Experimental measurement of velocity correlations for two microparticles in a plasma with ion flow

Velocity correlations are measured in a dusty plasma with only two microparticles. These correlations allow a characterization of the oscillatory modes and an identification of the effects of ion wakes. Ion wake effects are isolated by comparing two experiments with the microparticles aligned parallel vs perpendicular to the ion flow. From records of microparticle velocities, the one- and two-particle distribution functions f(1) and f(2) are obtained, and the two-particle correlation function g(2) ≡ f(2)-f(1)f(1) is calculated. Comparing the two experiments, we find that motion is much more correlated when the microparticles are aligned with the ion flow and the character of the oscillatory modes depends on the ion flow direction due to the ion wake.

Perpendicular diffusion of a dilute beam of charged dust particles in a strongly coupled dusty plasma

The diffusion of projectiles drifting through a target of strongly coupled dusty plasma is investigated in a simulation. A projectile's drift is driven by a constant force F. We characterize the random walk of the projectiles in the direction perpendicular to their drift. The perpendicular diffusion coefficient Dp⊥ is obtained from the simulation data. The force dependence of Dp⊥ is found to be a power law in a high force regime, but a constant at low forces. A mean kinetic energy Wp for perpendicular motion is also obtained. The diffusion coefficient is found to increase with Wp with a linear trend at higher energies, but an exponential trend at lower energies.

Mobility in a strongly coupled dusty plasma with gas

The mobility of a charged projectile in a strongly coupled dusty plasma is simulated. A net force F, opposed by a combination of collisional scattering and gas friction, causes projectiles to drift at a mobility-limited velocity up. The mobility μp=up/F of the projectile's motion is obtained. Two regimes depending on F are identified. In the high-force regime, μp∝F0.23, and the scattering cross section σs diminishes as up-6/5. Results for σs are compared with those for a weakly coupled plasma and for two-body collisions in a Yukawa potential. The simulation parameters are based on microgravity plasma experiments.

Effect of strong coupling on the dust acoustic instability

In a plasma containing charged dust grains, the dust acoustic instability (DAI) can be driven by ions streaming through the dust with speed less than the ion thermal speed. When the dust is strongly coupled in the liquid phase, the dispersion relation of the dust acoustic modes changes in a way that leads to an enhancement of the growth rate of the DAI. In this paper, we show how strong coupling enhances the DAI growth rate and consider application to microgravity experiments where subthermal ion flows are in general possible.

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.

Observation of temperature peaks due to strong viscous heating in a dusty plasma flow

Profound temperature peaks are observed in regions of high velocity shear in a 2D dusty plasma experiment with laser-driven flow. These are attributed to viscous heating, which occurs due to collisional scattering in a shear flow. Using measurements of viscosity, thermal conductivity, and spatial profiles of flow velocity and temperature, we determine three dimensionless numbers: Brinkman, Br = 0.5; Prandtl, Pr = 0.09; and Eckert, Ec = 5.7. The large value of Br indicates significant viscous heating that is consistent with the observed temperature peaks.

Energy transport in a shear flow of particles in a two-dimensional dusty plasma

A shear flow of particles in a laser-driven two-dimensional (2D) dusty plasma is observed in a study of viscous heating and thermal conduction. Video imaging and particle tracking yields particle velocity data, which we convert into continuum data, presented as three spatial profiles: mean particle velocity (i.e., flow velocity), mean-square particle velocity, and mean-square fluctuations of particle velocity. These profiles and their derivatives allow a spatially resolved determination of each term in the energy and momentum continuity equations, which we use for two purposes. First, by balancing these terms so that their sum (i.e., residual) is minimized while varying viscosity η and thermal conductivity κ as free parameters, we simultaneously obtain values for η and κ in the same experiment. Second, by comparing the viscous heating and thermal conduction terms, we obtain a spatially resolved characterization of the viscous heating.

Two-particle distribution and correlation function for a 1D dusty plasma experiment

Experimentally measured velocities are used to obtain the one- and two-particle distribution functions f(1) and f(2) and the two-particle correlation function g(2)≡f(2)-f(1)f(1). The fluctuating velocities of interacting charged microparticles were recorded by tracking their motion while they were immersed in a dusty plasma. The phase space was reduced by having only two particles in a harmonic one dimensional confining potential. In statistical theory, g(2) is usually said to be dominated by the randomness of collisions, but here we find that it is dominated by collective oscillatory modes.

Waves and instability in a one-dimensional microfluidic array

Motion in a one-dimensional (1-D) microfluidic array is simulated. Water droplets, dragged by flowing oil, are arranged in a single row. Due to their hydrodynamic interactions, the spacing between these droplets oscillates with a wave-like motion that is longitudinal or transverse. The simulation yields wave spectra that agree well with experiment. The wave-like motion has an instability which is confirmed to arise from nonlinearities in the interaction potential. The instability's growth is spatially localized. By selecting an appropriate correlation function, the interaction between the longitudinal and transverse waves is described.

Frequency-dependent shear viscosity of a liquid two-dimensional dusty plasma

The viscoelasticity of a two-dimensional (2D) liquid stronglycoupled dusty plasma is studied experimentally, without macroscopic shear. Positions and velocities of the dust particles, measured by video microscopy, are used as the inputs to the generalized Green-Kubo relation to obtain the complex viscosity η(ω). The real part of η(ω) (which corresponds to dissipation) diminishes gradually with frequency, while the imaginary part (which corresponds to elasticity) is peaked at a frequency below the 2D dusty plasma frequency. The viscoelastic approximation is found to accurately describe the 2D experimental results for η(ω), yielding the Maxwell relaxation time τ(M)=0.10 s. Results for η(ω) are compared to 2D molecular dynamics Yukawa simulations and to a previous experiment that was performed using an oscillating macroscopic shear.

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.

Synchronization mechanism and Arnold tongues for dust density waves

The nonlinear phenomenon of synchronization is characterized experimentally for dust density waves, i.e., dust acoustic waves, which are self-excited due to an ion streaming instability. The waves propagate in a dust cloud with a natural frequency of 22 Hz. We synchronize these waves to a different frequency using a driving electrode that sinusoidally modulates the ion density. We study four synchronized states, with frequencies that are multiples of 1, 2, 3, and 1/2 of the driving frequency. Comparing to phenomena that are typical of the van der Pol paradigm, we find that synchronization of our waves exhibit the signature of the suppression mechanism but not that of the phaselocking mechanism. Additionally, synchronization of our waves exhibits three characteristics that differ from the van der Pol paradigm: a threshold amplitude that can be seen in the Arnold tongue diagram, a branching of the 1:1 harmonic tongue at its lower extremity, and a nonharmonic state. The latter state appears to be a nonlinear oscillation; it is neither at the natural frequency nor a synchronized state.

Particle chains in a dilute dusty plasma with subsonic ion flow

Chains of charged dust particles are observed aligned with a subsonic ion flow. These chains are found in dilute regions, near the midplane of a parallel-plate radio-frequency plasma under microgravity conditions. The argon ion flow speed near these chains was estimated to be of order 10(2) m/s, corresponding to an ion acoustic Mach number M<0.1. The chains were observed to be stable in both the longitudinal and transverse directions. This stability suggests that there is a transverse restoring force. The transverse components of the ion-drag force or electrostatic wake-field forces could provide such a stabilizing effect. The chain appears to terminate with a final dust particle that is located in a dilute region; this observation suggests a possible attractive force in the longitudinal direction in the presence of a subsonic ion flow.

Green-Kubo relation for viscosity tested using experimental data for a two-dimensional dusty plasma

The theoretical Green-Kubo relation for viscosity is tested using experimentally obtained data. In a dusty plasma experiment, micron-sized dust particles are introduced into a partially ionized argon plasma, where they become negatively charged. They are electrically levitated to form a single-layer Wigner crystal, which is subsequently melted using laser heating. In the liquid phase, these dust particles experience interparticle electric repulsion, laser heating, and friction from the ambient neutral argon gas, and they can be considered to be in a nonequilibrium steady state. Direct measurements of the positions and velocities of individual dust particles are then used to obtain a time series for an off-diagonal element of the stress tensor and its time autocorrelation function. This calculation also requires the interparticle potential, which was not measured experimentally but was obtained using a Debye-Hückel-type model with experimentally determined parameters. Integrating the autocorrelation function over time yields the viscosity for shearing motion among dust particles. The viscosity so obtained is found to agree with results from a previous experiment using a hydrodynamical Navier-Stokes equation. This comparison serves as a test of the Green-Kubo relation for viscosity. Our result is also compared to the predictions of several simulations.

Polygon construction to investigate melting in two-dimensional strongly coupled dusty plasma

The polygon construction method of Glaser and Clark is used to characterize melting and crystallization in a two-dimensional (2D) strongly coupled dusty plasma. Using particle positions measured by video microscopy, bonds are identified by triangulation, and unusually long bonds are deleted. The resulting polygons have three or more sides. Geometrical defects, which are polygons with more than three sides, are found to proliferate during melting. Pentagons are found in liquids, where they tend to cluster with other pentagons. Quadrilaterals are a less severe defect, so that disorder can be characterized by the ratio of quadrilaterals to pentagons. This ratio is found to be less in a liquid than in a solid or a superheated solid. Another measure of disorder is the abundance of different kinds of vertices, according to the type of polygons that adjoin there. Unexpectedly, spikes are observed in the abundance of certain vertex types during rapid temperature changes. Hysteresis, revealed by a plot of a disorder parameter vs temperature, is examined to study sudden heating. The hysteresis diagram also reveals features suggesting a possibility of latent heat in the melting and rapid cooling processes.

Errors in particle tracking velocimetry with high-speed cameras

Velocity errors in particle tracking velocimetry (PTV) are studied. When using high-speed video cameras, the velocity error may increase at a high camera frame rate. This increase in velocity error is due to particle-position uncertainty, which is one of the two sources of velocity errors studied here. The other source of error is particle acceleration, which has the opposite trend of diminishing at higher frame rates. Both kinds of errors can propagate into quantities calculated from velocity, such as the kinetic temperature of particles or correlation functions. As demonstrated in a dusty plasma experiment, the kinetic temperature of particles has no unique value when measured using PTV, but depends on the sampling time interval or frame rate. It is also shown that an artifact appears in an autocorrelation function computed from particle positions and velocities, and it becomes more severe when a small sampling-time interval is used. Schemes to reduce these errors are demonstrated.

Identifying anomalous diffusion and melting in dusty plasmas

Anomalous diffusion in liquids and the solid-liquid phase transition (melting) are studied in two-dimensional Yukawa systems. The self-intermediate scattering function (self-ISF), calculated from simulation data, exhibits a temporal decay, or relaxation, with a characteristic relaxation time. This decay is found to be useful for distinguishing normal and anomalous diffusion in a liquid, and for identifying the solid-liquid phase transition. For liquids, a scaling of the relaxation time with length scale is found. For the solid-liquid phase transition, the shape of the self-ISF curve is found to be a sensitive indicator of phase. Friction has a significant effect on the timing of relaxation, but not the melting point.

Mode coupling for phonons in a single-layer dusty plasma crystal

New modes in a dusty plasma result from coupling of differently polarized phonons. A single horizontal layer of charged microparticles, confined so that vertical as well as horizontal motions are possible, usually exhibits three modes. An experiment shows that mode coupling leads to a new hybrid mode and another new mode. Coupling also leads to a recently reported hybrid mode and nondispersive mode, shown here to occur in an unmelted lattice. A linear theory based on ion wakes is able to predict some, but not all, of these modes. Other multiphase systems could exhibit similar mode coupling.

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.

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.

Evolution of shear-induced melting in a dusty plasma

The spatiotemporal development of melting is studied experimentally in a 2D dusty plasma suspension. Starting with an ordered lattice, and then suddenly applying localized shear, a pair of counterpropagating flow regions develop. A transition between two melting stages is observed before a steady state is reached. Melting spreads with a front that propagates at the transverse sound speed. Unexpectedly, coherent longitudinal waves are excited in the flow region.

Gas flow driven by thermal creep in dusty plasma

Thermal creep flow (TCF) is a flow of gas driven by a temperature gradient along a solid boundary. Here, TCF is demonstrated experimentally in a dusty plasma. Stripes on a glass box are heated by laser beam absorption, leading to both TCF and a thermophoretic force. The design of the experiment allows isolating the effect of TCF. A stirring motion of the dust particle suspension is observed. By eliminating all other explanations for this motion, we conclude that TCF at the boundary couples by drag to the bulk gas, causing the bulk gas to flow, thereby stirring the suspension of dust particles. This result provides an experimental verification, for the field of fluid mechanics, that TCF in the slip-flow regime causes steady-state gas flow in a confined volume.

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.