Reduced Shear Rate Research Articles

Experimental Study of Flow and Heat Transfer in Granular Media

AbstractIn this paper, granular flow is studied using particle image velocimetry (PIV) in two different geometries, that is, rectangular box and cylindrical bladed mixer. Effects of parameters like blade rake angle, bed height, moisture content, and the number of blades were studied. The shear rate and velocity magnitude of granular bed were calculated using PIV. The presence of moisture in the granular bed added additional cohesive forces and reduced shear rate between different layers of particles. Shear rate and shear forces were maximal at the tip of the blade. Temperature variations in the granular bed were measured experimentally and results were compared for static and mixing beds.

Exact Results for Non-Newtonian Transport Properties in Sheared Granular Suspensions: Inelastic Maxwell Models and BGK-Type Kinetic Model.

The Boltzmann kinetic equation for dilute granular suspensions under simple (or uniform) shear flow (USF) is considered to determine the non-Newtonian transport properties of the system. In contrast to previous attempts based on a coarse-grained description, our suspension model accounts for the real collisions between grains and particles of the surrounding molecular gas. The latter is modeled as a bath (or thermostat) of elastic hard spheres at a given temperature. Two independent but complementary approaches are followed to reach exact expressions for the rheological properties. First, the Boltzmann equation for the so-called inelastic Maxwell models (IMM) is considered. The fact that the collision rate of IMM is independent of the relative velocity of the colliding spheres allows us to exactly compute the collisional moments of the Boltzmann operator without the knowledge of the distribution function. Thanks to this property, the transport properties of the sheared granular suspension can be exactly determined. As a second approach, a Bhatnagar-Gross-Krook (BGK)-type kinetic model adapted to granular suspensions is solved to compute the velocity moments and the velocity distribution function of the system. The theoretical results (which are given in terms of the coefficient of restitution, the reduced shear rate, the reduced background temperature, and the diameter and mass ratios) show, in general, a good agreement with the approximate analytical results derived for inelastic hard spheres (IHS) by means of Grad's moment method and with computer simulations performed in the Brownian limiting case (m/mg→∞, where mg and m are the masses of the particles of the molecular and granular gases, respectively). In addition, as expected, the IMM and BGK results show that the temperature and non-Newtonian viscosity exhibit an S shape in a plane of stress-strain rate (discontinuous shear thickening, DST). The DST effect becomes more pronounced as the mass ratio m/mg increases.

Inspiratory resistance training transiently improves endothelium-dependent dilation in young adults

Introduction: Inspiratory resistance training (IRT) is a resisted breathing exercise originally devised to improve diaphragmatic strength. We have shown IRT to be a potent non-pharmacological therapy that yields significant reductions in resting blood pressure. When performed daily for 6 weeks, systolic blood pressure is reduced by ~9 mmHg, secondary to reductions in systemic vascular resistance. Whereas the effects of IRT on the vasculature have been described over the intermediate term, the acute responses that mediate these longer-term adaptations have not been fully characterized. Purpose: Our primary aim was to quantify the acute effects of a single bout of IRT on (endothelium-dependent dilation) EDD in healthy men and women. Secondarily, our goal was to determine the acute effects of IRT on arterial stiffness. Methods: Nitric oxide-mediated EDD and ischemia-induced maximal shear rate were assessed with brachial artery flow-mediated dilation (FMD), and arterial stiffness was assessed via carotid-femoral pulse wave velocity (PWV). Twenty healthy young adults (22.9 ± 3.4 years; 10 males, 10 females) were randomized to the experimental (IRT; 5 sets of 6 breaths at 50% of maximal inspiratory pressure with 1-minute rest intervals) and control (time-matched supine rest) conditions in a crossover design, with at least 48 hours between visits. FMD and PWV were performed before, 10 minutes after, and 40 minutes after the assigned intervention. Statistical analysis included repeated measures ANOVA with Sidak post hoc analyses. Results: All values are mean difference ± SD. There were no between-day differences in EDD at baseline (mean difference: 0.08 ± 3.03%; p=0.908). EDD was significantly increased from baseline at 10 minutes post-IRT (+1.86 ± 2.75%; p=0.025), but returned to baseline levels at 40 minutes post-IRT (-0.10 ± 3.00%; p=0.998). During the control condition, EDD was unchanged from baseline at 10 minutes post-rest and 40 minutes post-rest ( p=0.136). Lastly, maximal shear rate following 5 minutes of forearm blood flow occlusion was not different from baseline at any time point following IRT ( p=0.749) and thus, the change in EDD is not a result of a modified hyperemic response. However, in the control condition maximal shear rate was significantly lower at 40 minutes post-rest, relative to baseline (mean difference -9.94 ± 2.64 per second; p=0.005), although the reduced shear rate did not impact EDD at 40 minutes post-rest. Arterial stiffness was unchanged from baseline in response to IRT ( p=0.217) or the rest intervention ( p=0.150). Conclusions: In healthy young adult men and women, a single bout of IRT elicits a transient enhancement in EDD. The effect endures for at least 10 minutes but is extinguished at 40 minutes post IRT. Repeated acute enhancements in EDD may contribute to sustained IRT-related reductions in vascular resistance after 6 weeks of traini This work was supported by NIA/NIH Grant Number: 1R01AG065346-01A1 (EFB), NIH Training Grant Number: 5T32HL007249-44 (DT), and NIH/NHLBI Grant Number: 1K01HL153326-01 (DHC) This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Temperature dependent onset of shear thinning in supercooled glass-forming network liquids.

The onset of shear thinning and the transition from Newtonian to non-Newtonian behavior in the viscous flow of select chalcogenide and oxide network glass-forming liquids in the deeply supercooled regime and its temperature dependence are studied using parallel plate rheometry. In all cases, the onset occurs at a shear rate γ̇c that is several orders of magnitude lower than the shear relaxation rate τ0 -1 and the former increases with increasing temperature. These results are in good qualitative agreement with the predictions of the existing models of shear relaxation and shear thinning based on the nonlinear Langevin equation theory, random first order transition theory, and the free volume model. However, in contrast to the theoretical predictions, the reduced shear rate W0 (=τ0γ̇c) at the onset is found to range between 10-3 and 10-5 and decrease with increasing temperature. This temperature dependence becomes stronger with increasing fragility of the liquid. These results likely indicate that the shear thinning mechanism in network liquids could be fundamentally different from those in molecular, metallic, or polymeric glass-formers.

Discontinuous shear thickening in concentrated mixtures of isotropic-shaped and rod-like particles tested through mixer type rheometry

In this work, the effect of rigid rods on the discontinuous shear thickening (DST) transition in mixtures of smaller isotropic-shaped (calcium carbonate—CC) and larger rod-like (polyamide or glass) particles dispersed in water is experimentally established. The CC suspension in water is considered as a shear thickening matrix filling the pores of the fiber network. The DST in the matrix originates from the competition between the applied shear stress and the steric repulsion between adsorbed superplasticizer molecules. It is characterized by a typical S-shape of the flow curves, irregular oscillations of the shear rate in response to the applied shear stress, and some thixotropy. An addition of rods shifts the DST transition to lower critical shear rates, as explained by an increase in the suspension viscosity such that the shear rate to reach the onset stress of DST decreases. This behavior is satisfactorily reproduced by the reduced shear rate approach of Ohl and Gleissle [J. Rheol. 37, 381–406 (1993)] and, to a lesser extent, by the homogenization approach of Chateau et al. [J. Rheol. 52, 489–506 (2008)], both assuming random rod orientation. At fiber volume fractions, φ f ≥ 0.04, the mixture undergoes jamming, which is likely associated with the percolation threshold of the fiber network, nearly independent of the CC particle concentration. This idea is qualitatively supported by a modified homogenization approach, assuming that viscous dissipation mostly occurs in the vicinity of the contacts between fibers. The results of this work are believed to be useful for optimal formulations of fiber-reinforced cementitious materials.

Electrospinning of Cyclodextrin Nanofibers: The Effect of Process Parameters

Cyclodextrin (CD) nanofibers have recently emerged as high-performance materials owing to their large surface area-to-volume ratio, along with the presence of high active CD content for their applications in drug delivery and water treatment. Even though there are several studies on the polymer-free electrospinning of CD molecules of different types, the effects of electrospinning process parameters on the morphology and diameter of the resultant fibers have not addressed yet. In this study, the influence of electrospinning process variables on the morphology and diameter of the resultant CD nanofibers is systematically studied using two different solvent systems, i.e., water and N, N-dimethylformamide (DMF). On adjusting the electrospinning process parameters (i.e., electrical field, flow rate, tip-to-collector distance (TCD), and needle diameter), uniform CD nanofibers could be produced from aqueous and DMF solutions. Generally, the electrospinning of thicker fibers was observed by increasing the applied voltage and flow rate due to higher mass flow. Increasing TCD boosted the fiber diameter. Likewise, the use of needles with larger diameters resulted in the electrospinning of thicker fibers from DMF solutions, which might be attributed to higher viscosity due to reduced shear rate.

Direct gyrokinetic comparison of pedestal transport in JET with carbon and ITER-like walls

This paper compares the gyrokinetic instabilities and transport in two representative JET pedestals, one (pulse 78697) from the JET configuration with a carbon wall (C) and another (pulse 92432) from after the installation of JET’s ITER-like Wall (ILW). The discharges were selected for a comparison of JET-ILW and JET-C discharges with good confinement at high current (3 MA, corresponding also to low ) and retain the distinguishing features of JET-C and JET-ILW, notably, decreased pedestal top temperature for JET-ILW. A comparison of the profiles and heating power reveals a stark qualitative difference between the discharges: the JET-ILW pulse (92432) requires twice the heating power, at a gas rate of e s−1, to sustain roughly half the temperature gradient of the JET-C pulse (78697), operated at zero gas rate. This points to heat transport as a central component of the dynamics limiting the JET-ILW pedestal and reinforces the following emerging JET-ILW pedestal transport paradigm, which is proposed for further examination by both theory and experiment. ILW conditions modify the density pedestal in ways that decrease the normalized pedestal density gradient a/Ln, often via an outward shift in relation to the temperature pedestal. This is attributable to some combination of direct metal wall effects and the need for increased fueling to mitigate tungsten contamination. The modification to the density profile increases , thereby producing more robust ion temperature gradient (ITG) and electron temperature gradient driven instability. The decreased pedestal gradients for JET-ILW (92432) also result in a strongly reduced shear rate, further enhancing the ion scale turbulence. Collectively, these effects limit the pedestal temperature and demand more heating power to achieve good pedestal performance. Our simulations, consistent with basic theoretical arguments, find higher ITG turbulence, stronger stiffness, and higher pedestal transport in the ILW plasma at lower .

Simple shear flow in granular suspensions: inelastic Maxwell models and BGK-type kinetic model

The Boltzmann kinetic equation for low-density granular suspensions under simple shear flow is considered to determine the velocity moments through the fourth degree. The influence of the interstitial gas on solid particles is modeled by a viscous drag force term plus a stochastic Langevin-like term. Two independent but complementary approaches are followed to achieve exact results. First, to keep the structure of the Boltzmann collision operator, the so-called inelastic Maxwell models (IMM) are considered. In this model, since the collision rate is independent of the relative velocity of the two colliding particles, the forms of the collisional moments can be obtained without the knowledge of the velocity distribution function. As a complement of the previous effort, a Bhatnagar–Gross–Krook (BGK)-type kinetic model adapted to granular gases is solved to get the velocity moments of the velocity distribution function. The analytical predictions of the rheological properties (which are exactly obtained in terms of the coefficient of restitution and the reduced shear rate ) show in general an excellent agreement with event-driven simulations performed for inelastic hard spheres. In particular, both theoretical approaches show clearly that the temperature and non-Newtonian viscosity exhibit an shape in a plane of stress–strain rate (discontinuous shear thickening effect). With respect to the fourth-degree velocity moments, we find that while those moments have unphysical values for IMM in a certain region of the parameter space of the system, they are well defined functions of both and in the case of the BGK kinetic model. The explicit shear-rate dependence of the fourth-degree moments beyond this critical region is also obtained and compared against available computer simulations.

Basic Mechanical Properties of Wet Granular Materials: A DEM Study

Numerical simulations, by the discrete element method (DEM), of a model granular assembly, made of spherical balls, are used to investigate the influence of a small amount of an interstitial wetting liquid, forming capillary bridges between adjacent particles, on two basic aspects of granular material rheology: (1) the plastic response in isotropic compression, and (2) the critical state under monotonic shear strain, and its generalization to steady, inertial flow. Tensile strength F0=πΓa, in contacts between beads of diameter aa joined by a small meniscus of a liquid with surface tension Γ, introduces a new force scale and a new dimensionless control parameter, P∗=a2P/F0, for grains of diameter a under confining stress P. Under low P*, as cohesion dominates, capillary cohesion may stabilize very loose structures. Upon increasing pressure P in isotropic compression, such structures gradually collapse. The resulting irreversible compaction is well described by the classical linear relation between logP* and void ratio in some range, until a dense structure forms that retains its stability without cohesion as confinement dominates for large P*. In steady shear flow, with uniform velocity gradient γ˙=∂v1/∂x2γ˙=∂v1/∂x2 under normal stress P=σ22, the apparent internal friction coefficient, which is defined as μ∗=σ12/σ22, depends on P* and inertial number (reduced shear rate) I=γ˙√m/aP, and so does solid fraction Φ. The material exhibits, as P* decreases, a strongly enhanced resistance to shear (larger μ*). In the quasistatic limit, for I→0, it is roughly predicted by a simple effective pressure assumption by which the capillary forces are deemed equivalent to an isotropic pressure increase applied to the dry material as long as P*≥1, while the yield criterion approximately assumes the Mohr-Coulomb form. At lower P*, such models tend to break down as liquid bonding, causing connected clusters to survive over significant strain intervals, strongly influences the microstructure. Systematic shear banding is observed at very small P*

Gate shape optimization using design of experiment to reduce the shear rate around the gate

Numerical analysis is used to optimize the gate shape of the mold part in the molding process. The objective of this research was to develop a procedure that will optimize the gate shape of the mold part by using Design of Experiments approach. The computer-aided engineering software Moldflow was used to simulate the plastic injection molding process and the Minitab software was used to analyze the computational results from Moldflow. The Bulk Molding Compounds (BMC) UNI-203S thermoset material was chosen as the molding material. Four different types of gate shapes were analyzed to find the gate shape to be used in the optimization. The Type 3 gate shape was selected as basis for the gate optimization because this shape yielded the minimum shear rate around the gate among all. The thickness, width, length and angle of the gate were selected as the design variables. Erosion around a gate due to repetitive shear flow during molding process was considered as an important issue to extend the service life of the expensive mold. It is normally very difficult to prevent erosion due to high injection pressure and repetitive use of the mold, especially in certain molding parts as BMC reflector in automotive parts, so it has become the subject of researches. The effectiveness of design variables was evaluated by observing shear rate around the gate. The objective of the optimization was to minimize the average shear rate around the gate. Response Surface Method was applied to identify the optimum values of the design variables. The computed optimum values were validated numerically. The optimized gate shape showed the reduced shear rate by about 11%.

Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. II. Shear modulus, relaxation-elasticity connections, and rheology

We apply the quiescent and mechanically driven versions of nonlinear Langevin equation theory to study how particle softness influences the shear modulus, the connection between shear elasticity and activated relaxation, and nonlinear rheology of the repulsive Hertzian contact model of dense soft sphere fluids. Below the soft jamming threshold, the shear modulus follows a power law dependence on volume fraction over a narrow interval with an apparent exponent that grows with particle stiffness. To a first approximation, the elastic modulus and transient localization length are controlled by a single coupling constant determined by local fluid structure. In contrast to the behavior of hard spheres, an approximately linear relation between the shear modulus and activation barrier is predicted. This connection has recently been observed for microgel suspensions and provides a microscopic realization of the elastic shoving model. Yielding, shear and stress thinning of the alpha relaxation time and viscosity, and flow curves are also studied. Yield strains are relatively weakly dependent on volume fraction and particle stiffness. Shear thinning commences at values of the effective Peclet number far less than unity, a signature of stress-assisted activated relaxation when barriers are high. Apparent power law reduction of the viscosity with shear rate is predicted with a thinning exponent less than unity. In the vicinity of the soft jamming threshold, a power law flow curve occurs over an intermediate reduced shear rate range with an apparent exponent that decreases as fluid volume fraction and/or repulsion strength increase.

Reply to “Letter to the editor: ‘Assessment of flow-mediated dilation in humans: a methodological and physiological guideline'”

reply: We would like to thank Mc Loughlin and Mc Loughlin (4a) for their response and for bringing attention to the appropriate selection of transducer operating frequency for flow-mediated dilation investigations. We agree that employing a transducer with a higher central frequency (i.e., 12 MHz) will yield a greater detail resolution in the axial plane when interrogating vessels such as the brachial artery, and this would provide a greater sensitivity in detecting small changes in flow-evoked vasodilatation. However, in our review (8), we discussed not only the brachial artery but also the common femoral (9), profunda femoris (12), superficial femoral (1, 2, 10, 12), popliteal (5, 6, 11), and posterior tibial (3, 7) arteries. When these lower-limb vessels are insonated at an optimal region in terms of flow conditions, for example, at a distance where entrance effects are minimized, the artery depth is often greater than that expected for a typical brachial artery. Given that the average attenuation coefficient is 0.5 dB·cm−1·MHz−1 (4), there is considerable degradation of image quality when employing a high-frequency probe while imaging a deeper lying vessel. This can render the image unusable when combined with automated analysis software. The subsequent trade-off between detail resolution and depth penetration is a further consideration for researchers when performing flow-mediated dilation investigations; however, the minimum transducer recommended is 7.5 MHz for all peripheral arteries so as to maintain adequate detail resolution. Certainly, we advocate the use of higher transducer frequencies (i.e., 12 MHz) when investigating more superficial vessels such as the brachial and radial arteries.

Molecular dynamics simulations of supramolecular polymer rheology

Using equilibrium and nonequilibrium molecular dynamics simulations, we studied the equilibrium and rheological properties of dilute and semidilute solutions of head-to-tail associating polymers. In our simulation model, a spontaneous complementary reversible association between the donor and the acceptor groups at the ends of oligomers was achieved by introducing a combination of truncated pseudo-Coulombic attractive potential and Lennard Jones repulsive potential between donor, acceptor, and neighboring groups. We have calculated the equilibrium properties of supramolecular polymers, such as the ring/chain equilibrium, average molecular weight, and molecular weight distribution of self-assembled chains and rings, which all agree well with previous analytical and computer modeling results. We have investigated shear thinning of solutions of 8- and 20-bead associating oligomers with different association energies at different temperatures and oligomer volume fractions. All reduced viscosity data for a given oligomer length can be collapsed into one master curve, exhibiting two power-law regions of shear-thinning behavior with an exponent of -0.55 at intermediate ranges of the reduced shear rate β and -0.8 (or -0.9) at larger shear rates. The equilibrium viscosity of supramolecular solutions with different oligomer lengths and associating energies is found to obey a power-law scaling dependence on oligomer volume fraction with an exponent of 1.5, in agreement with the experimental observations for several dilute or semidilute solutions of supramolecular polymers. This implies that dilute and semidilute supramolecular polymer solutions exhibit high polydispersity but may not be sufficiently entangled to follow the reptation mechanism of relaxation.

Phase and Rheological Behavior of Cetyldimethylbenzylammonium Salicylate (CDBAS) and Water

AbstractThe temperature–composition phase diagram in the diluted region of the cationic surfactant cetyldimethylbenzylammonium salicylate/water system was studied with a battery of techniques. The Krafft temperature (Tk = 33 ± 1 °C) was measured by differential scanning calorimetry, polarizing microscopy, conductimetry, viscosimetry, and rheometry. The critical vesicle concentration (cvc, ∼0.002 wt%) and a vesicle–micellar transition (cvm, ∼0.005 wt%) was detected at a temperature of 35 °C. Below Tk and concentrations ≤2 wt%, a transparent solution is formed (I). Above 2–8.5 wt%, a lamellar (L1) phase forms. At higher concentrations and up to 12 wt%, a second lamellar phase (L2) is detected. From 12.4 to 15.5 wt%, an emulsion phase (E) is formed. Rheological dynamic measurements for the I phase indicate that the system exhibits a predominantly viscous behavior (G′ < G″) for concentrations lower than the overlap or entanglement concentration (Ce, ∼0.75 wt%). At higher concentrations, wormlike micelles form and the elastic behavior predominates (G′ > G″). The elastic (G′) modulus collapses in a concentration–time master curve in the whole reduced frequencies range ωτc examined, whereas the viscous modulus (G″) collapses only at reduced frequencies lower than 0.1. Reduced stress plotted as a function of the reduced shear rate yields a good superposition of the curves at the different concentrations up to the onset of the non‐linear behavior.

Impact of acute exposure to increased hydrostatic pressure and reduced shear rate on conduit artery endothelial function: a limb-specific response

Unlike quadrupeds, humans exhibit a larger hydrostatic pressure in the lower limbs compared with the upper limbs during a major part of the day. It is plausible that repeated episodes of elevated pressure in the legs may negatively impact the endothelium, hence contributing to the greater predisposition of atherosclerosis in the legs. We tested the hypothesis that an acute exposure to increased hydrostatic pressure would induce conduit artery endothelial dysfunction. In protocol 1, to mimic the hemodynamic environment of the leg, we subjected the brachial artery to a hydrostatic pressure gradient ( approximately 15 mmHg) by vertically hanging the arm for 3 h. Brachial artery flow-mediated dilation (FMD) was assessed in both arms before and following the intervention. In protocol 2, we directly evaluated popliteal artery FMD before and after a 3-h upright sitting (pressure gradient approximately 48 mmHg) and control (supine position) intervention. Our arm-hanging model effectively resembled the hemodynamic milieu (high pressure and low shear rate) present in the lower limbs during the seated position. Endothelium-dependent vasodilation at the brachial artery was attenuated following arm hanging (P < 0.05); however, contrary to our hypothesis, upright sitting did not have an impact on popliteal artery endothelial function (P > 0.05). These data suggest an intriguing vascular-specific response to increased hydrostatic pressure and reduced shear rate. Further efforts are needed to determine if this apparent protection of the leg vasculature against an acute hydrostatic challenge is attributable to posture-induced chronic adaptations.

Dynamical regimes and hydrodynamic lift of viscous vesicles under shear

The dynamics of two-dimensional viscous vesicles in shear flow, with different fluid viscosities etain and etaout inside and outside, respectively, is studied using mesoscale simulation techniques. Besides the well-known tank-treading and tumbling motions, an oscillatory swinging motion is observed in the simulations for large shear rate. The existence of this swinging motion requires the excitation of higher-order undulation modes (beyond elliptical deformations) in two dimensions. Keller-Skalak theory is extended to deformable two-dimensional vesicles, such that a dynamical phase diagram can be predicted for the reduced shear rate and the viscosity contrast etain/etaout. The simulation results are found to be in good agreement with the theoretical predictions, when thermal fluctuations are incorporated in the theory. Moreover, the hydrodynamic lift force, acting on vesicles under shear close to a wall, is determined from simulations for various viscosity contrasts. For comparison, the lift force is calculated numerically in the absence of thermal fluctuations using the boundary-integral method for equal inside and outside viscosities. Both methods show that the dependence of the lift force on the distance ycm of the vesicle center of mass from the wall is well described by an effective power law ycm(-2) for intermediate distances 0.8Rp< approximately ycm< approximately 3Rp with vesicle radius Rp. The boundary-integral calculation indicates that the lift force decays asymptotically as 1/[ycm ln(ycm)] far from the wall.

Master curves and radial distribution functions for shear dilatancy of liquid n-hexadecane via nonequilibrium molecular dynamics simulations

Shear dilatancy, a significant nonlinear behavior of nonequilibrium thermodynamics states, has been observed in nonequilibrium molecular dynamics (NEMD) simulations for liquid n-hexadecane fluid under extreme shear conditions. The existence of shear dilatancy is relevant to the relationship between the imposed shear rate gamma and the critical shear rate gamma(c). Consequently, as gamma<gamma(c), the intermolecular equilibrium distance of the fluid remains unchanged, while the nonequilibrium state of the fluid approaches equilibrium. In contrast to gamma>gamma(c), the intermolecular distance is lengthened substantially by strong shear deformation breaking the equilibrium thermodynamic state so that shear dilatancy takes place. Notably, a characteristic shear rate gamma(m), which depends on the root mean square molecular velocity and the average free molecular distance, is found in nonequilibrium thermodynamics state curves. Studies of the variations in the intermolecular radial distribution function (RDF) with respect to the shear rate provide a direct measure of the variation in the degree of intermolecular separation. Additionally, the variations of the RDF curve in the microscopic regime are consistent with those of the nonequilibrium thermodynamic state in the macroscopic world. By inspecting the overall shape of the RDF curve, it can be readily corroborated that the fluid of interest exists in the liquid state. More importantly, both primary characteristic values, the equilibrium thermodynamic state variable and a particular shear rate of gamma(p), are determined cautiously, with gamma(p) depending on the gamma(m) value and the square root of pressure. Thereby, the nonequilibrium thermodynamic state curves can be normalized as temperature-, pressure-, and density-invariant master curves, formulated by applying the Cross constitutive equation. Clearly, gamma(c) occurs at which a reduced shear rate gamma/gamma(p) approaches 0.1. Furthermore, the trends in the rates of shear dilatancy in both the constant-pressure and constant-volume NEMD systems under isothermal conditions conform to the cyclic rule of pressure, as a function of density and shear rate.

Structure and dynamics of cylindrical micelles at equilibrium and under shear flow

The dynamics and rheology of semidilute unentangled micellar solutions are investigated by Langevin dynamics mesoscopic simulations coupled to a microreversible kinetic model for scissions and recombinations. Two equilibrium state points, differing by the scission energy and therefore by the corresponding average micelle length, have been examined. The kinetic rates are tuned by an independent parameter of the model, whose range is chosen in such a way that the kinetics always strongly couple to the chain dynamics. Our results confirm, as predicted by Faivre and Gardissat, that the stress relaxation, as well as the monomer diffusion, is characterized by a time tauLambda, defined by the lifetime of a segment Lambda, whose Rouse relaxation time is equal to its lifetime. Moreover, the power-law dependence of the zero-shear viscosity versus tauLambda was evidenced. Under stationary shear, the chains are deformed and their average bond length is increased, which enhances the overall scission frequency. In turn, this induces an overall shortening of the chains in order to increase the overall corresponding chain-end recombination frequency, as required by the stationary conditions. Nonequilibrium simulations show that the chain deformation and orientation, as well as the rheology of the system, can be expressed as universal functions of a single reduced shear rate betaLambda=gammatauLambda (with gamma the bare shear rate). Furthermore, local analysis of the kinetics under stationary shear gives insights on the variation of the average length with shear rate.

Shear thinning near the critical point of xenon

We measured shear thinning, a viscosity decrease ordinarily associated with complex liquids, near the critical point of xenon. The data span a wide range of reduced shear rate: 10(-3)<gamma tau<700 , where gamma tau is the shear rate scaled by the relaxation time tau of critical fluctuations. The measurements had a temperature resolution of 0.01 mK and were conducted in microgravity aboard the Space Shuttle Columbia to avoid the density stratification caused by Earth's gravity. The viscometer measured the drag on a delicate nickel screen as it oscillated in the xenon at amplitudes 3 microm<x 0<430 microm and frequencies 1 Hz<omega/2pi<5 Hz . To separate shear thinning from other nonlinearities, we computed the ratio of the viscous force on the screen at gamma tau to the force at gamma tau approximately 0: C gamma triple bond F(x 0,omega tau,gamma tau)/F(x 0,omega tau,0) . At low frequencies, (omega tau)2<gamma tau , C gamma depends only on gamma tau , as predicted by dynamic critical scaling. At high frequencies, (omega tau)2>gamma tau , C gamma depends also on both x 0 and omega . The data were compared with numerical calculations based on the Carreau-Yasuda relation for complex fluids: eta(gamma)/eta(0)=[1+A gamma|gamma tau|]-x eta/(3+x eta) , where x eta=0.069 is the critical exponent for viscosity and mode-coupling theory predicts A gamma=0.121 . For xenon we find A gamma=0.137+/-0.029 , in agreement with the mode coupling value. Remarkably, the xenon data close to the critical temperature Tc were independent of the cooling rate (both above and below Tc ) and these data were symmetric about Tc to within a temperature scale factor. The scale factors for the magnitude of the oscillator's response differed from those for the oscillator's phase; this suggests that the surface tension of the two-phase domains affected the drag on the screen below Tc .

Statistical-mechanical theory of rheology: Lennard-Jones fluids

The generalized Boltzmann equation for simple dense fluids gives rise to the stress tensor evolution equation as a constitutive equation of generalized hydrodynamics for fluids far removed from equilibrium. It is possible to derive a formula for the non-Newtonian shear viscosity of the simple fluid from the stress tensor evolution equation in a suitable flow configuration. The non-Newtonian viscosity formula derived is applied to calculate the non-Newtonian viscosity as a function of the shear rate by means of statistical mechanics in the case of the Lennard-Jones fluid. For that purpose we have used the density-fluctuation theory for the Newtonian viscosity, the modified free volume theory for the self-diffusion coefficient, and the generic van der Waals equation of state to compute the mean free volume appearing in the modified free volume theory. Monte Carlo simulations are used to calculate the pair-correlation function appearing in the generic van der Waals equation of state and shear viscosity formula. To validate the Newtonian viscosity formula obtained we first have examined the density and temperature dependences of the shear viscosity in both subcritical and supercritical regions and compared them with molecular-dynamic simulation results. With the Newtonian shear viscosity and thermodynamic quantities so computed we then have calculated the shear rate dependence of the non-Newtonian shear viscosity and compared it with molecular-dynamics simulation results. The non-Newtonian viscosity formula is a universal function of the product of reduced shear rate (gamma*) times reduced relaxation time (taue*) that is independent of the material parameters, suggesting a possibility of the existence of rheological corresponding states of reduced density, temperature, and shear rate. When the simulation data are reduced appropriately and plotted against taue*gamma* they are found clustered around the reduced (universal) non-Newtonian viscosity formula. Thus we now have a molecular theory of non-Newtonian shear viscosity for the Lennard-Jones fluid, which can be implemented with a Monte Carlo simulation method for the pair-correlation function.