The Secrets of Shear Viscosity in Finite 2D Dusty Plasmas

Significance 

Dusty plasmas, also known as complex plasmas, are intriguing as they involve micro-sized dust particles immersed in a plasma environment comprising ions, electrons, and neutral gas. Due to the highly charged dust particles, their interactions are significantly stronger than thermal kinetic, exhibiting structural and kinetic properties of solids and fluids. Unlike conventional fluids, dusty plasmas exhibit unique characteristics due to their long-range particle interactions, primarily described by the screened Yukawa potential. This potential depends on parameters such as the dust particle charge, the Debye screening length, and the interparticle distance. These parameters play a pivotal role in characterizing the behavior of dusty plasmas. In a new study published in the peer-reviewed Physics of Plasmas by PhD student Yang Liu; Natascha Blosczyk; Professor Dietmar Block from the Institute of Experimental and Applied Physics (IEAP) at University of Kiel in Germany conducted a comprehensive investigation to understand and quantify shear viscosity in finite 2D dusty plasmas. The authors emphasized that dusty plasmas provide a unique opportunity to simultaneously investigate both microscopic and macroscopic aspects of fluid dynamics. Typically, in most systems, only macroscopic properties are accessible, making it challenging to understand the underlying microscopic interactions. However, in dusty plasmas, researchers can bridge this gap, gaining valuable insights into statistical properties at both levels.

The study began with an introduction to the importance of shear viscosity in various fields and highlighted the unique properties of dusty plasmas, which allow for the study of both microscopic and macroscopic behavior simultaneously. The researchers defined dusty plasmas, explaining that they consist of micro-sized highly charged dust particles immersed in a plasma environment. They also introduced the interaction potential used to describe the particle interactions in these plasmas. The study focused on two key dimensionless parameters: the screening parameter and the coupling parameter, which describe the characterization of the system state. The researchers explained that when the coupling parameter is significantly greater than 1, the system is considered strongly coupled. In such systems, particle interactions dominate, and the plasma behaves like a liquid or solid. The study emphasized the importance of understanding the viscous properties of strongly coupled dusty plasmas, especially when studying shear flows. Transport coefficients, such as shear viscosity, play a significant role in characterizing these systems. They discussed various methods to determine shear viscosity in dusty plasmas, including using laser beams and rheometers to produce shear flows and calculating viscosity from velocity profiles, as well as the Green-Kubo relation based on equilibrium fluctuations.

One of the primary objectives of the study was to address the challenges posed by finite systems. They noted that most previous research assumed infinite systems, but many experiments involve finite systems, making it necessary to investigate the impact of boundary conditions and statistics. The study described the simulation method used, a Langevin dynamics simulation, which solved the equations of motion for particles in the system. To create shear flow patterns, the researchers introduced two opposing parallel laser beams as an external force, simulating laser-induced shear flows in the dusty plasma. The authors discussed the effects of boundary conditions on flow patterns and homogeneity. It highlighted the need to identify regions suitable for the Green-Kubo approach to create a region of equilibrium based on a finite statistical scale that eliminates the influence of large-scale coherent flow patterns near the boundaries. They also discussed the long-time tail problem in the autocorrelation functions of shear stress fluctuations, emphasizing the importance of fast decay in the correlation functions to avoid computational issues. Moreover, the study investigated the statistical requirements for obtaining reliable shear viscosity estimates in finite systems. It determined that a minimum of 100 particles in the calculation area was necessary for accurate results. Furthermore, the researchers explored how shear viscosity scales with the screening parameter and the effective coupling parameter in finite 2D dusty plasmas. They determined the melting point of the system and analyzed how it influenced the scaling. The study compared its findings with prior research on shear viscosity in dusty plasmas, highlighting the agreement and discrepancies in the results obtained through different methods and under various conditions. Finally, the researchers ensured that their choice of laser drive parameters did not significantly impact the obtained viscosity values, confirming the robustness of their approach.

Overall, the new study makes significant contributions to our understanding of shear viscosity in finite 2D dusty plasmas. The authors demonstrated that the Green-Kubo relation can be applied successfully in finite shear systems, provided proper care is taken to account for boundary effects, flow patterns, and statistical significance. The findings provide valuable insights into the behavior of complex plasmas, which have applications in diverse fields, including materials science, astrophysics, and laboratory plasma physics. This research opens the door to further exploration of transport properties in complex plasmas and highlights the importance of considering finite system effects when studying these exotic materials. The results of Yang Liu et al study have implications for experimental work with dusty plasmas and advance our understanding of fundamental fluid properties in unique plasma environments.

Reference

Yang Liu; Natascha Blosczyk; Dietmar Block. Viscosity of finite Yukawa liquids. Phys. Plasmas 30, 043705 (2023); doi: 10.1063/5.0143768

Go to Phys. Plasmas

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