two-state) oscillators in a low Reynolds number fluid, and interact solely through the forces of hydrodynamic origin. In this work, we consider the case of fully deterministic dynamics, find analytical solutions of the equation of motion in the long-wavelength (continuum) limit, and investigate numerically the short-wavelength limit. We prove the existence of metachronal waves below a characteristic wavelength. Such waves are unstable and become stable only if the sign of the coupling is reversed. We also find that with normal hydrodynamic interaction, the metachronal pattern has the form of stable trains of traveling wave packets sustained by the onset of anti-coordinated beating of consecutive rowers.

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PubMed2004

Steady-state solutions of hydrodynamic traffic models.

We investigate steady-state solutions of hydrodynamic traffic models in the absence of any intrinsic inhomogeneity on roads such as on-ramps. It is shown that typical hydrodynamic models possess seven different types of inhomogeneous steady-state solutions. The seven solutions include those that have been reported previously only for microscopic models. The characteristic properties of wide jam such as moving velocity of its spatiotemporal pattern and/or out-flux from wide jam are shown to be uniquely determined and thus independent of initial conditions of dynamic evolution. Topological considerations suggest that all of the solutions should be common to a wide class of traffic models. The results are discussed in connection with the universality conjecture for traffic models. Also the prevalence of the limit-cycle solution in a recent study of a microscopic model is explained in this approach.

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PubMed2004

Hydrodynamic coupling of two rotating spheres trapped in harmonic potentials.

We theoretically study in detail the hydrodynamic coupling of two equal-sized colloidal spheres at low Reynolds numbers assuming the particles to be harmonically trapped with respect to both their positions and orientations. By taking into account the rotational motion, we obtain a rich spectrum of collective eigenmodes whose properties we determine on the basis of pure symmetry arguments. Extending recent investigations on translational correlations [J.-C. Meiners and S. R. Quake, Phys. Rev. Lett. 82, 2211 (1999)], we derive the complete set of autocorrelation and cross-correlation functions emphasizing the coupling of rotation to translation which we illustrate in a few examples. An important feature of our system is the self-coupling of translation and rotation of one particle mediated by the neighboring particle that is clearly visible in the appropriate autocorrelation function. This coupling is a higher-order effect and therefore not included in the widely used Rotne-Prager approximation for the hydrodynamic mobilities.

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PubMed2004

Hydrodynamic limit of multichain driven diffusive models.

A class of models, generalizing asymmetric exclusion process for many parallel interacting channels, is proposed. We couple the models with boundary reservoirs, study boundary-driven phase transitions, and show that usually taken hydrodynamic description fails. The adequate hydrodynamic limit is then derived. We support our findings with Monte Carlo simulations of the original stochastic system.

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PubMed2004

Hydrodynamic interactions between rotating helices.

Escherichia coli bacteria use rotating helical flagella to swim. At this scale, viscous effects dominate inertia, and there are significant hydrodynamic interactions between nearby helices. These interactions cause the flagella to bundle during the "runs" of bacterial chemotaxis. Here we use slender-body theory to solve for the flow fields generated by rigid helices rotated by stationary motors. We determine how the hydrodynamic forces and torques depend on phase and phase difference, show that rigid helices driven at constant torque do not synchronize, and solve for the flows. We also use symmetry arguments based on kinematic reversibility to show that for two rigid helices rotating with zero phase difference, there is no time-averaged attractive or repulsive force between the helices.

Escherichia coli↗
PubMed2004

van der Waals normal form for a one-dimensional hydrodynamic model.

Phase separation in a fluidized granular system is studied. We consider a one-dimensional hydrodynamic model that mimics a two-dimensional fluidized granular system with a vibrating wall and without gravity, which exhibits a phase separation. Close to the critical point, by means of an adiabatic elimination of the temperature, we deduce the van der Waals normal form, which is the equation that describes the slow dynamics of the system and predicts the qualitative behavior in different regions of parameters. This allows us to understand the origin of the effective viscosity and the spatial saturation at the onset of the bifurcation. The hydrodynamic model and van der Waals normal form exhibit a behavior similar to the one observed in molecular dynamics simulations.

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PubMed2004

Hydrodynamics of probabilistic ballistic annihilation.

We consider a dilute gas of hard spheres in dimension d> or =2 that upon collision either annihilate with probability p or undergo an elastic scattering with probability 1-p . For such a system neither mass, momentum, nor kinetic energy is a conserved quantity. We establish the hydrodynamic equations from the Boltzmann equation description. Within the Chapman-Enskog scheme, we determine the transport coefficients up to Navier-Stokes order, and give the closed set of equations for the hydrodynamic fields chosen for the above coarse-grained description (density, momentum, and kinetic temperature). Linear stability analysis is performed, and the conditions of stability for the local fields are discussed.

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PubMed2005

Hard rod gas with long-range interactions: Exact predictions for hydrodynamic properties of continuum systems from discrete models.

One-dimensional hard rod gases are explicitly constructed as the limits of discrete systems: exclusion processes involving particles of arbitrary length. Those continuum many-body systems in general do not exhibit the same hydrodynamic properties as the underlying discrete models. Considering as examples a hard rod gas with additional long-range interaction and the generalized asymmetric exclusion process for extended particles, it is shown how a correspondence between continuous and discrete systems must be established instead. This opens up a possibility to exactly predict the hydrodynamic behavior of this continuum system under Eulerian scaling by solving its discrete counterpart with analytical or numerical tools. As an illustration, simulations of the totally asymmetric exclusion process are compared to analytical solutions of the model and applied to the corresponding hard rod gas. The case of short-range interaction is treated separately.

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PubMed2005

Influence of impurities on hydrodynamic solitons.

The interaction between impurities and solitary waves has been experimentally observed on the surface of a defective water layer subjected to vertical vibration. A slightly rugged surface on one sidewall of the water layer serves as the impurity, making the layer breadth at the defect slightly different elsewhere. A wide-breadth impurity will attract or pin not only the hydrodynamic breather at lower driving frequency, but also the kink at higher driving frequency, while a narrow-breadth one will repel them. Using a multiple scale expansion method, a nonlinear Schro dinger equation with an impurity term (NLSI) was derived from the basic hydrodynamic equation. Furthermore, we present numerical calculations that show good agreement between the NLSI-based theoretical model and the experimental results.

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PubMed2005

Simulation method to resolve hydrodynamic interactions in colloidal dispersions.

A computational method is presented to resolve hydrodynamic interactions acting on solid particles immersed in incompressible host fluids. In this method, boundaries between solid particles and host fluids are replaced with a continuous interface by assuming a smoothed profile. This enabled us to calculate hydrodynamic interactions both efficiently and accurately, without neglecting many-body interactions. The validity of the method was tested by calculating the drag force acting on a single cylindrical rod moving in an incompressible Newtonian fluid. This method was then applied in order to simulate sedimentation process of colloidal dispersions.

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