Green-Kubo relation for viscosity tested using experimental data for a 2D dusty plasma

Abstract

The theoretical Green-Kubo relation for viscosity is tested using experimentally obtained data. In a dusty plasma experiment, micron-size 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 amongst 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.

11 pages, 5 figures, 1 table, in press Physical Review E 2011

References in corpus (13)

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• Shear Flows and Shear Viscosity in a Two-Dimensional Yukawa System (Dusty Plasma)
• Accurate particle position measurement from images
• Crystallization of a quasi-two-dimensional granular fluid
• Shear viscosity of two-dimensional Yukawa systems in liquid state
• Solid superheating observed in two-dimensional strongly-coupled dusty plasma
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• Test of the Stokes-Einstein relation in a two-dimensional Yukawa liquid
• Time correlation functions and transport coefficients of two-dimensional Yukawa liquids
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Cited by in corpus (21)

• Statistical mechanics of a chiral active fluid
• Observation of temperature peaks due to strong viscous heating in a dusty plasma flow
• Superdiffusion of 2D Yukawa liquids due to a perpendicular magnetic field
• Practical formula for the shear viscosity of Yukawa fluids
• Frequency-dependent shear viscosity of a liquid 2D dusty plasma
• Energy Transport in a Shear Flow of Particles in a 2D Dusty Plasma
• Longitudinal viscosity of 2D Yukawa liquids
• Phonon spectra of two-dimensional liquid dusty plasmas on a one-dimensional periodic substrate
• Depinning dynamics of two-dimensional dusty plasmas on a one-dimensional periodic substrate
• Structures and Diffusion of Two Dimensional Dusty Plasmas on One Dimensional Periodic Substrates
• Dynamical states in two-dimensional charged dust particle clusters in plasma medium
• Continuous and Discontinuous Transitions in the Depinning of Two-Dimensional Dusty Plasmas on a One-Dimensional Periodic Substrate
• Directional Locking in a 2D Yukawa Solid Modulated by a 2D Periodic Substrate
• Phonon spectra of a two-dimensional solid dusty plasma modified by two-dimensional periodic substrates
• Oscillation-like diffusion of two-dimensional liquid dusty plasmas on one-dimensional periodic substrates with varied widths
• Experiment and model for a Stokes layer in a strongly coupled dusty plasma
• Superlubric-pinned transition of a two-dimensional solid dusty plasma under a periodic triangular substrate
• Shear Viscosity in Two-Dimensional Dipole Systems
• Identification of time scales of the violation of the Stokes-Einstein relation in Yukawa liquids
• Heat transport in a flowing complex plasma in microgravity conditions
• Dynamical commensuration effect in a two-dimensional Yukawa solid modulated by periodic substrates