Finite-size effects in the static structure factor S(k) and S(0) for a two-dimensional Yukawa liquid.

Finite-size effects in the static structure factor S(k) are analyzed for an amorphous substance. As the number of particles is reduced, S(0) increases greatly, up to an order of magnitude. Meanwhile, there is a decrease in the height of the first peak S_{peak}. These finite-size effects are modeled accurately by the Binder formula for S(0) and our empirical formula for S_{peak}. Procedures are suggested to correct for finite-size effects in S(k) data and in the hyperuniformity index H≡S(0)/S_{peak}. These principles generally apply to S(k) obtained from particle positions in noncrystalline substances. The amorphous substance we simulate is a two-dimensional liquid, with a soft Yukawa interaction modeling a dusty plasma experiment.

Comparison of the static structure factor at long wavelengths for a dusty plasma liquid and other liquids.

Especially small values of the static structure factor S(k) at long wavelengths, i.e., small k, were obtained in an analysis of experimental data, for a two-dimensional dusty plasma in its liquid state. For comparison, an analysis of S(k) data was carried out for many previously published experiments with other liquids. The latter analysis indicates that the magnitude of S(k) at small k is typically in a range 0.02-0.13. In contrast, the corresponding value for a dusty plasma liquid was found to be as small as 0.0139. Another basic finding for the dusty plasma liquid is that S(k) at small k generally increases with temperature, with its lowest value, noted above, occurring near the melting point. Simulations were carried out for the dusty plasma liquid, and their results are generally consistent with the experiment. Since a dusty plasma has a soft interparticle interaction, our findings support earlier theoretical suggestions that a useful design strategy for creating materials having exceptionally low values of S(0), so-called hyperuniform materials, is the use of a condensed material composed of particles that interact softly at their periphery.

Frequency-dependent complex viscosity obtained for a liquid two-dimensional dusty plasma experiment.

Strongly coupled plasmas in a liquid phase can be characterized by a complex viscosity η(ω), which is a function of frequency. Data from a single experiment with dusty plasma were analyzed to compare η(ω) obtained by two fundamentally distinct methods. In a nonequilibrium method, a pair of counterpropagating laser beams, separated by a gap, applied a sinusoidal shear to a two-dimensional liquid, and η(ω) was determined using the constitutive relation. In an equilibrium method, there was no externally applied shear, so η(ω) could be calculated with a generalized Green-Kubo relation. The results for these two methods are compared for the real and imaginary parts of η(ω). For both parts, it is confirmed that the two methods yield results that agree qualitatively in their trends with frequency, with the real part diminishing with ω and the imaginary part increasing with ω, as expected for viscoelastic liquids. Quantitatively, the values of η(ω) obtained by the two methods differ slightly. For the experiment that we analyze, values for the real and imaginary parts of η(ω) are substantially greater than those reported in an earlier experiment, which we attribute to shear thinning effects in the earlier experiment. The experiment we analyze was designed to minimize shear thinning, unlike the earlier experiment.

Shock width measured under liquid and solid conditions in a two-dimensional dusty plasma.

Widths of shocks are compared, under liquid and solid conditions, for a two-dimensional layer of charged microspheres levitated in a plasma. In this strongly coupled dusty plasma, a shock was launched as a blast wave by moving an exciter wire at a supersonic speed and then bringing it to a halt. Runs were repeated with the layer of microspheres prepared two ways: a crystallinelike solid and a liquid. The liquid was sustained using laser heating, with conditions that were otherwise the same as in the solid. The shock width was found to be less in a liquid than in a solid, where it was four to six lattice constants. These measurements were based on the high-gradient region of density profiles. The profiles were obtained from particle coordinates, measured by high-speed video imaging. The spatial resolution was improved by combining particle coordinates, in the shock's frame of reference, from a sequence of images.

Experiment and model for a Stokes layer in a strongly coupled dusty plasma.

A Stokes layer, which is a flow pattern that arises in a viscous fluid adjacent to an oscillatory boundary, was observed in an experiment using a two-dimensional strongly coupled dusty plasma. Liquid conditions were maintained using laser heating, while a separate laser manipulation applied an oscillatory shear that was localized and sinusoidal. The evolution of the resulting flow was analyzed using space-time diagrams. These figures provide an intuitive visualization of a Stokes layer, including features such as the depth of penetration and wavelength. Another feature, the characteristic speed for the penetration of the oscillatory flow, also appears prominently in space-time diagrams. To model the experiment, the Maxwell-fluid model of a Stokes layer was generalized to describe a two-phase liquid. In our experiment, the phases were gas and dust, where the dust cloud was viscoelastic due to strong Coulomb coupling. The model is found to agree with the experiment, in the appearance of the space-time diagrams, and in the values of the characteristic speed, depth of penetration, and wavelength.

Fluctuation theorem convergence in a viscoelastic medium demonstrated experimentally using a dusty plasma.

The convergence of the steady-state fluctuation theorem (SSFT) is investigated in a shear-flow experiment performed in a dusty plasma. This medium has a viscoelastic property characterized by the Maxwell relaxation time τ_{M}. Using measurements of the time series of the entropy production rate, for subsystems of various sizes, it is discovered that the SSFT convergence time decreases with the increasing system size until it eventually reaches a minimum value of τ_{M}, no matter the size of the subsystem. This result indicates that the convergence of the SSFT is limited by the energy-storage property of the viscoelastic medium.

Experimental determination of shock speed versus exciter speed in a two-dimensional dusty plasma.

A shock that is continuously driven by a moving exciter will propagate at a speed that depends on the exciter speed. We obtained this dependence experimentally, in a strongly coupled dusty plasma that was prepared as a single two-dimensional layer of charged microparticles. Attaining this result required an experimental advance, developing a method of driving a shock continuously, which we did using an exciter moving at a constant supersonic speed, analogous to a piston in a cylinder. The resulting compressional pulse was a shock that propagated steadily without weakening, ahead of the moving exciter. We compare our experimental results to an empirical form M_{shock}=1+sM_{exciter}, and to the prediction of a recent simulation.

Dusty plasma experiment to confirm an expression for the decay of autocorrelation functions.

Statistical physicists recently proposed an expression for an autocorrelation function (ACF) [Belousov and Cohen, Phys. Rev. E 94, 062124 (2016)2470-004510.1103/PhysRevE.94.062124] that has, until now, not been tested experimentally. The expression captures the early behavior of the ACF decay, when the ACF is flattened. Using experimental data from a nonequilibrium steady-state dusty plasma, we confirm that the expression's use extends to liquidlike strongly coupled plasmas. A transition in the shape of the ACF is identified, and we suggest that it corresponds to the onset of collisional scattering.

Experimental demonstration that a free-falling aerosol particle obeys a fluctuation theorem.

We investigate the fluctuating motion of an aerosol particle falling in air. Using a Millikan-like setup, we tracked a 1-µm sphere falling at its terminal velocity. We observe occurrences of particles undergoing upward displacements against the force of gravity, so that negative work is done briefly. These negative-work events have a probability that is shown to obey the work fluctuation theorem. This experimental confirmation of the theorem's applicability to aerosols leads us to develop and demonstrate an application: an in situ measurement of an aerosol particle's mass.

Overestimation of Viscosity by the Green-Kubo Method in a Dusty Plasma Experiment.

The Green-Kubo (GK) method is widely used in simulations of strongly coupled plasmas to obtain the viscosity coefficient. However, the method's applicability, which is often taken for granted, has not been tested experimentally. We report an experimental test using a two-dimensional strongly coupled dusty plasma. We find that the GK viscosity is ≈60% larger than the result of a benchmark hydrodynamic method, obtained in the same experiment with the same conditions except for the presence of shear.

Characterization of three-dimensional structure using images.

The pair correlation function g(r) and the number density n for particles in a three-dimensional (3D) sample can be determined from a single two-dimensional (2D) image. The 2D image is obtained experimentally with a simple setup: a cross-sectional slab of particles is illuminated with a laser sheet and imaged with a single camera. After image analysis, to find positions of particles in two dimensions, along with their brightness, one obtains g(r), also known as the radial distribution function. The key for attaining high accuracy is to use only the particles that are brighter than a filter level, which we refine to achieve greater accuracy. The density n is obtained from g(r). This method is demonstrated in a dusty plasma experiment. Accuracy is quantified using simulation data; errors of 2% for both the pair correlation function and the number density are achievable. The method is useful for dusty plasmas and colloids.

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.

Superdiffusion of two-dimensional Yukawa liquids due to a perpendicular magnetic field.

Stochastic transport of a two-dimensional (2D) dusty plasma liquid with a perpendicular magnetic field is studied. Superdiffusion is found to occur especially at higher magnetic fields with ß of order unity. Here, ß = ω(c)/ω(pd) is the ratio of the cyclotron and plasma frequencies for dust particles. The mean-square displacement MSD = 4D(α)t(α) is found to have an exponent α > 1, indicating superdiffusion, with α increasing monotonically to 1.1 as ß increases to unity. The 2D Langevin molecular dynamics simulation used here also reveals that another indicator of random particle motion, the velocity autocorrelation function, has a dominant peak frequency ω(peak) that empirically obeys ω(peak)(2) = ω(c)(2) + ω(pd)(2)/4.

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.

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.

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.

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.