Transport coefficients of the Yukawa one-component plasma

Energy stable scheme for random batch molecular dynamics

The computational bottleneck of molecular dynamics is pairwise additive long-range interactions between particles. The random batch Ewald (RBE) method provides a highly efficient and superscalable solver for long-range interactions, but the stochastic nature of this algorithm leads to unphysical self-heating effect during the simulation. We propose an energy stable scheme (ESS) for particle systems by employing a Berendsen-type energy bath. The scheme removes the notorious energy drift, which exists due to the force error even when a symplectic integrator is employed. Combining the RBE with the ESS, the new method provides a perfect solution to the computational bottleneck of molecular dynamics at the microcanonical ensemble. Numerical results for a primitive electrolyte and all-atom pure water systems demonstrate the attractive performance of the algorithm, including its dramatically high accuracy, linear complexity, and overcoming the energy drift for long-time simulations.

Pseudo hard-sphere viscosities from equilibrium Molecular Dynamics

Transport coefficients like shear, bulk and longitudinal viscosities are sensitive to the intermolecular interaction potential and finite size effects when are numerically determined. For the hard-sphere (HS) fluid, such transport properties are determined almost exclusively with computer simulations. However, their systematic determination and analysis throughout shear stress correlation functions and the Green-Kubo formalism can not be done due to discontinuous nature of the interaction potential. Here, we use the pseudo hard-sphere (PHS) potential to determine pressure correlation functions as a function of volume fraction in order to compute mentioned viscosities. Simulation results are compared to available event-driven molecular dynamics of the HS fluid and also used to propose empirical corrections for the Chapman-Enskog zero density limit of shear viscosity. Moreover, we show that PHS potential is a reliable representation of the HS fluid and can be used to compute transport coefficients. The molecular simulation results of the present work are valuable for further exploration of HS-type fluids or extend the approach to compute transport properties of hard-colloid suspensions.

Excess entropy and Stokes-Einstein relation in simple fluids

The Stokes-Einstein (SE) relation between the self-diffusion and shear viscosity coefficients operates in sufficiently dense liquids not too far from the liquid-solid phase transition. By considering four simple model systems with very different pairwise interaction potentials (Lennard-Jones, Coulomb, Debye-Hückel or screened Coulomb, and the hard sphere limit) we identify where exactly on the respective phase diagrams the SE relation holds. It appears that the reduced excess entropy s_{ex} can be used as a suitable indicator of the validity of the SE relation. In all cases considered the onset of SE relation validity occurs at approximately s_{ex}≲-2. In addition, we demonstrate that the line separating gaslike and liquidlike fluid behaviours on the phase diagram is roughly characterized by s_{ex}≃-1.

Vibrational model of thermal conduction for fluids with soft interactions

A vibrational model of heat transfer in simple liquids with soft pairwise interatomic interactions is discussed. A general expression is derived, which involves an averaging over the liquid collective mode excitation spectrum. The model is applied to quantify heat transfer in a dense Lennard-Jones liquid and a strongly coupled one-component plasma. Remarkable agreement with the available numerical results is documented. A similar picture does not apply to the momentum transfer and shear viscosity of liquids.

Spontaneous generation of temperature anisotropy in a strongly coupled magnetized plasma

A magnetic field was recently shown to enhance field-parallel heat conduction in a strongly correlated plasma whereas cross-field conduction is reduced. Here we show that in such plasmas, the magnetic field has the additional effect of inhibiting the isotropization process between field-parallel and cross-field temperature components, thus leading to the emergence of strong and long-lived temperature anisotropies when the plasma is locally perturbed. An extended heat equation is shown to describe this process accurately.

Effect of correlations on heat transport in a magnetized strongly coupled plasma

In a classical ideal plasma, a magnetic field is known to reduce the heat conductivity perpendicular to the field, whereas it does not alter the one along the field. Here we show that, in strongly correlated plasmas that are observed at high pressure and/or low temperature, a magnetic field reduces the perpendicular heat transport much less and even enhances the parallel transport. These surprising observations are explained by the competition of kinetic, potential, and collisional contributions to the heat conductivity. Our results are based on first-principle molecular dynamics simulations of a one-component plasma.

Analytic structure of a drag-driven confined dust vortex flow in plasma

Flow structure of a dust medium electrostatically suspended and confined in a plasma presents a unique setup where the spatial scale of a volumetric drive by the plasma flow might exceed that of the boundaries confining the dust. By means of a formal implementation of a two-dimensional hydrodynamic model to a confined dust flow and its analytic curvilinear solutions, it is shown that the eigenmode spectrum of the dust vortex flow can lose correlations with the driving field even at the low dust Reynolds numbers as a result of strong shear and finer scales introduced in the equilibrium dust vorticity spectrum by the boundaries. While the boundary effects can replace the desired turbulent processes unavailable in this regime, the shear observable in most of the dust vortex flows is identified to have a definite exponent of dependence on the dust viscosity over a substantially large range of the latter. These results and scalings allow quantification of the notion of dusty plasma medium as a paradigm for a wide range of natural flow processes having scales inaccessible to ordinary laboratory experiments.

Microscopic origin of shear relaxation in a model viscoelastic liquid

An atomistic description of shear stress relaxation in a viscoelastic liquid is developed from first principles through accurate molecular dynamic simulations in a model Yukawa system. It is shown that the relaxation time τ(M)(ex) of the excess part of the shear stress autocorrelation function provides a correct measure of the relaxation process. Below a certain critical value Γ(c) of the Coulomb coupling strength, the lifetime of local atomic connectivity τ(LC) converges to τ(M)(ex) and is the microscopic origin of the relaxation. At Γ≫Γ(c), i.e., in the potential energy dominated regime, τ(M)(ex)→τ(M) (the Maxwell relaxation time) and can, therefore, fully account for the elastic or "solidlike" behavior. Our results can help provide a better fundamental understanding of viscoelastic behavior in a variety of strongly coupled systems such as dusty plasmas, colloids, and non-Newtonian fluids.

Dust-acoustic shocks in strongly coupled dusty plasmas

Electrostatic dust-acoustic shock waves are investigated in a viscous, complex plasma consisting of dust particles, electrons, and ions. The system is modelled using the generalized hydrodynamic equations, with strong coupling between the dust particles being accounted for by employing the effective electrostatic temperature approach. Using a reductive perturbation method, it is demonstrated that this model predicts the existence of weakly nonlinear dust-acoustic shock waves, arising as solutions to Burgers's equation, in which the nonlinear forces are balanced by dissipative forces, in this case, associated with viscosity. The evolution and stability of dust-acoustic shocks is investigated via a series of numerical simulations, which confirms our analytical predictions on the shock characteristics.

Longitudinal viscosity of two-dimensional Yukawa liquids

The longitudinal viscosity η(l) is obtained for a two-dimensional (2D) liquid using a Green-Kubo method with a molecular dynamics simulation. The interparticle potential used has the Debye-Hückel or Yukawa form, which models a 2D dusty plasma. The longitudinal η(l) and shear η(s) viscosities are found to have values that match very closely, with only negligible differences for the entire range of temperatures that is considered. For a 2D Yukawa liquid, the bulk viscosity η(b) is determined to be either negligibly small or not a meaningful transport coefficient.

Static and dynamic shear viscosity of a single-layer complex plasma

The static and dynamic (complex) shear viscosity of a single-layer dusty plasma is measured by applying, respectively, a stationary and a periodically modulated shear stress, induced by the light pressure of manipulating laser beams. Under static conditions we observe a decrease of the viscosity with increasing shear rate, the so-called shear-thinning behavior. Under oscillating shear both the magnitude and the ratio of the dissipative and elastic contributions to the complex viscosity show strong frequency dependence, as the system changes from viscous to elastic in nature with increasing excitation frequency. Accompanying molecular dynamics simulations explain and support the experimental observations.

Viscoelastic response of Yukawa liquids

The viscoelastic properties of strongly coupled Yukawa liquids are characterized by computing the complex shear viscosity η(ω) . This is done using three methods of molecular-dynamics simulation: equilibrium, nonequilibrium, and Langevin dynamics, all with a mutually repulsive Yukawa interparticle potential. A change from viscous to elastic response is observed with increasing frequency, as well as a decrease of the magnitude of the viscosity with increasing frequency. The Langevin simulation reveals that the dependence of the complex viscosity on the friction has a different character for hot and cool liquids. At ω=0 , we find that as friction increases, the viscosity diminishes at high temperature but increases at low temperature. In addition to finding its frequency dependence, we also derive the wave-number (length-scale) dependence of the shear viscosity.

Time-correlation functions and transport coefficients of two-dimensional Yukawa liquids

The existence of coefficients for diffusion, viscosity, and thermal conductivity is examined for two-dimensional (2D) liquids. Equilibrium molecular dynamics simulations are performed using a Yukawa potential and the long-time behavior of autocorrelation functions is tested. Advances reported here as compared to previous 2D Yukawa liquid simulations include an assessment of the thermal conductivity, using a larger system size to allow meaningful examination of longer times, and development of improved analysis methods. We find that the transport coefficient exists for diffusion at high temperature and viscosity at low temperature, but not in the opposite limits. The thermal conductivity coefficient does not appear to exist at high temperature. Further advances in computing power could improve these assessments by allowing even larger system sizes and longer time series.

Shear viscosity of strongly coupled Yukawa liquids

We present molecular-dynamics calculations of the shear viscosity of three-dimensional strongly coupled Yukawa liquids which are frequently used as a model system of complex plasmas. The results obtained using two independent nonequilibrium simulation methods are critically compared with each other and with earlier published data for a wide range of plasma coupling (Gamma) and screening (kappa) parameters. The non-Newtonian behavior of the liquid, manifested as a decrease of the shear viscosity with increasing shear rate (shear thinning), and the validity of the Stokes-Einstein relation at high coupling strength are also demonstrated.

Free thermal convection in complex plasma with background-gas friction

The onset of free thermal convection in complex fluids with background friction is theoretically investigated. It is shown that in the limit when friction prevails--opposite to the classic Rayleigh-Bénard case--the onset is determined by a renormalized Rayleigh number and also depends on the Prandtl number. Such convection should be observable in experiments with complex plasmas.

Non-newtonian viscosity of complex-plasma fluids

Investigations of shear flows in three-dimensional complex-plasma fluids produced in a dc discharge were carried out. The shear was induced either by an inhomogeneous gas flow or by a laser beam. The viscosity of complex plasmas was measured over a broad range of shear rates, up to the hydrodynamic limit when the discreteness becomes important. Analysis of the measurements reveals non-Newtonian behavior of complex plasmas accompanied by substantial shear thinning.

Kinetic characterization of strongly coupled systems

We propose a simple method to determine the local coupling strength Gamma experimentally, by linking the individual particle dynamics with the local density and crystal structure of a 2D plasma crystal. By measuring particle trajectories with high spatial and temporal resolution we obtain the first maps of Gamma and temperature at individual particle resolution. We employ numerical simulations to test this new method, and discuss the implications to characterize strongly coupled systems.

Shear viscosity and shear thinning in two-dimensional Yukawa liquids

A two-dimensional Yukawa liquid is studied using two different nonequilibrium molecular dynamics simulation methods. Shear viscosity values in the limit of small shear rates are reported for a wide range of Coulomb coupling parameter and screening lengths. At high shear rates it is demonstrated that this liquid exhibits shear thinning; i.e., the viscosity eta diminishes with increasing shear rate. It is expected that two-dimensional dusty plasmas will exhibit this effect.

Shear viscosity of two-dimensional Yukawa systems in the liquid state

The shear viscosity of a two-dimensional (2D) liquid was calculated using molecular dynamics simulations with a Yukawa potential. The viscosity has a minimum at a Coulomb coupling parameter Gamma of about 17, arising from the temperature dependence of the kinetic and potential contributions. Previous calculations of 2D viscosity were less extensive as well as for a different potential. The stress autocorrelation function was found to decay rapidly, contrary to earlier work. These results are useful for 2D condensed matter systems and are compared to a dusty plasma experiment.

Viscosity and mutual diffusion in strongly asymmetric binary ionic mixtures

We present molecular dynamics simulation results for the viscosity and mutual diffusion constant of a strongly asymmetric binary ionic mixture. We compare the results with available theoretical models previously tested for much smaller asymmetries. For the case of viscosity we propose a predictive framework based on the linear mixing rule, while for mutual diffusion we discuss some consistency problems of widely used Boltzmann-equation-based models.

Shear flows and shear viscosity in a two-dimensional Yukawa system (dusty plasma)

The shear viscosity of a two-dimensional liquid-state dusty plasma was measured experimentally. A monolayer of highly charged polymer microspheres, with a Yukawa interaction, was suspended in a plasma sheath. Two counterpropagating Ar+ laser beams pushed the particles, causing shear-induced melting of the monolayer and a shear flow in a planar Couette configuration. By fitting the particle velocity profiles in the shear flow to a Navier-Stokes model, the kinematic viscosity was calculated; it was of order 1 mm(2) s(-1), depending on the monolayer's parameters and shear stress applied.

Description of strongly coupled Yukawa fluids using the variational modified hypernetted chain approach

The variational modified hypernetted chain approach as proposed by J. Stat. Phys. 42, 437 (1986)] is used to describe strongly coupled Yukawa fluids. The integral equations of interest can be solved using the spherical harmonic oscillator wave functions as a seed. Comparisons are done with simulation results for equation of state and transport coefficients over the entire fluid domain for a wide range of the system parameters.

Thermal conductivity of strongly coupled Yukawa liquids

The thermal conductivity of strongly coupled Yukawa liquids, being relevant to dusty plasmas, is calculated from nonequilibrium molecular dynamics simulations. The calculations cover a wide range of plasma coupling (Gamma) and screening (kappa) parameters and yield data which are generally in good agreement with the results of recent independent calculations. An improved analytical formula, relating the thermal conductivity to the reduced temperature and to the screening length, is proposed.

Gibbs-Bogolyubov inequality and transport properties for strongly coupled Yukawa fluids

The Gibbs-Bogolyubov inequality is used to establish a mapping between the Yukawa system and both the hard-sphere and the one-component reference systems. The transport coefficients of self-diffusion, shear viscosity, and thermal conductivity are computed for the Yukawa fluid using known properties of the reference systems. Comparisons are made with simulation results. For sufficiently strong screening, the hard-sphere reference system yields a lower upper bound of the Yukawa Helmholtz free energy and a better estimate of the Yukawa transport coefficients.