Viscosity of a dusty plasma liquid

We present the results of our experimental study of the flow of a dusty plasma liquid produced by macroparticles in an argon plasma. The dependences of shear viscosity for such a liquid on the magnitude of the external force inducing the dusty plasma liquid flow and on the plasma-generating gas pressure are analyzed. We have established that the viscosity of a dusty plasma medium decreases with increasing shear stress in it, while the viscosity of such a liquid increases with buffer gas pressure. The flow of a dusty plasma liquid under the action of an external force has been found to resemble the plastic deformation of a Bingham body. We suggest that the formation of crystal-like dusty plasma clusters in a “liquid” phase can be responsible for the non-Newtonian behavior of the dusty plasma liquid flow.     

Influence of shear viscosity of quark-gluon plasma on elliptic flow in ultrarelativistic heavy-ion collisions

We investigate the influence of a temperature-dependent shear viscosity over entropy density ratio η/s on the transverse momentum spectra and elliptic flow of hadrons in ultrarelativistic heavy-ion collisions. We find that the elliptic flow in √S(NN)=200 GeV Au+Au collisions at RHIC is dominated by the viscosity in the hadronic phase and in the phase transition region, but largely insensitive to the viscosity of the quark-gluon plasma (QGP). At the highest LHC energy, the elliptic flow becomes sensitive to the QGP viscosity and insensitive to the hadronic viscosity.     

Calculation of the Viscosity of Polymer Melts Based on Measurements of the Recovered Rubber-Like Deformation

On the basis of a model of polymer flow, considering the forces of entropic elasticity of extended macromolecules within the Eyring's concept, the relationships between the shear rate, shear stress, viscosity, and recovered rubber-like deformation were derived. The reduction of activation energy of the flow, by an amount proportional to the recovered rubber-like deformation, leads to an exponential decrease of viscosity with increasing shear rates; this nonlinear dependence of viscosity on shear rate (and shear stress) is defined as the viscosity anomaly of polymers. The measurement of deformation recovery after the cessation of polymer flow in the mode of constant shear rate or shear stress on a rotational viscometer confirmed the validity of the theoretical dependences.     

Processing Polymer Melts under Rheo-Fluidification Flow Conditions,Part 2: Simple Flow Simulations

The flow equations for melts submitted to conditions of Rheo-Fluidification processing described in Part 1 are determined and solved numerically. The pressure flow from an extruder feed end and drag flow from the modulated rotation of the rotor, i.e., under extrusion conditions with both cross-rotational and oscillatory flow, are combined. The value of pressure, shear stress, and viscosity along the flow path of the melt (a helicoidal motion around a divergent conic surface), for a given throughput and temperature, as the melt is moved through an annular gap of constant thickness are calculated. The simulation is restricted to the simpler case of low throughput where elongational flow can be assumed to be negligible and shear dominates the viscosity expression. The classic lubrication approximation hypothesis applied to a power law fluid is used. This assumption appears justified because of the geometry of the die, which consists of a thin annulus of 2 mm extended over a die length of 570 mm (see Part 1). The viscosity is expressed as a function of strain rate, which is calculated from the contribution of pressure flow, rotational flow, and superposed oscillation. The combined shear rate is calculated assuming a vectorial combination of the individual shear rates, following Cogswell who verified this hypothesis, and according to our own validation of this assumption on the same polymer, using a Couette without vibration.     

Jets in tokamaks: A theoretical study

A new class of bifurcation of the momentum balance equations for a tokamak plasma is presented. The solution exhibits a monopolar localized jet of ExB flow. The jet is generated by the reduction of turbulent viscosity due to ExB velocity shear. Strong jets of localized plasma flow have been observed in tokamaks as a precursor to the development of a transport barrier region with reduced turbulent transport. The jet solution is shown to fit well with the experimental observations.     

High Pressure High Temperature Dynamic Rheometry of Sulfonated Polyacrylamide Solutions in Electrolyte Media as Used for Oil Recovery Applications

Sulfonated polyacrylamide (SPAA) solutions were prepared and the effects of pressure, polymer concentration, and water temperature, pH and salinity on their rheological behavior were investigated using a concentric cylinder dynamic rheometer equipped with a high pressure cell. According to the rheological flow curves the shear stress of SPAA solutions increased less than in proportion to their shear rates; that is, a shear thinning effect occurred. For polymer solutions containing 15,000 ppm of SPAA, shear viscosity, and stress were nearly insensitive to pressure. However, the shear viscosity and stress of SPAA solutions were affected by temperature and this effect was more evident at lower pressure. The flow curves indicated the shear viscosity and stress of the samples increased with increasing SPAA concentration and pH of the water, but were decreased with increasing water salinity and temperature.     

Flow birefringence,stress optical rule and rheology of four micellar solutions with the same low shear viscosity

The flow birefringence and the rheological properties of four viscoelastic solutions having nearly the same zero shear viscosity and subjected to shear flows are investigated in the linear and non-linear domains. The surfactant used for the samples is the cetyltrimethylammonium chloride in water at the concentration of 100 mmol/l with an organic salt, the sodium salicylate. The low shear viscosity curve versus the salt concentration is non-monotonic and has two maxima separated by a minimum forming four domains in which the salt concentration is chosen. For the two solutions belonging to the inner branch, i.e. between the two maxima, a simple Maxwellian behaviour is observed and shear banding occurs as confirmed by the flow birefringence pictures. Contrary to the results of P. Fisher (1996) where the unstable flow regime is restricted to the first decreasing part of the low shear viscosity curve of a cetylpyridinium chloride solution, we show that shear banding exits in a wider domain of the salt concentration. Received 18 November 2002 / Published online: 1 April 2003 RID="a" ID="a"e-mail: Decruppe@lpli.sciences.univ-metz.fr     

Shear viscosity for inelastic hard spheres

The hydrodynamic equations of the Enskog theory for inelastic hard spheres is considered as a model for rapid flow granular fluids at finite densities. A detailed analysis of the shear viscosity of the granular fluid has been done using homogenous cooling state (HCS) and uniform shear flow (USF) models. It is found that shear viscosity is sensitive to the coefficient of restitution α and pair correlation function at contact. The collisional part of the Newtonian shear viscosity is found to be dominant than its kinetic part.     

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.     

Two-pion interferometry for viscous hydrodynamic sources

The space-time evolution of the (1+1)-dimensional viscous hydrodynamics with an initial quark-gluon plasma (QGP) produced in ultrarelativistic heavy ion collisions is studied numerically. The particle-emitting sources undergo a crossover transition from the QGP to hadronic gas. We take into account a usual shear viscosity for the strongly coupled QGP as well as the bulk viscosity which increases significantly in the crossover region. The two-pion Hanbury-Brown-Twiss (HBT) interferometry for the viscous hydrodynamic sources is performed. The HBT analyses indicate that the viscosity effect on the two-pion HBT results is small if only the shear viscosity is taken into consideration in the calculations. The bulk viscosity leads to a larger transverse freeze-out configuration of the pion-emitting sources, and thus increases the transverse HBT radii. The results of the longitudinal HBT radius for the source with Bjorken longitudinal scaling are consistent with the experimental data.     

Mechanical behavior of pathological and normal red blood cells in microvascular flow based on modified level-set method

The research of the motion and deformation of the RBCs is important to reveal the mechanism of blood diseases. A numerical method has been developed with level set formulation for elastic membrane immersed in incompressible fluid. The numerical model satisfies mass and energy conservation without the leaking problems in classical Immersed Boundary Method(IBM), at the same time, computing grid we used can be much smaller than the general literatures. The motion and deformation of a red blood cell(including pathological normal status) in microvascular flow are simulated. It is found that the Reynolds number and membrane's stiffness play an important role in the transmutation and oscillation of the elastic membrane. The normal biconcave shape of the RBC is propitious to create high deformation than other pathological shapes. With reduced viscosity of the interior fluid both the velocity of the blood and the deformability of the cell reduced. With increased viscosity of the plasma both the velocity of the blood and the deformability of the cell reduced. The tank treading of the RBC membrane is observed at low enough viscosity contrast in shear flow. The tank tread fixed inclination angle of the cell depends on the shear ratio and viscosity contrast, which can be compared with the experimental observation well.     

Flow Characteristics of Partially Hydrolyzed Polyacrylamides during Converging into a Capillary

Partially hydrolyzed polyacrylamides (HPAMs) are the most widely used polymers in enhanced oil recovery (EOR). This study presents capillary flow measurements of three different molecular weight HPAMs in synthetic brine. Polymer solutions having similar viscoelasticity were forced to flow through a 0.23 mm (radius) stainless steel capillary to investigate their flow characteristics including mobility reduction (apparent viscosity) and mechanical stability, represented by the extent of mechanical degradation (DR). The results indicated that the apparent viscosity of the polymer solutions markedly dropped with increasing flow rate until 5 mL/min, corresponding to the shear rate of 8,730s^?1; after that a slight viscosity decrease was observed. The high-molecular-weight HPAMs (6.5 and 8.0 × 10⁶ g/mol) began to have slightly greater apparent viscosity than the low-molecular-weight HPAM (1.0×10⁶ g/mol) above the shear rate of 26,180 s^?1; this might result from the occurrence of the coil-stretch transition. All the HPAMs experienced very similar percentages of mechanical degradation (10%) at shear rates between 1750 and 8730 s^?1; however, above 8730s^?1 the high-molecular-weight HPAMs exhibited a steep increase in mechanical degradation (DR). On the other hand, in the case of the low-molecular-weight HPAM, the DR curve almost leveled off at 12%. Therefore, low-molecular-weight HPAMs are generally suggested for EOR applications. These results, we suggested, should be useful to improve the efficiency of polymer EOR by minimizing mechanical degradation.     

Rheological Behavior of Blends of Poly(Phenylene Sulfide) with a Thermotropic Liquid Crystalline Aromatic Poly(Ether Ester)

A new type of thermotropic liquid crystalline aromatic poly(ether ester) (PEE) was prepared from 1,3-bis(4′-carboxyphenoxy)benzene, 1,4-diacetoxybenzene, and p-acetoxybenzoic acid through a melt transesterification process. The rheological behavior of blends of poly(phenylene sulfide) (PPS) with PEE was studied using a high-pressure capillary rheometer with the shear rate range of 50 s^?1 to 3000 s^?1. The results show that according to the range of shear rate, the flow curves of PEE/PPS blends can be divided into three zones: a first shear-thinning zone (n < 1, “n” represents non-Newtonian indexes), a shear-thickening zone (n > 1), and a second shear-thinning zone (n < 1), and the former two zones are more obvious with the increase of PEE content or elevated temperature. In the second shear-thinning zone, the PPS melt is close to a Newtonian fluid at high temperature and high shear rate; meanwhile the non-Newtonian behavior of the PPS melt at high temperature is enhanced with the addition of PEE. The apparent viscosity of PPS melts sharply dropped after adding PEE, especially at relatively low temperature and low shear rate. The curve of apparent viscosity vs. shear rate starts to flatten out after adding PEE, suggesting that the addition of PEE lowers the sensitivity of PPS to shear rate. As the content of PEE increases, the activation energy of the viscous flow, ΔE_η, of PPS decreases, which means that adding PEE weakens the temperature sensitivity of the apparent viscosity of the PPS melt. It can clearly be seen that the addition of PEE is beneficial to the processing of PPS.     

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.     

200 A GeV Au + Au collisions serve a nearly perfect quark-gluon liquid

A new robust method to extract the specific shear viscosity (η/s)(QGP) of a quark-gluon plasma (QGP) at temperatures T(c) < T ? 2T(c) from the centrality dependence of the eccentricity-scaled elliptic flow v2/ε measured in ultrarelativistic heavy-ion collisions is presented. Coupling viscous fluid dynamics for the QGP with a microscopic transport model for hadronic freeze-out we find for 200 A GeV Au + Au collisions that v2/ε is a universal function of multiplicity density (1/S)(dN(ch)/dy) that depends only on the viscosity but not on the model used for computing the initial fireball eccentricity ε. Comparing with measurements we find 1<4π(η/s)(QGP) < 2.5 where the uncertainty range is dominated by model uncertainties for the values of ε used to normalize the measured v2.     

Negative viscosity due to magnetic properties of a non-dilute suspension composed of ferromagnetic rod-like particles with magnetic moment normal to the particle axis

The negative viscosity of a colloidal dispersion composed of ferromagnetic rod-like particles, which have a magnetic moment normal to the particle axis, have been investigated. A simple shear flow problem has been treated to clarify the particle orientational distribution and rheological properties of such a semi-dense dispersion, under circumstances of an external magnetic field applied in the direction normal to the shear plane of a simple shear flow. The results obtained here are summarized as follows. For the cases of a very strong magnetic field and magnetic interactions between particles, the magnetic moment of the rod-like particles is significantly restricted in the magnetic field direction, so that the particle approximately aligns in the shear flow direction. Also, the particle can easily rotate around the axis of the cluster almost freely even in a simple shear flow. Characteristic orientational properties of the particle cause negative viscosity, as in the previous study for a dilute dispersion. However, magnetic particle-particle interactions have a function to make such negative viscosity decrease.     

Effect of shear equilibrium flow in Tokamak plasma on resistive wall modes

A code named LARWM with non-ideal magnetohydrodynamic equations in cylindrical model is used to describe the instability in Tokamak plasma surrounded by a conducting wall with finite resistivity. We mainly take three factors related to the shear equilibrium plasma flow into consideration to study the stabilizing effect of the shear flow on the resistive wall modes (RWMs). The three factors are the velocity amplitude of flow, the shear rate of flow on plasma surface, and the inertial energy of equilibrium plasma flow. In addition, a local shear plasma flow is also calculated by the LARWM code. Consequently, it is found that the inertial energy of the shear equilibrium plasma flow has an important role in the stabilization of the RWMs.     

Color-electric conductivity in a viscous quark-gluon plasma

Several different transport processes, such as heat, momentum, and charge transports, may occur simultaneously in a thermal plasma system. The corresponding transport coefficients are heat conductivity, shear viscosity, and electric conductivity. In the present study, we investigate the color-electric conductivity of the quark-gluon plasma(QGP) in the presence of shear viscosity, focusing on the connection between the charge transport and momentum transport. To achieve this goal, we solve the viscous chromohydrodynamic equations obtained from the QGP kinetic theory associated with the distribution function modified by shear viscosity. According to the solved color fluctuations of hydrodynamic quantities, we obtain the induced color current through which the color-electric conductivity is derived. Numerical analysis shows that the conductivity properties of the QGP are mainly demonstrated by the longitudinal part of the color-electric conductivity. Shear viscosity has an appreciable impact on real and imaginary parts of the color-electric conductivity in some frequency regions.     

Study on Steady Shear Rheological Behavior of Concentrated Suspensions of Sulfonated Polyacrylamide/Na-Montmorillonite Nanoparticles

Concentrated suspensions of sulfonated polyacrylamide (SPA)/Na⁺-montmorillonite (Na-MMT) were prepared and their stability and steady shear rheological properties were described as a function of nanoparticle and polymer concentration and temperature. The results showed that the Na-MMT nanoparticles suspensions were stable in the absence and presence of SPA and no sedimentation was seen. The Z-average particle sizes for the SPA/Na-MMT suspensions increased in the presence of SPA. Rheological investigations showed that the SPA solutions and SPA/Na-MMT suspensions displayed non-Newtonian behavior in almost the whole range of shear rate. All the suspensions exhibited a shear-thinning flow character as shear rate increased. The flow curves indicated the shear viscosity and stress of the samples were decreased with increasing nanoparticles concentration up to 1.5 wt%, but for Na-MMT loading greater than 1.5 wt% there was an increase in shear viscosity and stress of the suspensions. Increasing of SPA concentration had more effect on increasing the rheological properties of SPA/Na-MMT suspensions than increasing of nanoclay content. Shear viscosity and stress of the suspensions increased with increasing SPA concentration and decreased with increasing temperature from 50°C to 70°C.     

Shear instability in fluids with a density-dependent viscosity

We present a shear instability, which can be triggered in compressible fluids with density-dependent viscosity at shear rates above critical. The instability mechanism is generic: It is based on density-dependent viscosity, compressibility, as well as flow two-(three-)dimensionality that provides coupling between streamwise and transversal velocity components and density variations. The only factor stabilizing the instability is fluid elasticity. The corresponding eigenvalue problem for a plane Couette flow is solved analytically in the limiting cases of large and small wave numbers.