2D Yukawa Liquids Research Articles

Viscosity of finite Yukawa liquids

The shear viscosity of a finite two-dimensional (2D) Yukawa liquid is calculated using non-equilibrium Langevin simulations. Two counter-propagating shear forces are used to push the particles and cause shear-induced melting of the cluster. The melting temperature of the 2D cluster system is used to derive the effective coupling parameter Γ * of this finite system and allows us to investigate the relationship between shear viscosity and system properties Γ * and κ. The simulation data shows that the value of the shear viscosity rises for coupling parameters Γ * > 20 and follows a simple universal scaling for appropriate normalization. It is further found that the Green–Kubo relation is applicable to determine viscosity in finite non-equilibrium systems with Γ * < 80.

Bulk moduli of two-dimensional Yukawa solids and liquids obtained from periodic compressions

Langevin dynamical simulations are performed to determine the bulk modulus in two-dimensional (2D) dusty plasmas from uniform periodic radial compressions. The bulk modulus is calculated directly from its physical definition of the ratio of the internal pressure/stress to the volume strain. Under various conditions, the bulk moduli obtained agree with the previous theoretical derivations from completely different approaches. It is found that the bulk moduli of 2D Yukawa solids and liquids are almost independent of the system temperature and the external compressional frequency.

Determination of best particle tracking velocimetry method for two-dimensional dusty plasmas.

A practical procedure of determining the best choice of particle tracking velocimetry (PTV) methods for the analysis of two-dimensional (2D) dusty plasmas is provided. Using the measured particle positions with errors, the algorithm of PTV introduces further systematic errors while calculating particle velocities. To better quantify the errors, computer simulations of 2D Yukawa liquids are performed so that the true particle positions and velocities are precisely known. Synthetic data are achieved by varying the time interval between frames and adding the uncertainty with the different magnitude to the particle position data. Various PTV methods are used to calculate the velocity data from the achieved synthetic data, and the obtained velocity data from these PTV methods are compared with the true velocity data using two diagnostics to determine the best PTV method for various conditions. The results of various PTV methods with the simulation data are further confirmed by the demonstration using the 2D dusty plasma experimental data. This practical procedure is also applicable to determine the best PTV method for dusty plasmas in different conditions, such as those in Tokamaks, and for other physical systems, including colloids, granular materials, and fluid mechanics.

Effect of particle mass inhomogeneity on the two-dimensional Rayleigh–Bénard system of Yukawa liquids: A molecular dynamics study

The effect of particle mass inhomogeneity on the evolution of macroscale fluid flow in the Rayleigh–Bénard system of two-dimensional Yukawa liquids is studied using “first principles” classical molecular dynamics simulations. We find that Rayleigh–Bénard convection cells (RBCCs) formed in the quasi-steady-state become unstable at later times as a result of introducing a small fraction (≤2% of the total particles) of particle mass inhomogeneity in a Yukawa system made up of point particles of uniform charges. The unstable RBCCs, after passing through several intermediate states, give rise to a unidirectional shear flow in the direction perpendicular to the external gravity. Depending on the fraction and phase space of the particle mass inhomogeneity introduced in the system, the unidirectional shear flow further evolves to give shearless parallel flow. We use single or dual particle mass distributions of various forms, such as Gaussian distribution, Dirac-delta distribution, or a combination of both, around different mean values in order to introduce particle mass inhomogeneity. The role of system size on the emergence of various intermediate fluid flow states is also investigated. Furthermore, by introducing an inhomogeneity in charge commensurate with mass inhomogeneity, we demonstrate the robustness of our findings. Finally, for the case of decreasing correlation strength and for otherwise identical parameters, it is shown that the particle mass inhomogeneity fails to generate shear flows from RBCCs in 2D Yukawa liquids.

Phase of particle-level velocity perturbations determines the fate of Rayleigh–Bénard convection cells in 2D Yukawa liquids

Using “first principles” molecular dynamics (MD) simulations, the sensitivity of two-dimensional Rayleigh–Bénard convection cells (RBCCs) to the phase and amplitude of particle-level velocity perturbations is demonstrated in strongly coupled Yukawa liquids. We find that RBCCs are retained only for “odd” phase values of particle-level velocity perturbations, whereas, for “even” phase values, RBCCs undergo transition to a horizontal shear flow, which eventually evolves to a horizontal shearless parallel flow. The parallel macroscale flow grows algebraically before saturation, and the growth rate itself is found to increase with the amplitude of the perturbation. The fluid enstrophy as a function of time constructed from MD data shows the existence of a credible minimization mechanism under play, for such transitions.

Shock-induced melting of two-dimensional Yukawa systems from TH−PH Hugoniot curves

The TH−PH Hugoniot curves of compressional shocks in 2D Yukawa systems are derived from the combination of the Rankine–Hugoniot relation around the shock front and the universal relationship for the temperature in the postshock region. From the equation of state of 2D Yukawa liquids, the equilibrium melting curve for 2D Yukawa systems is derived using the two variables of the temperature T and the pressure P. It is found that the obtained TH−PH Hugoniot curves are intercepted by the equilibrium melting curve, indicating the existence of shock-induced phase transition at these crossing points. To confirm this prediction, molecular dynamical simulations of 2D Yukawa systems of κ=0.75 for the conditions around the crossing point are performed. In the postshock region, the calculated various diagnostics of static structural measures, like the Voronoi diagram, the defect ratio, the probability distribution of the shape factors ξ, the pair correlation function g(r), and the static structure factor S(q), suggest that, for our studied system, the shock-induced melting happens when the compressional speed of the boundary is 0.212a0ωpd<vleft<0.283a0ωpd, the same as the prediction from the crossing point.

Universal relationship of compression shocks in two-dimensional Yukawa systems.

Using molecular dynamical simulations, compressional shocks in two-dimensional (2D) dusty plasmas are quantitatively investigated under various conditions. A universal relationship between the thermal and the drift velocities after shocks is discovered in 2D Yukawa systems. Using the equation of state of 2D Yukawa liquids, and the obtained pressure from the Rankine-Hugoniot relation, an analytical relation between the thermal and the drift velocities is derived, which well agrees with the discovered universal relationship for various conditions.

Fickian yet non-Gaussian diffusion in two-dimensional Yukawa liquids.

We investigate Fickian diffusion in two-dimensional (2D) Yukawa liquids using molecular dynamics simulations. We compute the self-van Hove correlation function G_{s}(r,t) and the self-intermediate scattering function F_{s}(k,t), and we compare these functions with those obtained from mean-squared displacement (MSD) using the Gaussian approximation. According to this approximation, a linear MSD with time implies a Gaussian behavior for G_{s}(r,t) and F_{s}(k,t) at all times. Surprisingly, we find that these functions deviate from Gaussian at intermediate timescales, indicating the failure of the Gaussian approximation. Furthermore, we quantify these deviations by the non-Gaussian parameter, and we find that the deviations increase when the temperature of the liquid decreases. The origin of the non-Gaussian behavior may be the heterogeneous dynamics of dust particles observed in 2D Yukawa liquids.

Dynamics and transport of magnetized two-dimensional Yukawa liquids

Laboratory dusty plasma typically refers to a collection of micron-sized solid dust particles immersed in the plasma environment, as a result, these dust particles are negatively charged to thousands of elementary charges. Due to the electrical shielding provided by free electrons and ions, the interaction between these dust particles can be modeled as the Yukawa potential. These dust particles are strongly coupled due to their high charges, so that they exhibit collective behaviors of solids and liquids. Magnetic fields are often experimentally introduced in the modulation of dusty plasmas, and later the equivalent “magnetized” dusty plasma experiment is performed, so that magnetized Yukawa systems can be experimentally achieved now. Here, we review a series of results of collective behaviors and different transport processes of magnetized two-dimensional (2D) Yukawa liquids from Langevin dynamical simulations. From the obtained spectra of the simulation results, the vibrational density of states has only one dominant peak frequency, which can be analytically expressed as a function of the cyclotron and plasma frequencies, suggesting that the cyclotron motion of dust particles has been coupled with their thermal motion. It is also found that the statistics of particle motion with a strong magnetic field tend to deviate from the classical Maxwellian distribution. When the ratio of the cyclotron and plasma frequencies for dust particles is around the order of unity, the motion of dust particles tends to be superdiffusive. As the magnetic field increases, the shear viscosity increases with the magnetic field when the Yukawa liquid is cold; however, when the Yukawa liquid is hot, the variation trend of shear viscosity is reversed. It is also found that the structural relaxation time and the diffusion coefficient can be described as a power law relationship with two distinct values of the exponent at low and high temperatures, respectively.

Shear modulus of two-dimensional Yukawa or dusty-plasma solids obtained from the viscoelasticity in the liquid state.

Langevin dynamical simulations of two-dimensional (2D) Yukawa liquids are performed to investigate the shear modulus of 2D solid dusty plasmas. Using the known transverse sound speeds, we obtain a theoretical expression of the shear modulus of 2D Yukawa crystals as a function of the screening parameter κ, which can be used as the candidate of their shear modulus. The shear relaxation modulus G(t) of 2D Yukawa liquids is calculated from the shear stress autocorrelation function, consisting of the kinetic, potential, and cross portions. Due to their viscoelasticity, 2D Yukawa liquids exhibit the typical elastic property when the time duration is much less than the Maxwell relaxation time. As a result, the infinite frequency shear modulus G_{∞}, i.e., the shear relaxation modulus G(t) when t=0, of a 2D Yukawa liquid should be related to the shear modulus of the corresponding quenched 2D Yukawa solid (with the same κ value), with all particles suddenly frozen at their locations of the liquid state. It is found that the potential portion of the infinite frequency shear modulus for 2D Yukawa liquids at any temperature well agrees with the shear modulus of 2D Yukawa crystals with the same κ obtained from the transverse sound speeds. Thus, we find that the shear modulus of 2D Yukawa solids can be obtained from the motion of individual particles of the corresponding Yukawa liquids using their viscoelastic property.

Relationship between relaxation time and diffusion of magnetized two-dimensional Yukawa liquids

Structural relaxation and self-diffusion of magnetized two-dimensional (2D) Yukawa liquids are investigated using Langevin dynamical simulations. The structural relaxation time τα is obtained from the self-intermediate scattering function, while the self-diffusion coefficient D is calculated from the mean-squared displacement. It is discovered that, for the magnetized 2D Yukawa liquids with the coupling parameter of Γ, the relationship between τα and D can be expressed as D ∝ (1/ταΓ)ξ with two distinct values of the exponent ξ at low and high temperatures, respectively. At low temperatures, the exponent ξ decreases with the applied magnetic field, which is attributed to the dynamical heterogeneity caused by the magnetic field. At high temperatures, it is found that both D and ταΓ obey the Arrhenius behaviors, reasonably leading to the discovered D ∝ (1/ταΓ)ξ relationship.

Dynamical heterogeneities of cold 2D Yukawa liquids

Dynamical heterogeneities of 2D liquid dusty plasmas at different temperatures are investigated systematically using Langevin dynamical simulations. From the simulated trajectories, various heterogeneity measures have been calculated, such as the distance matrix, the averaged squared displacement, the non-Gaussian parameter, and the four-point susceptibility. It is found that, for 2D Yukawa liquids, both spatial and temporal heterogeneities in dynamics are more severe at a lower temperature near the melting point. For various temperatures, the calculated non-Gaussian parameter of 2D Yukawa liquids contains two peaks at different times, indicating the most heterogeneous dynamics, which are attributed to the transition of different motions and the α relaxation time, respectively. In the diffusive motion, the most heterogeneous dynamics for a colder Yukawa liquid happen more slowly, as indicated by both the non-Gaussian parameter and the four-point susceptibility.

Sound speed and diffusion in 2D Yukawa liquids: Effect of dipole–dipole interaction

The two‐dimensional (2D) Yukawa liquid with an additional screened dipole–dipole interaction is considered in connection with the 2D system of charged dust particles in complex plasmas. Particularly, the sound speed and diffusion in the case the Yukawa interaction potential dominant over the screened dipole–dipole interaction are analysed. Increase in the value of the sound speed and suppression of the super‐diffusion due to the additional dipole–dipole interaction are reported. This effect is explained by the stronger inter‐particle correlations induced by the additional dipole–dipole interaction.

Strong coupling effects on the relationship between internal energy and pressure for two-dimensional liquid dusty plasmas

Previously, the relationship between internal energy and pressure of two-dimensional (2D) strongly coupled liquid dusty plasmas was assumed to be approximately the same as that for the ideal gas [Oxtoby et al., Phys. Rev. Lett. 111, 015002 (2013)], which is a non-coupling system. To study the strong coupling effects on this relationship, the internal energy and pressure of 2D liquid dusty plasmas are obtained using equilibrium Yukawa molecular dynamics simulations. It is found that, for 2D Yukawa liquids, the internal energy and pressure follow a much more complicated relationship than that for the ideal gas. Especially at lower temperatures and for larger screening parameters, their relationship deviates from the ideal gas behavior much more. An analytical relationship between the internal energy and pressure for 2D Yukawa liquids has been obtained empirically by fitting.

Equations of state and diagrams of two-dimensional liquid dusty plasmas

Recently, the pressure of two-dimensional (2D) Yukawa liquids has been calculated from the simulations of isochores [Feng et al., J. Phys. D: Appl. Phys. 49, 235203 (2016)], which is applicable to 2D dusty plasmas. Thus, the equation of state for 2D strongly coupled liquid dusty plasmas is obtained. Isobars and isotherms of 2D liquid dusty plasmas are derived from this equation of state. For 2D liquid dusty plasmas, the surface corresponding to this equation of state has also been obtained in the 3D space of the pressure, the temperature, and the screening parameter which is related to the volume in the equilibrium state.

Numerical experiment of thermal conductivity in two-dimensional Yukawa liquids

A newly improved homogenous nonequilibrium molecular dynamics simulation (HNEMDS) method, proposed by the Evans, has been used to compute the thermal conductivity of two-dimensional (2D) strongly coupled complex (dusty) plasma liquids (SCCDPLs), for the first time. The effects of equilibrium external field strength along with different system sizes and plasma states (Γ, κ) on the thermal conductivity of SCCDPLs have been calculated using an enhanced HNEMDS method. A simple analytical temperature representation of Yukawa 2D thermal conductivity with appropriate normalized frequencies (plasma and Einstein) has also been calculated. The new HNEMDS algorithm shows that the present method provides more accurate results with fast convergence and small size effects over a wide range of plasma states. The presented thermal conductivity obtained from HNEMDS method is found to be in very good agreement with that obtained through the previously known numerical simulations and experimental results for 2D Yukawa liquids (SCCDPLs) and with the three-dimensional nonequilibrium molecular dynamics simulation (MDS) and equilibrium MDS calculations. It is shown that the HNEMDS algorithm is a powerful tool, making the calculations very efficient and can be used to predict the thermal conductivity in 2D Yukawa liquid systems.

Homogeneous Nonequilibrium Molecular Dynamics Evaluation of Thermal Conductivity in 2D Yukawa Liquids

The thermal conductivity of two-dimensional (2D) complex (dusty) plasma liquids (CDPLs) has been explored using a homogenous nonequilibrium molecular dynamics (HNEMD) technique in a canonical ensemble, for the first time. The effects of an external force field along with different plasma parameters of the Coulomb coupling ( $$\varGamma $$ ) and screening ( $$\kappa $$ ) strengths on the thermal conductivity of CDPLs have been investigated using improved HNEMD simulations. The new simulations show that the thermal conductivity is dependent on the temperature in the 2D Yukawa liquids and provides more reliable results than previously known numerical results. It is shown that a simple analytical temperature representation of Yukawa thermal conductivities with a suitable normalized Einstein frequency is performed. The obtained simulation results are in satisfactory agreement with the earlier nonequilibrium molecular dynamics, equilibrium molecular dynamics simulations, and experimental data, for the whole range of plasma parameters ( $$\varGamma ,\,\kappa $$ ).

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.

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.

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)