Equilibrium molecular dynamics simulation of shear viscosity of two-dimensional complex (dusty) plasmas

Shear viscosity is examined throughout the entire range of strongly coupled states of two-dimensional complex (dusty) plasma liquids (CDPLs). We have employed equilibrium molecular dynamics (EMD) simulation to compute the shear viscosity coefficients of CDPLs. In the strongly coupled liquid region, the values of valid viscosity coefficient can be estimated only in order of magnitude. The variations in the valid viscosity coefficients with screening strength (κ) and Coulomb coupling strengths (Γ) are observed. A systematic dependence of shear viscosity on κ is observed for an intermediate and higher Γ. The investigations showed that the position of the minimum viscosity coefficient shifts towards higher Γ as κ increases. The computational results for the entire range of liquid states of the strongly coupled dusty plasma obtained using the shear autocorrelation functions are in good agreement with the available simulation results and experimental data. It is shown that new simulations extended the range of plasma states (Γ, κ) used in our earlier simulation results for the existence of a finite minimum possible viscosity coefficient and it is also dependent on plasma states.     

Shear flows and shear viscosity in a two-dimensional Yukawa system (dusty plasma)

The shear viscosity of a two-dimensional liquid-state dusty plasma was measured experimentally. A monolayer of highly charged polymer microspheres, with a Yukawa interaction, was suspended in a plasma sheath. Two counterpropagating Ar+ laser beams pushed the particles, causing shear-induced melting of the monolayer and a shear flow in a planar Couette configuration. By fitting the particle velocity profiles in the shear flow to a Navier-Stokes model, the kinematic viscosity was calculated; it was of order 1 mm(2) s(-1), depending on the monolayer's parameters and shear stress applied.     

Shear viscosity and shear thinning in two-dimensional Yukawa liquids

A two-dimensional Yukawa liquid is studied using two different nonequilibrium molecular dynamics simulation methods. Shear viscosity values in the limit of small shear rates are reported for a wide range of Coulomb coupling parameter and screening lengths. At high shear rates it is demonstrated that this liquid exhibits shear thinning; i.e., the viscosity eta diminishes with increasing shear rate. It is expected that two-dimensional dusty plasmas will exhibit this effect.     

Shear viscosity of two-dimensional Yukawa systems in the liquid state

The shear viscosity of a two-dimensional (2D) liquid was calculated using molecular dynamics simulations with a Yukawa potential. The viscosity has a minimum at a Coulomb coupling parameter Gamma of about 17, arising from the temperature dependence of the kinetic and potential contributions. Previous calculations of 2D viscosity were less extensive as well as for a different potential. The stress autocorrelation function was found to decay rapidly, contrary to earlier work. These results are useful for 2D condensed matter systems and are compared to a dusty plasma experiment.     

Ultrasonic scattering cross sections of shell-encapsulated gas bubbles immersed in a viscoelastic liquid: first and second harmonics

The oscillations of gas bubbles, without shell, immersed in viscoelastic liquids and driven by an acoustic wave have been the subject of several investigations. They demonstrate that the viscosity coefficient and the spring constant of the liquid have significant influence on the scattering cross section of the gas bubble. For shell-encapsulated gas bubbles, the investigations have been concentrated to bubbles immersed in a pure viscous liquid. This present work computes the ultrasonic scattering cross section, first and second harmonics, of shell-encapsulated gas bubbles immersed in a viscoelastic liquid. The theoretical model of the bubble oscillation is based on the generalized Rayleigh-Plesset equation of motion of a spherical cavity immersed in a viscoelastic liquid represented by a three-parameter linear Oldroyd model. The scattering cross section is computed for Albunex type of bubble (shell thickness=15 nm, shell shear viscosity=1.77 Pas, shell modulus of rigidity=88.8 MPa) irradiated by a 3.5 MHz ultrasonic pressure wave with an amplitude of 30 kPa. The results demonstrate that encapsulated bubbles respond independently of the surrounding liquid being pure viscous or viscoelastic as long as the surrounding liquid shear viscosity is as low as 10(-3) Pas. Nevertheless, for higher shear viscosities, the bubble responds differently if the surrounding liquid is pure viscous or viscoelastic. In general, the scattering cross sections of first and second harmonics are larger for the viscoelastic liquid.     

Structures and properties of the potassium-doped carbon clusters KCn/KCn +/KCn −(n = 1−10)

We have reported a theoretical study on the interaction mechanism between dust particles in the presence of asymmetric ion flow and an external magnetic field in complex plasma. The recent experimental and numerical results on the particle-wake interaction ensures the dominance of the wake effect in the subsonic regime of plasma flow using the cold ion approximation. The recent developments in dusty plasma research and its growing interest towards more realistic magnetized dusty plasma scenarios also demand serious attention to study the wake effect both in the sub and supersonic regimes in the presence of a magnetic field. It is a challenging task to develop a correct, quantitative theory of wake potential for different regimes of magnetic field and ion flow velocity. Analytic expressions for the wake potential have been reported in this paper for both subsonic and supersonic regimes in the presence of an external magnetic field along with Debye-Hückel type potentials. The results show that the wake potential plays a dominant role in the subsonic regime and its strength increases with an increase in magnetic field. The behaviour of the wake potential is found to have an interesting effect on the Coulomb crystallization of dust grains and is studied with the help of molecular dynamic (MD) simulation.     

Experimental observations of transverse shear waves in strongly coupled dusty plasmas

We report experimental observations of transverse shear waves in a three-dimensional dusty plasma that is in the strongly coupled fluid regime. These spontaneous oscillations occur when the ambient neutral pressure is reduced below a threshold value and the measured dispersion characteristics of these waves are found to be in good agreement with predictions of a viscoelastic theory of dusty plasmas.     

Shear Viscosity of Dusty Plasma Obtained on the Basis of the Langevin Dynamics

Shear viscosity of dusty plasma was calculated on the basis of the Langevin dynamics. Shear viscosity is considered as a function of many parameters and buffer plasma pressure is among them. Complicated dependence of viscosity on plasma pressure is considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bubble oscillation and inertial cavitation in viscoelastic fluids

Non-linear acoustic oscillations of gas bubbles immersed in viscoelastic fluids are theoretically studied. The problem is formulated by considering a constitutive equation of differential type with an interpolated time derivative. With the aid of this rheological model, fluid elasticity, shear thinning viscosity and extensional viscosity effects may be taken into account. Bubble radius evolution in time is analyzed and it is found that the amplitude of the bubble oscillations grows drastically as the Deborah number (the ratio between the relaxation time of the fluid and the characteristic time of the flow) increases, so that, even for moderate values of the external pressure amplitude, the behavior may become chaotic. The quantitative influence of the rheological fluid properties on the pressure thresholds for inertial cavitation is investigated. Pressure thresholds values in terms of the Deborah number for systems of interest in ultrasonic biomedical applications, are provided. It is found that these critical pressure amplitudes are clearly reduced as the Deborah number is increased.     

Effect of shape factor on the electrokinetic response of slot-like capillaries

The effect of the shape factor on the electrokinetic response of pressure-driven liquid flow through slot-like capillaries is analyzed in this work. The electrokinetic response is found by first solving for the electrical potential using the Poisson–Boltzmann equation, and then using it as an input to construct an external force term in the Navier–Stokes equation. It is found that flow properties are significantly modified for small pore sizes with hydraulic radius in the range of microns and submicrons, according to the properties of the electrolyte solution. The modified flow rate in the presence of such electrokinetic effects can be less than 50% of the predictions expected with conventional flow models such as Darcy's equation. Apparent viscosities larger than expected are calculated using the reduced flow. Actual values are dependent on the capillary dimensions, pressure gradient, solid-surface conductivity, and properties of the electrolyte fluid. For a rectangular capillary cross-sectional geometry the apparent viscosity and friction coefficients values decrease with the shape factor in a nontrivial way. These results are relevant for the modelling of certain porous formations of interest to the oil industry.     

Characteristics of single and dual radio-frequency (RF) plasma sheaths

The characteristics of radio-frequency (RF) plasma sheaths have been topics of much scientific study for decades, and have also been of great importance in the manufacture of integrated circuits and fabricating microelectromechanical systems (MEMS), as well as in the study of physical phenomena in dusty plasmas. The sheaths behave special properties under various situations where they can be treated as collisionless or collisional, single-or dual-RF, one-or two-dimensional (1D or 2D) sheaths, etc. This paper reviews our recent progress on the dynamics of RF plasma sheaths using a fluid method that includes the fluid equations and Poission’s equation coupled with an equivalent circuit model and a hybrid method in which the fluid model is combined with the Monte-Carlo (MC) method. The structures of RF sheaths behave differently in various situations and plasma parameters such as the ion density, electron temperature, as well as the external parameters such as the applied frequency, power, gas pressure, magnetic field, are crucial for determining the characteristics of plasma sheaths.     

Stationary velocity and charge distributions of grains in dusty plasmas

Within the kinetic approach the velocity and the charge distributions of grains in stationary dusty plasmas are calculated and the relations between the effective temperatures of such distributions and plasma parameters are established. It is found that the effective temperature which determines the velocity grain distribution could be anomalously large due to the action of accelerating ionic bombarding force. The possibility to apply the results obtained to the explanation of the increasing grain temperature in the course of Coulomb-crystal melting by reduction of the gas pressure is discussed.     

Stability of the collisional plasma flow in a magnetic field

A collisional plasma flow moving along a magnetic field at a velocity lower than the speed of sound is considered. It has been found that stationary small perturbations increase downstream in the flow. The mechanism of the increase is related to the fact that subsonic ideal-plasma flows respond to external perturbations primarily by a change in the pressure of the plasma. As a result, the pressure under perturbation of the velocity changes so that the stationary flow is decelerated and accelerated if the force is directed along and against the velocity, respectively. This phenomenon can be explained under the assumption that the effective mass of the plasma is negative. If the velocity of the flow is inhomogeneous in the transverse direction, the viscosity force plays a role of the external perturbing force. In this case, the effective transverse viscosity coefficient, which should be treated as negative, can be renormalized instead of the effective mass. The sign of the effective specific heat or the effective transverse thermal conductivity coefficient changes similarly if the velocity of the flow is lower than the speed of sound but is higher than the thermal velocity of ions calculated from the sum of the ion and electron temperatures. A downstream increase in the stationary perturbations is called in this work spatial instability. The downstream growth rate has been determined. The numerical analysis of the evolution of perturbations illustrates the development of the spatial instability of subsonic collisional plasma flows moving along the magnetic field.     

Lattice-Boltzmann Simulations of Particle-Fluid Suspensions

This paper reviews applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions. We first summarize the available simulation methods for colloidal suspensions together with some of the important applications of these methods, and then describe results from lattice-gas and lattice-Boltzmann simulations in more detail. The remainder of the paper is an update of previously published work,^{(69, 70)} taking into account recent research by ourselves and other groups. We describe a lattice-Boltzmann model that can take proper account of density fluctuations in the fluid, which may be important in describing the short-time dynamics of colloidal particles. We then derive macro-dynamical equations for a collision operator with separate shear and bulk viscosities, via the usual multi-time-scale expansion. A careful examination of the second-order equations shows that inclusion of an external force, such as a pressure gradient, requires terms that depend on the eigenvalues of the collision operator. Alternatively, the momentum density must be redefined to include a contribution from the external force. Next, we summarize recent innovations and give a few numerical examples to illustrate critical issues. Finally, we derive the equations for a lattice-Boltzmann model that includes transverse and longitudinal fluctuations in momentum. The model leads to a discrete version of the Green–Kubo relations for the shear and bulk viscosity, which agree with the viscosities obtained from the macro-dynamical analysis. We believe that inclusion of longitudinal fluctuations will improve the equipartition of energy in lattice-Boltzmann simulations of colloidal suspensions.     

On the orientational characteristics and transport coefficients of an oblate spheroidal hematite particle in a simple shear flow

We have developed the basic equation of the orientational distribution function of oblate spheroidal hematite particles with rotational Brownian motion in a simple shear flow under an applied magnetic field. An oblate spheroidal hematite particle has an important characteristic in that it is magnetized in a direction normal to the particle axis. Since a dilute dispersion is addressed in the present study, we have taken into account only the friction force (torque) whilst neglecting the hydrodynamic interactions among the particles. This basic equation has been solved numerically in order that we may investigate the dependence of the orientational distribution on the magnetic field strength, shear rate and rotational Brownian motion and the relationship between the orientational distribution and the transport coefficients such as viscosity and diffusion coefficient. We found that if the effect of the magnetic field is more dominant, the particle inclines in such a way that the oblate surface aligns in the magnetic field direction. If the Peclet number increases and the effect of the shear flow becomes more dominant, the particle inclines such that the oblate surface tilts in the shear flow direction. The viscosity due to the magnetic torque is shown to increase as the magnetic field increases, since the magnetic torque due to the applied magnetic field becomes the more dominant effect. Moreover, the viscosity increase is shown to be more significant for a larger aspect ratio or for a more oblate hematite particle. We have applied the analysis to the problem of particle sedimentation under gravity in the presence of a magnetic field applied in the sedimentation direction. The particles are found to sediment with the oblate surface aligning more significantly in the sedimentation direction as the applied magnetic field strength increases.     

Cutoff wave number for shear waves in a two-dimensional Yukawa system (dusty plasma)

The cutoff wave number for shear waves in a liquid-state strongly coupled plasma was measured experimentally. The phonon spectra of random particle motion were measured at various temperatures in a monolayer dusty plasma, where microspheres interact with a Yukawa potential. In the liquid state of this particle suspension, shear waves were detected only for wavelengths smaller than 20 to 40 Wigner-Seitz radii, depending on the Coulomb coupling parameter. The temperature of the suspension was controlled using a laser-heating method.     

Effect of Second Nonthermal Ion on the Characteristics of Dust Acoustic Solitary Waves in a Magnetized Dusty Plasma with Variable Dust Charge

The nonlinear dust acoustic solitary waves in a magnetized dusty plasma with nonthermal ions and variable dust electric charge is studied analytically. Using reductive perturbation method the Zakharov‐Kuznetsov (ZK) equation is derived and effect of nonthermal coefficient, external magnetic field, and variable dust electric charge on the amplitude and width of soliton in dusty plasma is investigated. With increasing the rate of dust charge variation with respect of plasma potential, the amplitude of generated solitary waves in magnetized dusty plasma increases to a constant magnitude while its width decreases. Increasing the nonthermal ions coefficient leads to a noticeable decrease in the amplitude of solitons while the width of soliton increases. The amplitude of generated solitary waves in such a dusty plasma is independent of applied external magnetic field but we will have more localized solitons with increasing the external magnetic field strength. It is found that solitons are strongly influenced by the direction of external magnetic field. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unified low-parametrical equation used to calculate the viscosity coefficient of argon

Using the previously obtained dependence of excess viscosity on internal energy density and low-parametric unified equation of state for calculation of thermodynamic properties of liquid, gas, and fluid, the equation for the excess viscosity of argon in the range of the “mixed” mechanism of momentum transfer in the shear flow was derived. Different versions of approximation of excess viscosity dependence on the density of interaction energy were compared, and the optimal version of this dependence was determined. A simple unified low-parametric equation was obtained for describing the coefficient of argon viscosity in a wide range of state parameters. It is shown that the proposed low-parametric equation for calculating the viscosity coefficient of liquid and gas allows reliable extrapolation beyond the studied region.     

I. Formation and rise of a bubble stream in a viscous liquid

The continuous emission of gas bubbles from a single ejection orifice immersed in a viscous fluid is considered. We first present a semi empirical model of spherical bubble growth under constant flow conditions to predict the bubble volume at the detachment stage. In a second part, we propose a physical model to describe the rise velocity of in-line interacting bubbles and we derive an expression for the net viscous force acting on the surrounding fluid. Experimental results for air/water-glycerol systems are presented for a wide range of fluid viscosity and compared with theoretical predictions. An imagery technique was used to determine the bubble size and rise velocity. The effects of fluid viscosity, gas flow rate, orifice diameter and liquid depth on the bubble stream dynamic were analyzed. We have further studied the effect of large scale recirculation flow and the influence of a neighbouring bubble stream on the bubble growth and rising velocity. Received: 23 July 1997 / Revised: 16 December 1997 / Accepted: 11 May 1998     

Jeans instability of an inhomogeneous streaming dusty plasma

The dynamics of a self-gravitating unmagnetized, inhomogeneous, streaming dusty plasma is studied in the present work. The presence of the shear flow causes the coupling between gravitational and electrostatic forces. In the absence of self-gravity, the fluctuations in the plasma may grow at the expense of the density inhomogeneity and for certain wavelengths, such an unstable mode may dominate the usual streaming instability. However, in the presence of self-gravity, the plasma inhomogeneity causes an overlap between Jeans and streaming modes and collapse of the grain will continue at all wavelengths.