Showing papers on "Shear thinning published in 2000"

Viscosity of guar gum and xanthan/guar gum mixture solutions

Abstract: The viscosity of diluted guar gum solutions and the viscosity of xanthan and guar gum mixture solutions have been studied. Guar gum solutions showed pseudoplastic behaviour. Apparent viscosity increased with gum concentration and decreased with the temperature at which viscosity was measured. A maximum in the plot of viscosity versus increasing dissolution temperature was observed at 60 °C. This behaviour was related to differences in molecular structure of the polymers solved at different temperatures. Mixtures of xanthan and guar gum showed a higher combined viscosity than that occurring in each separate gum. This synergistic interaction was affected by the gum ratio in the mixture and dissolution temperature of both gums. The effect of polysaccharide concentration (1.0, 1.5 and 2.0 kg m−3), xanthan/guar gum ratio (1/5, 4/2, 3/3, 4/2 and 5/1) and dissolution temperature (25, 40, 60 and 80 °C for both gums) on the viscosity of solutions of mixtures were studied. The highest viscosities were observed when 2.0 kg m−3 gum concentration was used together with a ratio of xanthan/guar gum of 3/3 (w/w) and dissolution temperature of 40 and 80 °C for xanthan and guar gum, respectively. © 2000 Society of Chemical Industry

Viscous fingering in a shear-thinning fluid

Abstract: We study the Saffman–Taylor instability in a rectangular Hele-Shaw cell. The driven fluid is a dilute (or semidilute) polymer solution, with a viscosity that exhibits shear thinning. Other non-Newtonian properties such as elastic effects are negligible under the present experimental conditions; the system thus allows for separate investigation of the influence of shear thinning on the instability. The experiments show that, for weak shear-thinning, the results for the width of the fingers as a function of the capillary number collapse onto the universal curve for Newtonian fluids, provided the shear-thinning viscosity is used to calculate the capillary number. For stronger shear thinning, narrower fingers are found. The experiment allows also for a study of the applicability of Darcy’s law to shear thinning fluids. For Newtonian fluids, this law gives the finger velocity as a function of the pressure gradient. For weakly shear-thinning fluids, we find that an effective Darcy’s law, in which the constant v...

An experimental determination of the stress–microstructure relationship in semi-concentrated fiber suspensions

Abstract: The relationship between the stress and the fiber orientation distribution in semi-dilute (nL3⪢1,nL2d 1) fiber suspensions was investigated. Here, n is the fiber number density, L the length, and d is the diameter. A highly viscous, index-matched suspension was developed to permit measurements of both the microstructure and rheology using the same suspension. By removing the ambiguity of comparing data taken using different suspending fluids and fibers, a more accurate evaluation of available stress–structure models was made possible. The measured period of rotation and the distribution among Jeffery orbits were compared to the results of a theory for hydrodynamic fiber interactions and a simulation incorporating mechanical contacts. At low concentrations, the period increased above the dilute, Jeffery value. As the fiber loading was increased, the period peaked and decreased to approach the dilute result. The distribution of orbits shifted slightly towards the vorticity axis with increasing concentration. The inclusion of a nematic potential in the hydrodynamic theory provided a possible explanation for the decrease in the period of rotation. Measurements of the viscosity and first normal stress differences of the same suspensions were compared to theoretical predictions based on the orientation results. The measured viscosity was in good agreement with the mechanical contact simulation results but was much larger than predicted by hydrodynamic theories. The high viscosity and the measurement of significant first normal stress differences are suggestive of an enhanced stress resulting from the presence of fiber–fiber contacts.

A model for the nonlinear rheology of associating polymers

Abstract: Theories for transient networks formed by associating telechelic polymers require that the kinetics of chain detachment and reattachment processes are somehow specified. We propose here very simple choices for such kinetics, that are nevertheless based on plausible molecular mechanisms. Specific evolution equations are then formulated for the populations of both elastically-active chains and chains temporarily detached from the network. By using typical closure approximations, the rheological model is finally elaborated into a set of ordinary differential equations. For steady shear flows, these nonlinear equations predict shear thickening at moderate shear rates followed by shear thinning at higher shear rates, in agreement with observations. In the limit of slow flows, analytical expressions for the viscosity and the relaxation times are also obtained.

Stress Components and Shear Thickening of Concentrated Hard Sphere Suspensions

Abstract: The elastic-like and viscous-like viscosity components of model, Brownian hard sphere suspensions were determined. The elastic-like component, sometimes called the thermodynamic component, is due to Brownian motion while the viscous-like component, sometimes called the hydrodynamic component, is due to hydrodynamic interaction between and drag on the particles. The three volume fractions tested were found to be above the glass transition volume fraction due to the absence of a zero shear viscosity. The hydrodynamic viscosity component was approximately independent of shear rate, yet the suspension demonstrated a large amount of shear thinning which was due to the elastic-like component. The measured stress components associated with shear thickening were distinctly different in each sample. Continuous shear thickening was measured for the sample with 0.54 volume fraction while the samples with volume fractions 0.59 and 0.63 showed discontinuous shear thickening. Shear thickening in these concentrated susp...

A molecular dynamics study of a short-chain polyethylene melt. I. Steady-state shear

Abstract: Utilizing a united atom potential model and reversible reference system propagator algorithm (rRESPA) multitimestep dynamics, we have performed equilibrium and nonequilibrium molecular dynamics simulations of a monodisperse C100H202 polyethylene melt at 448 K and 0.75 g/cm 3 . We report a variety of properties calculated at equilibrium including rotational relaxation time and self-diffusion coefficient as well as shear-enhanced diffusion and rheological properties calculated under steady-state shearing conditions. Shear thinning is observed in the viscosity and normal stress coefficients over the range of strain rates studied. A minimum in the hydrostatic pressure is observed at an intermediate strain rate that is associated with a minimum in the intermolecular Lennard‐Jones potential energy as well as transitions in the strain-rate-dependent behavior of several other viscous and structural properties of the system. The shear field also imposes significant alignment of the chains with the flow direction, approaching a limiting angle of approximately 3 at high strain rate. In addition, the self-diffusion coefficients (calculated in terms of the unconvected positions according to the Cummings‐Wang formalism) are markedly enhanced under shear compared to the equilibrium state (up to two orders of magnitude at the highest shear rate studied). © 2000 Elsevier Science B.V. All rights reserved.

Spreading Kinetics of Shear-Thinning Fluids in Wetting and Dewetting Modes

Abstract: The spreading dynamics of non-Newtonian fluids, in wetting and dewetting modes, plays a key role in numerous applications in particular in coating, adhesive bonding, and printing. The very common case of the shear-thinning behavior has been considered in this study. The wetting dynamics has been studied by depositing sessile drops on glass slides. The dewetting kinetics has been evaluated by measuring the rate of growth of dry zones nucleated in an unstable liquid film formed on Teflon-coated glass slides. The spreading kinetics of a liquid on a rigid substrate is governed by viscous dissipation in the liquid, the capillary driving force being compensated for by the braking force resulting from viscous shearing in the liquid. In the case where the liquid is not Newtonian but shear-thinning or pseudoplastic, a deviation from the classical hydrodynamic theory (Newtonian behavior) for wetting is obviously observed, in particular a slower wetting kinetics corresponding to an apparent increase of the liquid vi...

Effects of shear thinning on migration of neutrally buoyant particles in pressure driven flow of Newtonian and viscoelastic fluids

Abstract: The pattern of cross stream migration of neutrally buoyant particles in a pressure driven flow depends strongly on the properties of the suspending fluid. These migration effects have been studied by direct numerical simulation in planar flow. Shear thinning has a large effect when the inertia or elasticity is large, but only a small effect when they are small. At moderate Reynolds numbers, shear thinning causes particles to migrate away from the centerline, creating a particle-free zone in the core of the channel, which increases with the amount of shear thinning. In a viscoelastic fluid with shear thinning, particles migrate either toward the centerline or toward the walls, creating an annular particle-free zone at intermediate radii. The simulations also give rise to precise determination of slip velocity distributions in the various cases studied.

Influence of NaClO3 on the rheological behaviour of a micellar solution of CPCl

Abstract: It is now well know that a small addition of salt to a micellar solution often increases the zero-shear viscosity η0 of the solution, the understanding of the behaviour at high salt content is more questionable. In this situation, addition of more salt induces a decrease of η0. In this experimental work we investigate the linear and non-linear rheological behaviour of a new micellar system: CPCl (surfactant)/NaClO3 (salt). Studies of the evolution of η0 as well as G0 (the elastic modulus) or τR (the relaxation time) are in agreement with the hypothesis of a diminution of the mean micellar length when, after the maximum η0, the salt content increases. In the non-linear behaviour (non-Newtonian viscosity) the evolution of γ˙c, (which defines the occurrence of the shear thinning) with salt concentration CS is also in agreement with such a hypothesis.

Analysis of electro- and magneto-rheological flow mode dampers using Herschel-Bulkley model

Abstract: Electrorheological (ER) and magnetorheological (MR) fluid- based dampers are typically analyzed using Bingham-plastic shear flow analysis under quasi-steady fully developed flow conditions. An alternative perspective, supported by measurements reported in the literature, is to allow for post- yield shear thinning and shear thickening. To model these, the constant post-yield plastic viscosity in Bingham model can be replaced with a power law model dependent on shear strain rate that is known as the Herschel-Bulkley fluid model. Depending on the value of the flow behavior index number, varying degrees of post-yield shear thickening or thinning behavior can be analyzed. A nominal ER bypass damper is considered. Damping forces in the damper are analyzed by approximate parallel plate geometry. The impacts of flow behavior index on shear stress-strain relationship and velocity profile for variable electric field are also examined numerically. Then, analytical damping predictions of ER/MR flow mode dampers are compared using the nonlinear Bingham-plastic and nonlinear Herschel-Bulkley analyses.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Thermal chain model of electrorheology and magnetorheology.

Abstract: Steady shear simulations of electrorheology (ER) and magnetorheology (MR) in a uniaxial field are presented. These large scale simulations are three dimensional, and include the effect of Brownian motion. In the absence of thermal fluctuations, the expected shear thinning viscosity is observed and a striped phase is seen to rapidly form in a uniaxial field, with a shear slip zone in each sheet. However, as the influence of Brownian motion increases, the fluid stress decreases, especially at lower Mason numbers, and the striped phase eventually disappears, even when the fluid stress is still high. To account for the uniaxial steady shear data we propose a microscopic chain model of the role played by thermal fluctuations on the rheology of ER and MR fluids that delineates the regimes where an applied field can impact the fluid viscosity, and gives an analytical prediction for the thermal effect.

Rheology of a dilute emulsion of surfactant-covered spherical drops

Abstract: The rheology of a diluted emulsion of surfactant-covered spherical drops has been investigated. A diluted film of insoluble surfactant is assumed. A matrix formulation of the problem is derived and analyzed by perturbation expansions for low- and high-shear rates, and for high-viscosity drops; the high-viscosity expansion converges rapidly for a wide range of parameters. Our theory provides a quantitative description of shear thinning and normal stress differences that occur as a result of surfactant redistribution.

Dynamics of cooling domes of viscoplastic fluid

Abstract: A non-isothermal viscoplastic thin-layer theory is developed to explore the effects of surface cooling, yield stress, and shear thinning on the evolution of non-isothermal domes of lava and laboratory fluids. The fluid is modelled using the Herschel-Bulkley constitutive relations, but modified to have temperature-dependent viscosity and yield stress. The thin-layer equations are solved numerically to furnish models of expanding, axisymmetrical domes. Linear stability theory reveals the possibility of non-axisymmetrical, fingering-like instability in these domes. Finally, the relevance to lava and experiments is discussed.

Microstructures and Rheological Responses of Aqueous CTAB Solutions in the Presence of Benzyl Additives

Abstract: In this paper, we investigated the effects of various benzyl additives on the microstructure of a cationic surfactant, cetyltrimethylammonium bromide (CTAB), in aqueous medium. Benzyl derivatives considered here were sodium salicylate (NaSal), sodium benzoate (NaBen), and p-methylsalicylic acid (PMSA). The CTAB concentration ranged from 1 to 20 mM, and the molar ratio of an additive to CTAB was varied from 0.1 to 10.0. The experimental results showed that the CTAB solution exhibited a variety of rheological responses, such as shear thinning, shear thickening, and long time relaxation, under an applied shear field. In particular, the shear viscosity of a dilute CTAB solution, which showed pronounced shear thinning at low shear rates, exhibited shear thickening at high shear rates. As the shear rate was increased even more, the viscosity shear thinned again. The rheological response associated with microstructural transition was closely dependent on the concentrations and molecular structures of constituent...

Effect of dynamic cross-linking on melt rheological properties of polypropylene/ethylene-propylene-diene rubber blends

Abstract: Study of melts rheological properties of unvulcanized and dynamically vulcanized polypropylene (PP)/ethylene-propylene-diene rubber (EPDM) blends, at blending ratios 10–40 wt %, EPDM, are reported. Blends were prepared by melt mixing in an internal mixer at 190°C and rheological parameters have been evaluated at 220°C by single screw capillary rheometer. Vulcanization was performed with dimethylol phenolic resin. The effects of (i) blend composition; (ii) shear rate or shear stress on melt viscosity; (iii) shear sensitivity and flow characteristics at processing shear; (iv) melt elasticity of the extrudate; and (v) dynamic cross-linking effect on the processing characteristics of the blends were studied. The melt viscosity increases with increasing EPDM concentration and decreased with increasing intensity of the shear mixing for all compositions. In comparison to the unvulcanized blends, dynamically vulcanized blends display highly pseudoplastic behavior provides unique processing characteristics that enable to perform well in both injection molding and extusion. The high viscosity at low shear rate provides the integrity of the extrudate during extrusion, and the low viscosity at high shear rate enables low injection pressure and less injection time. The low die-swell characteristics of vulcanizate blends also give high precision for dimensional control during extrusion. The property differences for vulcanizate blends have also been explained in the light of differences in the morphology developed. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 1488–1505, 2000

Rheo-NMR of Semidilute Polyacrylamide in Water

Abstract: Rheo-NMR 1H spectroscopy has been performed on semidilute solutions of polyacrylamide (PAA) in water using a cylindrical Couette cell in which the solution in the annulus may be imaged in order to investigate spatially dependent NMR parameters. A number of interesting properties emerge. Shear banded flow is observed, in contrast to rheo-NMR studies of other semidilute polymers in which simple power-law shear thinning is found. Furthermore, we find that the PAA chain protons exhibit a marked T2 reduction under shear and that the recovery on shear cessation is indicative of slow reorganizational dynamics. The observed T2 recovery is multiexponential, the fast molecular relaxation times correlate well with the terminal times measured from the steady-state flow curve, and we interpret our findings in terms of shear-induced deformation of the Doi−Edwards tube. We suggest that slower relaxation processes may be due to hydrogen bond formation.

Influence of surfactant on rheological behaviors of injection-molded alumina suspensions

Abstract: The effect of three different surfactants, namely, stearic acid (SA), oleic acid (OA) and 12-hydroxystearic acid (HSA), on the rheological properties of injection-molded alumina suspensions has been investigated over a temperature range of 120–150°C and a shear-rate range of 1000–15 000 s−1. The suspension mixtures exhibited a pseudoplastic flow behavior and a viscosity (η) order of ηSA<ηOA<ηHSA over the shear-rate range tested. The yield stress of the suspensions, on the other hand, followed a reverse order as that of the viscosity and the suspension flow was highly dependent on the working temperature employed. A particulate network within the mixtures in a form of powder agglomerates was suspected to play a major role in the flow behavior observed, over which, different levels of powder agglomeration were resulted from the varying surfactants used. A model experiment by repeatedly shearing the suspensions under a fixed stress level partially confirmed the hypothesis. The suspension viscosity was reduced in a power-law fashion as the number of shears was increased and eventually a minimum viscosity was reached. This suggests that the particle network restructured itself upon the shear was applied, leading to breakup of the network and improvements in the particle packing.

The Role of Rheology in the Pipelining of Mineral Slurries

Abstract: This paper combines new experimental evidence and pipeline flow models to challenge widely held views in the literature. These include the existence of a yield stress and its determination, the existence of shear-thinning at high shear rates, and the continuum approximation which is routinely applied to these slurries. The implications of these critical points for laminar, laminar/turbulent transition and turbulent flow are investigated. It is shown that interpretation of rheological data at low and high shear rates is crucial for flow modelling in all three types of flow. It is concluded that the yield pseudoplastic model should be used for mineral slurries and low shear rate phenomena may be ignored. A high shear rate asymptote was not found or deemed necessary. The yield stress is fundamentally important for the laminar/turbulent transition and results in the critical velocity becoming independent of pipe diameter. Accurate rheology is important in smooth turbulent flow. Rough turbulent flow r...

LDPE melt rheology and the pom–pom model

Abstract: In their original contribution, McLeish and Larson [J. Rheol. 42 (1998) 81–110] established a constitutive sketch for a particular branched polymer, the pom–pom model. The orientation contribution to the stress tensor of the pom–pom polymer under flow is calculated using the tube concept of Doi and Edwards [J. Chem. Soc. Faraday Trans, Part 2, 11(74) (1978a) 1802–1817]. More recently, Inkson et al. [J. Rheol. 43 (1999) 873–896] succeeded in predicting the melt rheology of longchain-branched low-density polyethylenes at start-up of extensional and shear flows, using a multi-mode pom–pom model and a differential approximation of the original Doi–Edwards model for the orientation contribution. We compare the transient viscosity predictions, when using the original Doi–Edwards strain measure (in the independent alignment approximation) and the differential approximation. We conclude that the differential approximation is a crude approximation of the Doi–Edwards model for high Deborah number flows and for planar extension. In the case of the pom–pom model, the differential approximation introduces a strong relaxation process for shear flow that is not present in the full model. Using the original Doi–Edwards strain measure for the orientation contribution, we show that the pom–pom model predicts a strain hardening behaviour in the case of the second normal stress difference in planar extension, in contrast to experimental evidence. In shear flow, it is in quantitative disagreement with the experimentally observed amount of stress overshoot and shear thinning. We also analyse the pom–pom model predictions for stress relaxation after a step strain. The multi-mode pom–pom model does not show the time-strain separability observed experimentally for polymer melts over several decades of relaxation time.

Influence of Alignment of Crystalline Confining Surfaces on Static Forces and Shear in a Liquid Crystal, 4'-n-Pentyl-4-cyanobiphenyl

Abstract: Static force-distance relations as well as linear and nonlinear viscoelastic responses to oscillatory shear were studied in 4'-n-pentyl-4-cyanobiphenyl (5CB) confined between two muscovite mica surfaces at 25 °C. The orientation of the crystallographic axes of the mica sheets was varied from close to perfect alignment to a twist angle of i > 80°, and the sliding direction was kept parallel to the A optical axis of one mica sheet. The layering was unaffected by twist angle when the film thickness exceeded three molecular layers of 5CB in a planar orientation, but for two and three layers the adhesive minima in the oscillatory force- distance curve decreased in magnitude with increasing i. In the linear viscoelastic response (obtained with shear deformations of <20% of the film thickness), an elastic response dominated at shear frequencies of 0.13-130 Hz and small i, whereas a more liquidlike response appeared at low frequency for large i. Apparent discrepancies between the shear responses of alkylcyanobiphenyl films obtained in other investigations were resolved: during shear deformations of large amplitude, either stick-slip or smooth sliding was observed, depending on the number of layers but not on the surface alignment. At the film thickness of two layers, we observed stick-slip above a maximum limiting strain of 0.5 (at the smallest i), whereas at three layers, the sliding was continuous with shear thinning at strains larger than 0.7. The effective shear moduli and limiting shear stress decreased with increasing film thickness and misalignment. In contrast to the known friction behavior of muscovite mica in the absence of an intervening fluid layer, no local extrema were observed at i ) 30° and 60°, indicating that the shear response resulted from the structure of the film of anisotropic molecules and not directly from the surface crystal lattice.

Linear stability of viscoelastic Taylor–Couette flow: Influence of fluid rheology and energetics

Abstract: In this study we have theoretically investigated the effect of detailed fluid rheology (e.g., spectrum of relaxation times, shear thinning of first normal stresses, finite second normal stresses, and ratio of solvent to total viscosity) and energetics on the purely elastic instability of Taylor–Couette flow. The isothermal analysis showed that irrespective of the details of the fluid rheology, solvent to total viscosity ratio and gap width, the secondary flow is time-dependent and nonaxisymmetric. However, as the number of relaxation times is increased, the critical Deborah number reaches an asymptotic value which is approximately half of the critical Deborah number predicted by the single-mode constitutive equation. These results strengthen the conclusions of Al-Mubaiyedh et al. (1999) that have attributed the existence of a stationary secondary flow in the experiments of Baumert and Muller (1995, 1997) to the effect of energetics. The nonisothermal analyses predicted, for experimentally realizable value...

A numerical investigation of flows of shear‐thinning fluids with applications to blood rheology

Abstract: A new solver is presented for the flow of power-law fluids that extends a solver developed by Turek [FEATFLOW] for the Navier-Stokes fluid. This solver is convenient for simulating efficiently both steady and unsteady flows of shear-dependent fluids in a complex geometry. To illustrate the ability of the solver, two specific problems are chosen. First, steady flows of power-law fluids are studied in corrugated channels, and qualitative comparisons with real experiments are carried out. Attention is paid to the dependence of friction factor and dimensionless normal stress amplitude on the aspect ratio (amplitude versus wavelength of the sinusoidal channel) and to the occurrence of secondary flows. It is shown that the aspect ratio is not a sensible non-dimensional number in this geometry. Second, unsteady (pulsatile) flows of the power-law fluid (i.e. blood under certain circumstances) are simulated in the presence of stenosis and a very good coincidence with recent numerical studies is obtained. The description of the numerical scheme and theoretical background are also outlined

Sedimentation of a sphere near a vertical wall in an Oldroyd-B fluid

Abstract: A code based on the distributed Lagrange multiplier/fictitious domain method (DLM) is used to study the motion of a sphere sedimenting in a viscoelastic liquid near a vertical wall. The viscoelastic liquid is assumed to be shear thinning and modeled by a shear-thinning Oldroyd-B model. Our simulations show that when the Deborah number based on the sphere velocity is O(1) and its initial position is sufficiently close to the wall, it moves towards the wall. This tendency of a sedimenting sphere to move closer to the vertical wall is enhanced by shear thinning, and also by an increase in the Deborah number. In a Newtonian liquid, on the other hand, the sphere moves away from the vertical wall and attains a steady position between the channel center and the wall. The sense of rotation of a sedimenting sphere when it is close to the vertical wall, for both Newtonian and viscoelastic liquids, is anomalous, i.e. the sphere rotates as if rolling up the wall. However, when the sphere is away from the wall the direction of rotation reverses. These results are in agreement with the experimental data reported in [D.D. Joseph et al., J. Non-Newtonian Fluid Mech. 54 (1994) 45–86; Y.J. Liu et al., J. Non-Newtonian Fluid Mech. 50 (1993) 305–329; D.D. Joseph et al., Theoretical and Applied Rheology, Elsevier, Amsterdam, 1992, pp. 60–65; D.L.E. Becker et al., J. Non-Newtonian Fluid Mech. 63 (1996) 45–86]. In two dimensions, on the other hand, simulations show that a sedimenting cylinder moves away from the wall in both Newtonian and viscoelastic liquids. These numerical results prove that the attraction between a wall and a particle sedimenting in a viscoelastic liquid is a three-dimensional effect, i.e. exists for a sphere but not for a cylinder, and it is enhanced by shear thinning.

Viscous fingering in complex fluids

Abstract: Viscous fingers form when a less viscous fluid pushes a more viscous fluid in a linear channel. The instability of the interface results from a competition between viscous and capillary forces. We show here that by using complex fluids such as polymer or surfactant solutions one can act on the viscosity or the surface tension and modify the instability drastically. Two different polymer solutions, that exhibit either shear thinning or normal stress effects, are used. For the first fluid the viscous forces are altered leading to finger narrowing, whereas for the second fluid the viscous forces are supplemented by normal stresses, which leads to finger widening. For the surfactant solutions the modification of the capillary forces leads to finger widening.

Rheology of cellulosic N‐methylmorpholine oxide monohydrate solutions

Abstract: Shear dynamic and elongational rheology of concentrated solutions of cellulose in N-methylmorpholine oxide monohydrate (lyocell) were investigated at different temperatures and for two Hencky strains. Shear thinning and strain thinning behavior is characteristic for dynamic viscosity and effective elongational viscosity of lyocell solutions. Body forces, enthalpy, and entropy of orientation are high at low temperature and high deformation rates, showing a strong orientation effect. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 1369–1377, 2000