Frequency-dependent complex viscosity obtained for a liquid two-dimensional dusty plasma experiment
Abstract
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. As a result, the experiment we analyzemore »
- Publication Date:
- Research Org.:
- Univ. of Iowa, Iowa City, IA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1972223
- Alternate Identifier(s):
- OSTI ID: 1863410
- Grant/Contract Number:
- SC0014566
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. E
- Additional Journal Information:
- Journal Volume: 105; Journal Issue: 1; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Plasma transport; Dusty or complex plasma; Strongly-coupled plasmas; Viscoelasticity
Citation Formats
Berumen, Jorge, and Goree, J. Frequency-dependent complex viscosity obtained for a liquid two-dimensional dusty plasma experiment. United States: N. p., 2022.
Web. doi:10.1103/physreve.105.015209.
Berumen, Jorge, & Goree, J. Frequency-dependent complex viscosity obtained for a liquid two-dimensional dusty plasma experiment. United States. https://doi.org/10.1103/physreve.105.015209
Berumen, Jorge, and Goree, J. Fri .
"Frequency-dependent complex viscosity obtained for a liquid two-dimensional dusty plasma experiment". United States. https://doi.org/10.1103/physreve.105.015209. https://www.osti.gov/servlets/purl/1972223.
@article{osti_1972223,
title = {Frequency-dependent complex viscosity obtained for a liquid two-dimensional dusty plasma experiment},
author = {Berumen, Jorge and Goree, J.},
abstractNote = {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. As a result, the experiment we analyze was designed to minimize shear thinning, unlike the earlier experiment.},
doi = {10.1103/physreve.105.015209},
journal = {Physical Review. E},
number = 1,
volume = 105,
place = {United States},
year = {Fri Jan 28 00:00:00 EST 2022},
month = {Fri Jan 28 00:00:00 EST 2022}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Dust acoustic waves in strongly coupled dissipative plasmas
journal, December 2000
- Xie, B. S.; Yu, M. Y.
- Physical Review E, Vol. 62, Issue 6
Kolmogorov flow in two dimensional strongly coupled dusty plasma
journal, July 2014
- Gupta, Akanksha; Ganesh, R.; Joy, Ashwin
- Physics of Plasmas, Vol. 21, Issue 7
Asymptotic Time Behavior of Correlation Functions
journal, November 1970
- Ernst, M. H.; Hauge, E. H.; van Leeuwen, J. M. J.
- Physical Review Letters, Vol. 25, Issue 18
Reliable Viscosity Calculation from Equilibrium Molecular Dynamics Simulations: A Time Decomposition Method
journal, July 2015
- Zhang, Yong; Otani, Akihito; Maginn, Edward J.
- Journal of Chemical Theory and Computation, Vol. 11, Issue 8
Non-Gaussian statistics and superdiffusion in a driven-dissipative dusty plasma
journal, October 2008
- Liu, Bin; Goree, J.; Feng, Yan
- Physical Review E, Vol. 78, Issue 4
Experiment and model for a Stokes layer in a strongly coupled dusty plasma
journal, September 2021
- Berumen, Jorge; Goree, J.
- Physical Review E, Vol. 104, Issue 3
First Direct Measurement of Optical Phonons in 2D Plasma Crystals
journal, November 2009
- Couëdel, L.; Nosenko, V.; Zhdanov, S. K.
- Physical Review Letters, Vol. 103, Issue 21
Three-Particle Correlations in Nonideal Dusty Plasma
journal, July 2004
- Vaulina, O. S.; Petrov, O. F.; Fortov, V. E.
- Physical Review Letters, Vol. 93, Issue 3
Superdiffusion and Viscoelastic Vortex Flows in a Two-Dimensional Complex Plasma
journal, March 2006
- Ratynskaia, S.; Rypdal, K.; Knapek, C.
- Physical Review Letters, Vol. 96, Issue 10
Wake Formation and Wake Field Effects in Complex Plasmas: Wake Formation and Wake Field Effects in Complex Plasmas
journal, September 2012
- Block, D.; Carstensen, J.; Ludwig, P.
- Contributions to Plasma Physics, Vol. 52, Issue 10
Nonlinear dusty magnetosonic waves in a strongly coupled dusty plasma
journal, December 2019
- Wang, Yunliang
- AIP Advances, Vol. 9, Issue 12
Nonlinear wave propagation in a strongly coupled collisional dusty plasma
journal, June 2011
- Ghosh, Samiran; Gupta, Mithil Ranjan; Chakrabarti, Nikhil
- Physical Review E, Vol. 83, Issue 6
Superdiffusion in two-dimensional Yukawa liquids
journal, January 2007
- Liu, Bin; Goree, J.
- Physical Review E, Vol. 75, Issue 1
Complex plasmas: forces and dynamical behaviour
journal, November 2008
- Piel, A.; Arp, O.; Block, D.
- Plasma Physics and Controlled Fusion, Vol. 50, Issue 12
Effect of Nonthermal Electrons and Ions on Longitudinal Dust Acoustic Solitary Waves in a Strongly Coupled Dusty Plasma
journal, April 2018
- Ghai, Yashika; Saini, N. S.; Singh, Manpreet
- IEEE Transactions on Plasma Science, Vol. 46, Issue 4
Observation of Temperature Peaks due to Strong Viscous Heating in a Dusty Plasma Flow
journal, October 2012
- Feng, Yan; Goree, J.; Liu, Bin
- Physical Review Letters, Vol. 109, Issue 18
Observation of Coulomb-Crystal Formation from Carbon Particles Grown in a Methane Plasma
journal, June 1994
- Hayashi, Yasuaki; Tachibana, Kunihide
- Japanese Journal of Applied Physics, Vol. 33, Issue Part 2, No. 6A
Periodically sheared 2D Yukawa systems
journal, October 2015
- Kovács, Anikó Zsuzsa; Hartmann, Peter; Donkó, Zoltán
- Physics of Plasmas, Vol. 22, Issue 10
Laser method of heating monolayer dusty plasmas
journal, March 2006
- Nosenko, V.; Goree, J.; Piel, A.
- Physics of Plasmas, Vol. 13, Issue 3
Crystallization Dynamics of a Single Layer Complex Plasma
journal, September 2010
- Hartmann, Peter; Douglass, Angela; Reyes, Jorge C.
- Physical Review Letters, Vol. 105, Issue 11
Potential around a charged dust particle in a collisional sheath
journal, May 2007
- Kompaneets, R.; Konopka, U.; Ivlev, A. V.
- Physics of Plasmas, Vol. 14, Issue 5
Slow Plastic Creep of 2D Dusty Plasma Solids
journal, July 2014
- Hartmann, Peter; Kovács, Anikó Zs.; Douglass, Angela M.
- Physical Review Letters, Vol. 113, Issue 2
Overestimation of Viscosity by the Green-Kubo Method in a Dusty Plasma Experiment
journal, May 2017
- Haralson, Zach; Goree, J.
- Physical Review Letters, Vol. 118, Issue 19
Viscoelastic response of Yukawa liquids
journal, May 2010
- Donkó, Z.; Goree, J.; Hartmann, P.
- Physical Review E, Vol. 81, Issue 5
Ultracold neutral plasmas
journal, November 2016
- Lyon, M.; Rolston, S. L.
- Reports on Progress in Physics, Vol. 80, Issue 1
Longitudinal collective modes of strongly coupled dusty plasmas at finite frequencies and wavevectors
journal, January 2000
- Murillo, M. S.
- Physics of Plasmas, Vol. 7, Issue 1
Frequency-dependent shear viscosity of a liquid two-dimensional dusty plasma
journal, June 2012
- Feng, Yan; Goree, J.; Liu, Bin
- Physical Review E, Vol. 85, Issue 6
Cutoff wave number for shear waves and Maxwell relaxation time in Yukawa liquids
journal, June 2012
- Goree, J.; Donkó, Z.; Hartmann, P.
- Physical Review E, Vol. 85, Issue 6
Static and dynamic shear viscosity of a single-layer complex plasma
journal, July 2011
- Hartmann, Peter; Sándor, Máté Csaba; Kovács, Anikó
- Physical Review E, Vol. 84, Issue 1
Time-correlation functions and transport coefficients of two-dimensional Yukawa liquids
journal, February 2009
- Donkó, Z.; Goree, J.; Hartmann, P.
- Physical Review E, Vol. 79, Issue 2
The nonadiabatic dust charge variation on dust acoustic solitary and shock waves in strongly coupled dusty plasmas
journal, January 2016
- Wang, Yunliang; Guo, Xiaoyan; Lu, Yanzhen
- Physics Letters A, Vol. 380, Issue 1-2
Radiation pressure and gas drag forces on a melamine-formaldehyde microsphere in a dusty plasma
journal, January 2003
- Liu, Bin; Goree, J.; Nosenko, V.
- Physics of Plasmas, Vol. 10, Issue 1
Shear Viscosity and Shear Thinning in Two-Dimensional Yukawa Liquids
journal, April 2006
- Donkó, Z.; Goree, J.; Hartmann, P.
- Physical Review Letters, Vol. 96, Issue 14
Laser Heating of 2-D Dusty Plasmas Using a Random Arc Pattern
journal, April 2016
- Haralson, Zach; Goree, John
- IEEE Transactions on Plasma Science, Vol. 44, Issue 4
Generalized hydrodynamics model for strongly coupled plasmas
journal, July 2015
- Diaw, A.; Murillo, M. S.
- Physical Review E, Vol. 92, Issue 1
The Phenomenological Theory of Linear Viscoelastic Behavior
book, January 1989
- Tschoegl, Nicholas W.
- Springer Berlin, Heidelberg
The conception of a complex viscosity and its application to dielectrics
journal, January 1935
- Gemant, A.
- Transactions of the Faraday Society, Vol. 31
Measurement of the Interaction Potential of Microspheres in the Sheath of a rf Discharge
journal, January 2000
- Konopka, U.; Morfill, G. E.; Ratke, L.
- Physical Review Letters, Vol. 84, Issue 5
Shear Flows and Shear Viscosity in a Two-Dimensional Yukawa System (Dusty Plasma)
journal, October 2004
- Nosenko, V.; Goree, J.
- Physical Review Letters, Vol. 93, Issue 15
Who conceived the “complex viscosity”?
journal, March 2012
- Bird, R. Byron; Giacomin, A. Jeffrey
- Rheologica Acta, Vol. 51, Issue 6
Statistical physics of dense plasmas: Thermodynamics, transport coefficients and dynamic correlations
journal, May 1987
- Ichimaru, S.
- Physics Reports, Vol. 149, Issue 2-3
Frequency-dependent Stokes-Einstein relation in supercooled liquids
journal, May 2007
- Zangi, Ronen; Kaufman, Laura J.
- Physical Review E, Vol. 75, Issue 5
Driven transverse shear waves in a strongly coupled dusty plasma
journal, August 2008
- Bandyopadhyay, P.; Prasad, G.; Sen, A.
- Physics Letters A, Vol. 372, Issue 33
Nonlinear wave propagation in strongly coupled dusty plasmas
journal, March 2010
- Veeresha, B. M.; Tiwari, S. K.; Sen, A.
- Physical Review E, Vol. 81, Issue 3
High‐Frequency Elastic Moduli of Simple Fluids
journal, December 1965
- Zwanzig, Robert; Mountain, Raymond D.
- The Journal of Chemical Physics, Vol. 43, Issue 12
Temperature dependence of viscosity in a two-dimensional dusty plasma without the effects of shear thinning
journal, September 2016
- Haralson, Zach; Goree, J.
- Physics of Plasmas, Vol. 23, Issue 9
Statistical-Mechanical Foundation of the Ubiquity of Lévy Distributions in Nature
journal, November 1995
- Tsallis, Constantino; Levy, Silvio V. F.; Souza, André M. C.
- Physical Review Letters, Vol. 75, Issue 20
Strongly coupled plasmas: high-density classical plasmas and degenerate electron liquids
journal, October 1982
- Ichimaru, Setsuo
- Reviews of Modern Physics, Vol. 54, Issue 4
Structure of finite two-dimensional Yukawa lattices: Dust crystals
journal, November 2001
- Totsuji, Hiroo; Totsuji, Chieko; Tsuruta, Kenji
- Physical Review E, Vol. 64, Issue 6
Instabilities in strongly coupled ultracold neutral plasmas
journal, January 2011
- Rosenberg, M.; Shukla, P. K.
- Physica Scripta, Vol. 83, Issue 1
Equilibrium properties and phase diagram of two-dimensional Yukawa systems
journal, August 2005
- Hartmann, P.; Kalman, G. J.; Donkó, Z.
- Physical Review E, Vol. 72, Issue 2
Generalized viscoelastic theory of the glass transition for strongly coupled, classical, one-component plasmas
journal, June 1986
- Ichimaru, Setsuo; Tanaka, Shigenori
- Physical Review Letters, Vol. 56, Issue 26
Time-Correlation Functions and Transport Coefficients in Statistical Mechanics
journal, October 1965
- Zwanzig, R.
- Annual Review of Physical Chemistry, Vol. 16, Issue 1
Low frequency modes in strongly coupled dusty plasmas
journal, October 1998
- Kaw, P. K.; Sen, A.
- Physics of Plasmas, Vol. 5, Issue 10
Time dependent correlation functions and mode-mode coupling theories
journal, June 1975
- Pomeau, Y.; Résibois, P.
- Physics Reports, Vol. 19, Issue 2
Plasma Crystal: Coulomb Crystallization in a Dusty Plasma
journal, August 1994
- Thomas, H.; Morfill, G. E.; Demmel, V.
- Physical Review Letters, Vol. 73, Issue 5
Non‐neutral ion plasmas and crystals, laser cooling, and atomic clocks*
journal, May 1994
- Bollinger, J. J.; Wineland, D. J.; Dubin, Daniel H. E.
- Physics of Plasmas, Vol. 1, Issue 5
Green-Kubo relation for viscosity tested using experimental data for a two-dimensional dusty plasma
journal, October 2011
- Feng, Yan; Goree, J.; Liu, Bin
- Physical Review E, Vol. 84, Issue 4
Radiation pressure measurements on micron-size individual dust grains
journal, January 2003
- Abbas, M. M.
- Journal of Geophysical Research, Vol. 108, Issue A6
Velocity-Correlation Functions in Two and Three Dimensions: Low Density
journal, August 1972
- Dorfman, J. R.; Cohen, E. G. D.
- Physical Review A, Vol. 6, Issue 2
Diagnostics for transport phenomena in strongly coupled dusty plasmas
journal, November 2013
- Goree, J.; Liu, Bin; Feng, Yan
- Plasma Physics and Controlled Fusion, Vol. 55, Issue 12
Direct observation of Coulomb crystals and liquids in strongly coupled rf dusty plasmas
journal, June 1994
- Chu, J. H.; I., Lin
- Physical Review Letters, Vol. 72, Issue 25
Viscoelastic modes in a strongly coupled, cold, magnetized dusty plasma
journal, November 2010
- Banerjee, Debabrata; Mylavarapu, Janaki Sita; Chakrabarti, Nikhil
- Physics of Plasmas, Vol. 17, Issue 11
Accurate particle position measurement from images
journal, May 2007
- Feng, Y.; Goree, J.; Liu, Bin
- Review of Scientific Instruments, Vol. 78, Issue 5
Microstructural Evolution and Irreversibility in the Viscoelastic Response of Mesoscopic Dusty-Plasma Liquids
journal, March 2007
- Chan, Chia-Ling; I., Lin
- Physical Review Letters, Vol. 98, Issue 10
Viscosity calculated in simulations of strongly coupled dusty plasmas with gas friction
journal, May 2011
- Feng, Yan; Goree, J.; Liu, Bin
- Physics of Plasmas, Vol. 18, Issue 5
Errors in particle tracking velocimetry with high-speed cameras
journal, May 2011
- Feng, Yan; Goree, J.; Liu, Bin
- Review of Scientific Instruments, Vol. 82, Issue 5
Strongly coupled plasmas obey the fluctuation theorem for entropy production
journal, September 2017
- Wong, Chun-Shang; Goree, J.; Haralson, Zach
- Nature Physics, Vol. 14, Issue 1
Self-gravitational instability in magnetized finitely conducting viscoelastic fluid
journal, January 2013
- Prajapati, R. P.; Chhajlani, R. K.
- Astrophysics and Space Science, Vol. 344, Issue 2
Effect of rotation on the growth rate of magnetogravitational instability of a viscoelastic medium
journal, November 2014
- Dhiman, Joginder Singh; Sharma, Rajni
- Physica Scripta, Vol. 89, Issue 12