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 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.     

Shear induced anisotropy in two-dimensional liquids

The behavior of a dense two-dimensional soft disc liquid under shear is studied via nonequilibrium molecular dynamics. The structure factor for the liquid at a given shear rate is evaluated directly by plotting the particle positions, taken at random from the NEMD simulation at that shear, onto photographic film and using light scattering to obtain a diffraction pattern. The pair correlation function of this system is also extracted directly by histogramming the particle positions with respect to a given central particle as a function of separation and angle. The pair correlation function is compared to that approximated by a Fourier series expansion to rank ten. Results are reported as a function of shear rate from a shear rate of 0.1 (when the fluid is essentially Newtonian) to 10 (when the fluid can display a string phase). The appearance of the string phase is discussed and shown to be a consequence of the definition of temperature in the simulation algorithm. A modification of the algorithm is proposed. Comparisons between this work and previous work with three-dimensional liquids are given. The two-dimensional structure factor is compared with that obtained from a real colloidal suspension via light scattering.     

Shear viscosity of strongly coupled Yukawa systems on finite length scales

The Yukawa shear viscosity has been calculated using nonequilibrium molecular dynamics. Near the viscosity minimum, we find exponential decay consistent with the Navier-Stokes equation, with significant deviations on finite length scales for larger viscosity values. The viscosity is determined to be nonlocal on a scale length consistent with the correlation length, revealing the length scales necessary for obtaining transport coefficients in the hydrodynamic limit by nonequilibrium molecular dynamics methods. Our results are quasiuniversal with respect to excess entropy for excess entropies well below unity.     

Shear viscosity of a binary mixture of simple liquids

Russian Physics Journal -     

Frequency-dependent shear viscosity, sound velocity, and sound attenuation near the critical point in liquids. III. The shear viscosity

We compare theoretical results for the shear viscosity calculated in one-loop order within the field-theoretical method of the renormalization-group theory with experiments. Our expressions describe the nonasymptotic crossover in both temperature and density, and allow us to consider effects of finite gravitation and finite frequency at which the experiments are performed. In doing so we treat the critical exponent x(eta) of the shear viscosity as an independent parameter, keeping the one-loop value of the Kawasaki amplitude fixed. Within our model we also consider the temperature and density dependence of the thermal diffusion including gravitational effects.     

Two-dimensional Yukawa liquids: correlation and dynamics

A combined theoretical and molecular dynamics (MD) simulation study of the collective modes and their dispersion in a two-dimensional Yukawa system in the strongly coupled liquid state is presented. The theoretical analysis relies upon the quasilocalized charge approximation; the MD simulation generates static pair correlation functions and dynamical current-current correlation spectra.     

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.     

Thermodynamics and phase transitions in two-dimensional Yukawa systems

The results of numerical simulations of strongly-coupled two-dimensional dissipative Yukawa systems are presented. The thermodynamic characteristics of these systems were studied, namely the internal energy, the specific heat and the entropy. For the first time, it is discovered that the considered characteristics have two singular points on the melting line; one of these points corresponds to the first-order phase transition from crystal to the hexatic phase, and another point corresponds to the second-order phase transition from the hexatic phase to the isotropic liquid. The obtained results are compared to the existing numerical and analytical data.     

Thermodynamic properties of two-dimensional Yukawa systems

The simple analytical approximation for the energy densities in two-dimensional Yukawa systems is proposed for the wide range of parameters of non-ideal fluids. The use of this approach allows determining all thermodynamic functions and characteristics on the base of general thermodynamic relationships. The comparisons of obtained results with the numerical study of thermodynamic properties are presented. Simulations were performed for parameters typical for the laboratory dusty plasma experiments.     

Orientational order and topological defects in two-dimensional Yukawa systems

New numerical results concerned with formation of orientational order and topological defects in non-ideal systems of particles, interacted via screened Coulomb potential, are presented. Calculations have been performed in a wide range of parameters, corresponding to the experimental conditions in the laboratory dusty plasmas. Relations between a number of topological defects and shape of a bond-angular correlation function are obtained for the first time.     

Phase diagram of two-dimensional binary Yukawa mixtures

We have used Ramakrishnan–Yussouff (RY) density functional theory (DFT) to explore the topology of the phase diagram of two-component charge stabilised colloidal suspensions confined to a two-dimensional plane. The particles of the system interact via purely repulsive soft core Yukawa potential. Pair correlation functions (PCFs) used as input informations in DFT were calculated by solving both the hypernetted chain (HNC) and Percus–Yevick (PY) integral equation theories. To test the relative performance of the HNC and PY theories in the context of phase transitions, we have also studied the corresponding one-component systems. We found that RY DFT with HNC PCFs does not stabilise solid in both the one- and two-component cases, whereas the PY theory does. By considering the freezing into the substitutionally disordered triangular solid, we found that the temperature-composition phase diagrams of the binary mixture are narrow spindles whose thickness depends on the symmetry of the mixture components and the value of the screening constant of the Yukawa potential. Although the phase diagram obtained by RY DFT with structural inputs calculated by the PY theory is found to be shifted to higher temperature region in the temperature-composition plane, however, it captures qualitatively all the essential features of the phase diagram. Our results are in principle verifiable through computer simulations and experiments.     

Proposed lower bound for the shear viscosity to entropy density ratio in some dense liquids

Starting from relativistic quantum field theories, Kovtun et al. (2005) have quite recently proposed a lower bound η/s??/(4πkB), where η is the shear viscosity and s the volume density of entropy for dense liquids. If their proposal can eventually be proved, then this would provide key theoretical underpinning to earlier semiempirical proposals on the relation between a transport coefficient η and a thermodynamic quantity s. Here, we examine largely experimental data on some dense liquids, the insulators nitrogen, water, and ammonia, plus the alkali metals, where the shear viscosity η(T) for the four heaviest alkalis is known to scale onto an ‘almost universal’ curve, following the work of Tankeshwar and March a decade ago. So far, all known results for both insulating and metallic dense liquids correctly exceed the lower bound prediction of Kovtun et al.     

Dynamic Shear Viscosity in a 2D Yukawa System

We present non‐equilibrium molecular dynamics simulation studies on the dynamic (complex) shear viscosity of a 2D many‐particle system interacting via a Yukawa (Debye‐Hückel) type inter‐particle potential. Our investigations reveal the complex interplay of dissipative and elastic processes, as well as the effect of single particle resonances and enhanced collective excitations, and the influence of the external forces on the structural correlations in the system (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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 thinning and orientational ordering of wormlike micelles

Shear thinning and orientation of cylindrical surfactant and block copolymer micelles was investigated by rheo-SANS (small-angle neutron scattering) experiments. Shear thinning and orientation occur for shear rates (.)gamma tau(dis)>1, where tau(dis) is the disentanglement time of the micelles. Micelles align in the flow direction with an orientational distribution that can be well described by an Onsager-type distribution function. Over nearly the whole range of concentrations and for all cylindrical micelles investigated, the shear viscosity eta follows a simple eta approximately e(-aS) behavior as a function of the orientational order parameter S with the same prefactor a.     

Shear thinning and local melting of colloidal crystals

Phenomena such as shear thinning and thickening, occurring when complex materials are exposed to external forces, are generally believed to be closely connected to changes in the microstructure. Here, we establish a direct and quantitative relation between shear thinning in a colloidal crystal and the surface area of the locally melted region by dragging a probe particle through the crystal using optical tweezing. We show that shear thinning originates from the nonlinear dependence of the locally melted surface area on the drag velocity. Our observations provide unprecedented quantitative evidence for the intimate relation between mechanical properties and underlying changes in microscopic structure.     

Test of the Stokes-Einstein relation in a two-dimensional Yukawa liquid

The Stokes-Einstein relation, relating the diffusion and viscosity coefficients D and eta, is tested in two dimensions. An equilibrium molecular-dynamics simulation was used with a Yukawa pair potential. Regimes are identified where motion is diffusive and D is meaningful. The Stokes-Einstein relation, Deta proportional k(B)T, was found to be violated near the disordering transition; under these conditions collective particle motion exhibits dynamical heterogeneity. At slightly higher temperatures, however, the Stokes-Einstein relation is valid. These results may be testable in strongly coupled dusty plasma experiments.