Skip to main content

Visco-instability of shear viscoelastic collisional dusty plasma systems

  • M. Mahdavi-Gharavi (a1), K. Hajisharifi (a1) and H. Mehidan (a1)

In this paper, the stability of Newtonian and non-Newtonian viscoelastic collisional shear-velocity dusty plasmas is studied, using the framework of a generalized hydrodynamic (GH) model. Motivated by Banerjee et al.’s work (Banerjee et al., New J. Phys., vol. 12 (12), 2010, p. 123031), employing linear perturbation theory as well as the local approximation method in the inhomogeneous direction, the dispersion relations of the Fourier modes are obtained for Newtonian and non-Newtonian dusty plasma systems in the presence of a dust–neutral friction term. The analysis of the obtained dispersion relation in the non-Newtonian case shows that the inhomogeneous viscosity force depending on the velocity shear profile can be the genesis of a free energy source which leads the shear system to be unstable. Study of the dust–neutral friction effect on the instability of the considered systems using numerical analysis of the dispersion relation in the Newtonian case demonstrates that the maximum growth rate decreases considerably by increasing the collision frequency in the hydrodynamic regime, while this reduction can be neglected in the kinetic regime. Results show a more significant stabilization role of the dust–neutral friction term in the non-Newtonian cases, through decreasing the maximum growth rate at any fixed wavenumber and construction of the instable wavenumber region. The results of the present investigation will greatly contribute to study of the time evolution of viscoelastic laboratory environments with externally applied shear; where in these experiments the dust–neutral friction process can play a considerable role.

Corresponding author
Email addresses for correspondence:,
Hide All
Angelis, U. de 1992 The physics of dusty. Plasmas Phys. Scr. 45 (5), 465.
Banerjee, D., Janaki, M. S., Chakrabarti, N. & Chaudhri, M. 2010 Viscosity gradient-driven instability of ‘shear mode’ in a strongly coupled plasma. New J. Phys. 12 (12), 123031.
El-Awady, E. I. & Djebli, M. 2012 Dust acoustic waves in a collisional strongly coupled dusty plasmas. Astrophys. Space Sci. 342 (1), 105111.
Frenkel, Y. 1946 Kinetic Theory of Liquids. Clarendon.
Feng, Y., Goree, J. & Liu, B. 2012 Frequency-dependent shear viscosity of a liquid two-dimensional dusty plasma. Phys. Rev. E 85 (6), 066402.
Goertz, C. K. 1989 Dusty plasmas in the solar system. Rev. Geophys. 27 (2), 271292.
Gruzinov, A.2008 GRB: magnetic fields, cosmic rays, and emission from first principles? arXiv:0803.1182.
Horanyi, M., Houpis, H. L. F. & Mendis, D. A. 1988 Charged dust in the Earth’s magnetosphere. Astrophys. Space Sci. 144 (1–2), 215229.
Ikezi, H. 1986 Coulomb solid of small particles in plasmas. Phys. Fluids 29 (6), 17641766.
Ivlev, A. V., Steinberg, V., Kompaneets, R., Hofner, H., Sidorenko, I. & Morfill, G. E. 2007 Non-Newtonian viscosity of complex-plasma fluids. Phys. Rev. Lett. 98 (14), 145003.
Jana, S., Banerjee, D. & Chakrabarti, N. 2015 Stability of an elliptical vortex in a strongly coupled dusty plasma. Phys. Plasmas 22 (8), 083704.
Kaw, P. K. 2001 Collective modes in a strongly coupled dusty plasma. Phys. Plasmas 8 (5), 18701878.
Mendis, D. A. & Rosenberg, M. 1994 Cosmic dusty plasma. Annu. Rev. Astron. Astrophys. 32 (1), 419463.
Mishra, A., Kaw, P. K. & Sen, A. 2000 Instability of shear waves in an inhomogeneous strongly coupled dusty plasma. Phys. Plasmas 7 (8), 31883193.
Nunomura, S., Misava, T., Ohno, N. & Takamura, S. 1999 Instability of dust particles in a Coulomb crystal due to delayed charging. Phys. Rev. Lett. 83 (10), 1970.
Pesceli, H. L., Rasmussen, J. J. & Thomsen, K. 1984 Nonlinear interaction of convective cells in plasmas. Phys. Rev. Lett. 52 (24), 2148.
Rosenberg, M. & Kalman, G. 1997 Dust acoustic waves in strongly coupled dusty plasmas. Phys. Rev. E 56 (6), 7166.
Steinberg, V., Ivlev, A., Kompaneets, R. & Morfill, G. E. 2008 Shear instability in fluids with a density-dependent viscosity. Phys. Rev. Lett. 100 (25), 254502.
Shukla, P. K. & Mamun, A. A. 2001 Dust-acoustic shocks in a strongly coupled dusty plasma. IEEE Trans. Plasma Sci. 29 (2), 221225.
Tsytovich, V. N. & Havnes, O. 1993 Charging processes, dispersion properties and anomalous transport in dusty plasma. Comm. Plasma Phys. Control. Fusion 15 (5), 267280.
Thomas, H., Morfill, G. E., Demmel, V., Goree, J., Feuerbacher, B. & Mohlmann, D. 1994 Plasma crystal: Coulomb crystallization in a dusty plasma. Phys. Rev. Lett. 73 (5), 652.
Ussenov, Y. A., Ramazanov, T. S., Dzhuma Gulova, K. N. & Dosbolayen, M. K. 2014 Application of dust grains and Langmuir probe for plasma diagnostics. Eur. Phys. Lett. 105 (1), 15002.
Whipple, E. C., Northrop, T. G. & Mendis, D. A. 1985 The electrostatics of a dusty plasma. J. Geophys. Res. 90 (A8), 74057413.
Whipple, E. C. 1981 Potentials of surfaces in space. Rep. Prog. Phys. 44 (11), 1197.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
  • URL: /core/journals/journal-of-plasma-physics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed