Yukawa Liquids Research Articles

A molecular dynamics study of dipolar vortices in strongly coupled Yukawa liquids

Coherent dipolar vortices are a universal outcome of injecting linear momentum into a liquid. Once formed, these dipolar vortices can transport mass and momentum over large length scales and are hence a subject matter of intense research work. Using “first principles” classical molecular dynamics simulations, we report for the first time, formation and collision of dipolar vortices in a two-dimensional prototype strongly coupled liquid, namely, the Yukawa liquid. A dipolar vortex is seen to emerge from the self-organization of a sub-sonic jet profile. This dipole is seen to be very robust and, in general, shows a nonlinear relationship between vorticity and stream function. Starting from two jets injecting linear momentum in mutually opposite directions, we report on the centered head-on collisions between two dipolar vortices. Effect of background friction on the dipole evolution is investigated.

Thermal conductivity calculation of complex (dusty) plasmas

The thermal conductivity of three-dimensional (3D) strongly coupled complex (dusty) plasmas has been calculated through the improved Evan-Gillan nonequilibrium molecular dynamics (NEMD) algorithm. The extensive NEMD simulations are performed to study the performance of the algorithm and compared the results determined for perturbed heat energy current to the results obtained by equilibrium molecular dynamics (EMD) simulations. The calculations show that the present algorithm gives accurate results with fast convergence and small size effects over a wide range of plasma coupling and screening parameters. The present simulation results are in agreement with part of others NEMD and EMD data in the literature with simulation values generally overpredicting the thermal conductivity by 3%–20%, depending on plasma parameters. It is shown that the homogenous perturbed method can be employed to estimate the thermal conductivity and to understand the fundamental behaviors in 3D complex Yukawa liquids.

Shear viscosity and diffusion motion of two-dimensional dusty plasma liquids

A molecular dynamics method for studying diffusion motion and shear viscosity is presented for two-dimensional (2D) plasma liquids. The calculations obtained by using the mean-squared displacement (MSD), velocity autocorrelation function (VACF) and the shear autocorrelation function indicate that there is a diffusive motion for the lower coupling range of strongly coupled liquid states. In the MSD test, both states of a transition phase from normal diffusion to superdiffusion, and the extreme superdiffusion at intermediate coupling strength are dependent on screening strengths. The simulation data show that the position of extreme superdiffusion shifts towards higher coupling with an increase in screening strength, and the superdiffusion is nearly in a constant motion for higher coupling. A smooth transition from normal diffusion to superdiffusion exhibits the existence of superdiffusion at intermediate coupling strengths in the VACF test. A valid shear viscosity exists only at the intermediate and higher coupling parameters. It seems that the present calculations cannot establish a coupling between the viscosity and diffusion in 2D Yukawa liquids.

Cutoff wave number for shear waves and Maxwell relaxation time in Yukawa liquids

Because liquids cannot resist shear except over very short distances comparable to the atomic spacing, shear sound waves (i.e., transverse phonons) propagate only for very short wavelengths. A measure of this limit is the cutoff wave number k(c), which is sometimes called the critical wave number. Previously k(c) was determined in molecular dynamics (MD) simulations by obtaining the dispersion relation. Another approach is developed in this paper by identifying the wave number at the onset of a negative peak in the transverse current correlation function. This method is demonstrated using a three-dimensional MD simulation of a Yukawa fluid, which mimics dusty plasmas. In general, k(c) is an indicator of conditions where elastic and dissipative effects are approximately balanced. Additionally, the crossover frequency for the real and imaginary terms of the complex viscosity of a dusty plasma is obtained; this crossover frequency corresponds to the Maxwell relaxation time.

Thermal Conductivity of Three‐Dimensional Yukawa Liquids (Dusty Plasmas)

AbstractAn improved method is proposed to investigate the behavior of a Yukawa liquid under the action of an external field strength using computer simulated nonequilibrium molecular dynamics. The thermal conductivity calculations with appropriate normalizations, in the limit of low value field strengths, are estimated over a wide range of the Coulomb coupling and screening strengths. The new simulations provide more reliable data for the thermal conductivity than the previously known results for the Yukawa liquids. The calculations show that the thermal conductivity is dependent on both the Coulomb coupling and screening parameters in the three‐dimensional (3D) Yukawa liquids. The low value field strength simulation data are found to obey the universal and quasiuniversal scaling. It is shown that the homogenous nonequilibrium method can be used to predict the thermal conductivity in Yukawa systems and to understand the fundamental features of 3D dusty plasma liquids (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Shear Viscosity of Liquid‐Phase Yukawa Plasmas from Molecular Dynamics Simulations on Graphics Processing Units

AbstractWe have carried out million‐particle equilibrium molecular dynamics simulations of 3‐dimensional Yukawa liquids in order to determine the shear viscosity coefficient. The computations have been executed on Graphics Processing Unit (GPU) architectures with our largely parallelized code. The results cover the strongly coupled liquid phase, with Γ up to the vicinity of the freezing transition, for the 1 ≤ κ ≤ 3 domain of the screening parameter of the Yukawa potential. The good agreement of the present results with those obtained from earlier simulations of significantly smaller systems (consisting of several hundred to several thousand particles) verifies that the viscosity data derived in these smaller scale simulations are also acceptable (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The Roton Minimum: Is it a General Feature of Strongly Correlated Liquids?

AbstractThe roton minimum is a deep minimum in the collective excitation spectrum of the liquid, forming around fairly high k ‐values. We have discovered, through MD simulations, that this appears to be a general feature of strongly coupled liquids and is ubiquitous in 2D and 3D Yukawa liquids. We suggest that the physical origin of the roton minimum has to be sought in the quasi‐localization of particles in a strongly correlated liquid and in the ensuing formation of local microcrystals whose averaged frequency dispersion would show roton minimum‐like feature (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Excluded volume effects in macromolecular forces and ion-interface interactions

A charged Yukawa liquid confined in a slit nanopore is studied in order to understand excluded volume effects in the interaction force between the pore walls. A previously developed self-consistent scheme [S. Buyukdagli, C. V. Achim, and T. Ala-Nissila, J. Stat. Mech. 2011, P05033] and a new simpler variational procedure that self-consistently couple image forces, surface charge induced electric field, and pore modified core interactions are used to this aim. For neutral pores, it is shown that with increasing pore size, the theory predicts a transition of the interplate pressure from an attractive to a strongly repulsive regime associated with an ionic packing state, an effect observed in previous Monte Carlo simulations for hard core charges. We also establish the mean-field theory of the model and show that for dielectrically homogeneous pores, the mean-field regime of the interaction between the walls corresponds to large pores of size d > 4 Å. The role of the range of core interactions in the ionic rejection and interplate pressure is thoroughly analyzed. We show that the physics of the system can be split into two screening regimes. The ionic packing effect takes place in the regime of moderately screened core interactions characterized with the bare screening parameter of the Yukawa potential b ≲ 3/l(B), where l(B) is the Bjerrum length. In the second regime of strongly screened core interactions b ≳ 3/l(B), solvation forces associated with these interactions positively contribute to the ionic rejection driven by electrostatic forces and enhance the magnitude of the attractive pressure. For weakly charged pores without a dielectric discontinuity, core interactions make a net repulsive contribution to the interplate force and also result in oscillatory pressure curves, whereas for intermediate surface charges, these interactions exclusively strengthen the external pressure, thereby reducing the magnitude of the net repulsive interplate force. The pronounced dependence of the interplate pressure and ionic partition coefficients on the magnitude and the range of core interactions indicates excluded volume effects as an important ion specificity and a non-negligible ingredient for the stability of macromolecules in electrolyte solutions.

Instabilities in Yukawa Liquids

AbstractA strongly coupled Yukawa liquid is a system of charged particles which interact via a screened Coulomb interaction and in which the electrostatic energy between neighboring particles is larger than their thermal energy but not large enough for crystallization. Various plasma systems including ultracold neutral plasmas and complex (dusty) plasmas can exist in this strongly coupled liquid phase.Here we investigate instabilities driven by the relative streaming of plasma components in three‐dimensional Yukawa liquids with a focus on complex plasmas. This includes a dust acoustic instability driven by weakly coupled ions streaming through the dust liquid, and a dust‐dust instability driven by the counter‐streaming of strongly coupled dust grains. Compared to the Vlasov behavior we find there can be a substantial modification of the unstable wavenumber spectrum due to strong coupling effects (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Higher Harmonic Generation in Strongly Coupled Magnetized Two-Dimensional Yukawa Liquids

The excitation spectra of 2-D strongly coupled (liquid-like) Yukawa systems under the influence of a magnetic field perpendicular to the plane are found to sustain additional high-frequency modes at multiples of magnetoplasmon. These modes are reminiscent of the well-known Bernstein modes but show a number of important differences due to the strong coupling of the particles.

Coevolution of inverse cascade and nonlinear heat front in shear flows of strongly coupled Yukawa liquids

Using classical molecular dynamics (MD) simulations, we report on the development and propagation of a nonlinear heat front in parallel shear flows of a strongly coupled Yukawa liquid. At a given coupling strength, a subsonic shear profile is superposed on an equilibrated Yukawa liquid and Kelvin Helmholtz (KH) instability is observed. Coherent vortices are seen to emerge towards the nonlinear regime of the instability. It is seen that while inverse cascade leads to a continuous transfer of flow energy towards the largest scales, there is also a simultaneous transfer of flow energy into the thermal velocities of grains at the smallest scale. The latter is an effect of velocity shear and thus leads to the generation of a nonlinear heat front. In the linear regime, the heat front is seen to propagate at speed much lesser than the adiabatic sound speed of the liquid. Spatio-temporal growth of this heat front occurs concurrently with the inverse cascade of KH modes.

Non-invasive determination of the parameters of strongly coupled 2D Yukawa liquids

We derive a method for identifying the Yukawa model parameters of two-dimensional (2D) strongly coupled dusty plasmas. The method is based on non-invasive observation of the dust component of the plasma and comparison with a large body of simulation data in the form of simple analytical formulas. This approach requires only input from a time-series of configuration snapshots and particle velocities with no recourse to additional information about the system. In addition, we derive an effective coupling parameter for 2D Yukawa systems based on the height of the first maximum of the pair distribution function. Two variants—one valid in the high-coupling range, the other for arbitrary couplings of the liquid—are derived. Comparison to previous approaches to Yukawa coupling parameters shows that the present concept is more general and more accurate. Our results should be directly applicable as a simple, yet reliable diagnostic method for a variety of experiments, including dusty plasmas, colloidal suspensions, and ions in traps, and can be employed to facilitate comparisons between experiments, theory, and simulations.

Coherent Vortices in Strongly Coupled Liquids

Strongly coupled liquids are ubiquitous in both nature and laboratory plasma experiments. They are unique in the sense that their average potential energy per particle dominates over the average kinetic energy. Using "first principles" molecular dynamics (MD) simulations, we report for the first time the emergence of isolated coherent tripolar vortices from the evolution of axisymmetric flows in a prototype two-dimensional (2D) strongly coupled liquid, namely, the Yukawa liquid. Linear growth rates directly obtained from MD simulations are compared with a generalized hydrodynamic model. Our MD simulations reveal that the tripolar vortices persist over several turn over times and hence may be observed in strongly coupled liquids such as complex plasma, liquid metals and astrophysical systems such as white dwarfs and giant planetary interiors, thereby making the phenomenon universal.

Parallel shear flow instabilities in strongly coupled Yukawa liquids: A comparison of generalized hydrodynamic model and molecular dynamics results

Using a generalized hydrodynamic (GH) model, the growth rate spectra of Kelvin–Helmholtz (KH) instability has been obtained analytically for a step shear profile in strongly coupled Yukawa liquids. The class of shear flows studied is assumed to be incompressible in nature. The growth rate spectra calculated exhibit viscous damping at high mode numbers, destabilization at stronger coupling, and in the limit τm (viscoelastic relaxation time)→0, reduce to the regular Navier–Stokes growth rate spectra. A direct comparison is made with previous molecular dynamics (MD) simulations [Ashwin J. and R. Ganesh, Phys. Rev. Lett. 104, 215003 (2010)] of KH instability. We find that for a given value of Reynolds number R and coupling parameter 1<Γ<100, the GH and MD growth rates are in a qualitative agreement. The inclusion of the effect of shear heating as an effective coupling parameter Γe appears to improve the quantitative comparison as well.

Viscoelasticity of 2D Liquids Quantified in a Dusty Plasma Experiment

The viscoelasticity of two-dimensional liquids is quantified in an experiment using a dusty plasma. An experimental method is demonstrated for measuring the wave-number-dependent viscosity η(k), which is a quantitative indicator of viscoelasticity. Using an expression generalized here to include friction, η(k) is computed from the transverse current autocorrelation function, which is found by tracking random particle motion. The transverse current autocorrelation function exhibits an oscillation that is a signature of elastic contributions to viscoelasticity. Simulations of a Yukawa liquid are consistent with the experiment.

Kelvin Helmholtz Instability in Strongly Coupled Yukawa Liquids

Using "first principles" molecular dynamics simulations Kelvin Helmholtz instability has been observed for the first time at the particle level in two-dimensional strongly coupled Yukawa liquids. At a given coupling strength Γ a subsonic shear profile is superposed on an equilibrated Yukawa liquid and instability is observed. Linear growth rates computed directly from MD simulations are seen to increase with strong coupling. Vortex-roll formation in the nonlinear regime is reported.

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.

Anomalous and Fickian Diffusion in Two‐Dimensional Dusty Plasmas

AbstractWe provide an overview on diffusion in frictionless two‐dimensional Yukawa liquids as a model for dusty plasmas. Results are obtained for the combined influence of temperature and screening length on the character of diffusion, i.e., on the value of the diffusion exponent at long times (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of external drive on strongly coupled Yukawa systems: A nonequilibrium molecular dynamics study

Using nonequilibrium molecular dynamics (MD) simulations behavior of three-dimensional (3D) Yukawa system has been studied in the presence of a small amplitude drive along one direction (say z[over ] ). This drive has the general form V=V_{0} cos(k_{L}z)Theta(t-t_{0}) , where Theta(t-t_{0}) is a Heaviside step function in time at t=t_{0} and k_{L}=2pi/L , L being the size of the system; V0 is considered small compared to average interparticle potential energy. In particular, a 3D equilibrated Yukawa crystal (bcc) near solid-liquid transition is subjected to an external drive at times t> or =t_{0} at the largest possible scale. For a given k_{L} it is observed that there exists a critical amplitude (V_{0};{c}) of the external drive below which the crystalline order is preserved and above which (V_{0}> or =V_{0};{c}) the transition from bcc to strongly coupled Yukawa liquid is observed. This critical amplitude (V_{0};{c}) is sensitive to the location of the Yukawa solid in the (kappa,Gamma) phase space. Various signatures of melting, transients, and steady state in the presence of this drive are elucidated using extensive MD diagnostics such as loss of long-range crystalline order, change in diffusion from subnormal to normal, and the fall of transversal shear peak in the Fourier transform of the velocity autocorrelation function. The mechanism of heating in the transient state is attributed to the local heating of the system where the forces are maximum. It is shown that these local hot regions dissipate heat into surrounding regions ultimately leading to a uniform temperature throughout the system. Ion streaming due to external field has been neglected.

Wave spectra of two-dimensional Yukawa solids and liquids in the presence of a magnetic field

Thermally excited phonon spectra of two-dimensional Yukawa solids and liquids in the presence of an external magnetic field are studied using computer simulations. Special attention is paid to the variation of wave spectra in terms of several key parameters, such as the strength of coupling, the screening parameter, and the intensity of the magnetic field. In addition, comparisons are made with several analytical theories, including random-phase approximation, quasilocalized charge approximation, and harmonic approximation, and the validity of those theories is discussed in the present context.