Assessment of phenomenological models for viscosity of liquids based on nonequilibrium atomistic simulations of copper

The shear viscosity of liquid copper is studied using nonequilibrium molecular-dynamics simulations under planar shear flow conditions. We examined variation of viscosity as function of shear rate at a range of pressures (ca. 0 - 40 GPa). We analyzed these results using eight different phenomenological models and find that the observed non-Newtonian behavior is best described by the Powell-Eyring (PE) model: eta(gamma) = (eta(0)-eta(infinity))sinh(-1)(taugamma)(taugamma) + eta(infinity), where gamma is the shear rate. Here eta(0) (the zero-shear-rate viscosity) extracted from the PE fit is in excellent agreement with available experimental data. The relaxation time tau from the PE fit describes the shear response to an applied stress. This provides the framework for interpreting the shear flow phenomena in complex systems, such as liquid metal and amorphous metal alloys.     

The inflection point in the pressure dependence of viscosity under high pressure: a comprehensive study of the temperature and pressure dependence of the viscosity of propylene carbonate

The pressure dependence of the prototypical glass-former propylene carbonate has been investigated over a broad range of temperature and pressure that were inaccessible in previous investigations using dielectric spectroscopy. We find that the viscosity measurements validate the scaling relation, eta(T,V)=J(TV gamma), with a scaling parameter gamma close to that found from dielectric relaxation measurements. In the pressure dependence of the viscosity, we observe an inflection point in the log eta versus P response, similar to that found previously for other materials. However, this inflection has never been observed in dielectric relaxation measurements. Using the scaling property above, it is possible to determine the behavior of the dielectric relaxation time in this otherwise inaccessible experimental range and compare it with the viscosity measurements. We find that the behaviors of eta and tau are very similar, and a very good agreement between the function phi P calculated for these two quantities is found. Starting from the validity of the scaling properties, we show that the inflection point in the pressure dependence of the viscosity can be attributed to the convolution of the pressure dependences of the compressibility kappa T and the apparent activation energy at constant volume EV.     

Structural relaxation and rheological response of a driven amorphous system

The interplay between the structural relaxation and the rheological response of a simple amorphous system {a 80:20 binary Lennard-Jones mixture [W. Kob and H. C. Andersen, Phys. Rev. Lett. 73, 1376 (1994)]} is studied via molecular dynamics simulations. In the quiescent state, the model is well known for its sluggish dynamics and a two step relaxation of correlation functions at low temperatures. An ideal glass transition temperature of Tc=0.435 has been identified in the previous studies via the analysis of the system's dynamics in the framework of the mode coupling theory of the glass transition [W. Kob and H. C. Andersen, Phys. Rev. E 51, 4626 (1995)]. In the present work, we focus on the question whether a signature of this ideal glass transition can also be found in the case where the system's dynamics is driven by a shear motion. Indeed, the following distinction in the structural relaxation is found: In the supercooled state, the structural relaxation is dominated by the shear at relatively high shear rates gamma, whereas at sufficiently low gamma the (shear-independent) equilibrium relaxation is recovered. In contrast to this, the structural relaxation of a glass is always driven by shear. This distinct behavior of the correlation functions is also reflected in the rheological response. In the supercooled state, the shear viscosity eta decreases with increasing shear rate (shear thinning) at high shear rates, but then converges toward a constant as the gamma is decreased below a (temperature-dependent) threshold value. Below Tc, on the other hand, the shear viscosity grows as eta proportional, etax 1/gamma, suggesting a divergence at gamma=0. Thus, within the accessible observation time window, a transition toward a nonergodic state seems to occur in the driven glass as the driving force approaches zero. As to the flow curves (stress versus shear rate), a plateau forms at low shear rates in the glassy phase. A consequence of this stress plateau for Poiseuille-type flows is demonstrated.     

Rheological Behavior of Titanium Dioxide Suspensions

The rheological properties of titanium dioxide dispersed in water are measured over a wide range of powder concentrations, temperatures, and pH values. The value of intrinsic viscosity of titanium dioxide measured with an Ubbelohde capillary viscometer is 3.55, which is useful for determining the shape and aggregation property of the particles. The yield stress and steady shear viscosity of titanium dioxide with broad and narrow particle size distributions were measured over a wide range of solid volume fractions on a Brabender rheometer. It is observed that the rheological properties of the suspensions are quite different due to the difference in particle size distributions. Quemada, Casson, and Zhou's models were used to fit the experimental data and useful parameters were obtained. Calculated data are also in good agreement with the experimental data. As expected, the shear viscosity and yield stress decrease with increasing temperature. But when the temperature is around 50 degrees C, yield stress increases with increasing temperature while shear viscosity exhibits a complex behavior. The phenomena are very interesting and special. The Peclet number was used to analyze the shear thickening behavior. Models were also used to describe the shear viscosity under different temperatures and the master plots of the reduced variables eta/eta(infinity) vs t(c)gamma; at different temperatures are superimposed, which means the agreement is fair and the models are suitable to describe the rheological properties of titanium dioxide suspensions. pH effects were investigated on a Rheometrics RFS-II rheometer and it was found that pH can change the surface charge of the particles, which also affects the rheological behavior. The pH at which maximum shear viscosity and yield stress occur is in concordance with the isoelectric point. Copyright 2001 Academic Press.     

Adsorption behavior of oxyethylated surfactants at the air/water interface

The low-shear viscosity eta(0) of colloidal suspensions of acrylic latex or silica in aqueous gelatin has been measured at a temperature above the sol-gel transition. Measurements were made on dilution of a concentrated suspension with water or a gelatin solution. Thus, either the gelatin : colloid ratio was maintained or it was varied at constant aqueous gelatin concentration. Systems were studied with four lime-processed gelatins of different molecular weights at two concentrations of added salt. In addition, the latex particle size and the thickness of the adsorbed gelatin layer were measured by photon correlation spectroscopy (PCS) under dilute conditions. The dependence of the low-shear viscosity eta(0) on particle concentration was exponential and did not follow the well-established Krieger-Dougherty model for simple hard-sphere suspensions over the concentration range studied. A simple phenomenological model, eta(0)=eta(o)10(phi(e)/phi(s)), was found to predict the behavior well. Here, eta(o) is the viscosity of a gelatin solution of the corresponding solution concentration, phi(e) is proportional to the volume fraction of the particles, and phi(s) is a scaling factor, which was determined to have a value of 0.85. With this value of phi(s), the dimensions determined from PCS could be used to predict the viscosity values.     

Rheology of viscoelastic mixed surfactant solutions: effect of scission on nonlinear flow and rheochaos

The linear and nonlinear rheology of viscoelastic mixed anionic-zwitterionic surfactant solutions has been systematically investigated. In the linear viscoelastic regime, these systems display nearly Maxwellian behavior with a unique relaxation time, tau0, and a characteristic elastic plateau modulus, G0. Linear rheological data were used to calculate the repitation and breaking times of the micelles, tau(rep) and tau(b), respectively. Surprisingly, the elastic modulus G0 significantly increases with salt concentration c(s), whereas tau(b) decreases by 1 order of magnitude. The strong effect of c(s) on the material parameters and microstructure of rodlike micelles allowed for the systematic investigation of the effect of these parameters on nonlinear flow. For samples with relatively long tau(b), the quasi-static flow diagram (stress vs shear rate) shows a stress peak followed by a metastable branch (a region of decreasing shear stress), whereas for samples with relatively short tau(b), this phenomenon is not observed. Transient flow responses corroborate quasi-static flow findings and further reveal the significance of microscopic dynamic parameters on flow behavior. Shear stress time series were recorded at constant shear rates, and above a critical shear rate, gamma(c2), stress fluctuations are observed. The amplitude of these stress fluctuations, Delta sigma, was found to scale as Delta sigma approximately equal to G0(tau(b)| gamma - gamma(c2)|)beta with beta approximately 0.5. This scaling is observed for micellar systems with tau(b) ranging from 0.12 to 0.01 s and G0 ranging from 1 x 10(3) to 7 x 10(3) dyn/cm2.     

Crystal growth kinetics exhibit a fragility-dependent decoupling from viscosity

In this paper we establish the temperature dependence of the kinetic coefficient associated with crystal growth into the supercooled liquid for a wide range of organic and inorganic materials. We show that the kinetic coefficient for crystal growth scales with the shear viscosity eta as eta(-xi) and that the exponent depends systematically on the fragility of the liquid. The greater the fragility (i.e., deviation away from an Arrhenius temperature dependence for eta), the larger the difference 1-xi. We argue that this breakdown in scaling between the crystal growth kinetics and the viscosity is a manifestation of heterogeneous dynamics in supercooled liquids. In addition, we show that the absolute growth rate at intermediate viscosities is correlated with the entropy difference between the liquid and the crystal.     

Critical behavior of 2,6-dimethylpyridine-water: measurements of specific heat, dynamic light scattering, and shear viscosity

The specific heat C(p) at constant pressure, the shear viscosity eta(s), and the mutual diffusion coefficient D of the 2,6-dimethylpyridine-water mixture of critical composition have been measured in the homogeneous phase at various temperatures near the lower critical demixing temperature T(c). The amplitude of the fluctuation correlation length xi(0)=(0.198+/-0.004) nm has been derived from a combined evaluation of the eta(s) and D data. This value is in reasonable agreement with the one obtained from the amplitude A(+)=(0.26+/-0.01) J(g K) of the critical term in the specific heat, using the two-scale-factor universality relation. Within the limits of error the relaxation rate Gamma of order parameter fluctuations follows power law with the theoretical universal exponent and with the amplitude Gamma=(25+/-1)x10(9) s(-1). No indications of interferences of the critical fluctuations with other elementary chemical reactions have been found. A noteworthy result is the agreement of the background viscosity eta(b), resulting from the treatment of eta(s) and D data, with the viscosity eta(s)(nu=0) extrapolated from high-frequency viscosity data. The latter have been measured in the frequency range of 5-130 MHz using a novel shear impedance spectrometer.     

Is hairpin formation in single-stranded polynucleotide diffusion-controlled?

An intriguing puzzle in biopolymer science is the observation that single-stranded DNA and RNA oligomers form hairpin structures on time scales of tens of microseconds, considerably slower than the estimated time for loop formation for a semiflexible polymer of similar length. To address the origin of the slow kinetics and to determine whether hairpin dynamics are diffusion-controlled, the effect of solvent viscosity (eta) on hairpin kinetics was investigated using laser temperature-jump techniques. The viscosity was varied by addition of glycerol, which significantly destabilizes hairpins. A previous study on the viscosity dependence of hairpin dynamics, in which all the changes in the measured rates were attributed to a change in solvent viscosity, reported an apparent scaling of relaxation times (tau(r)) on eta as tau(r) approximately eta(0.8). In this study, we demonstrate that if the effect of viscosity on the measured rates is not deconvoluted from the inevitable effect of change in stability, then separation of tau(r) into opening (tau(o)) and closing (tau(c)) times yields erroneous behavior, with different values (and opposite signs) of the apparent scaling exponents, tau(o) approximately eta(-0.4) and tau(c) approximately eta(1.5). Under isostability conditions, obtained by varying the temperature to compensate for the destabilizing effect of glycerol, both tau(o) and tau(c) scale as approximately eta(1.1+/-0.1). Thus, hairpin dynamics are strongly coupled to solvent viscosity, indicating that diffusion of the polynucleotide chain through the solvent is involved in the rate-determining step.     

Shear viscosity of molten alkali halides from equilibrium and nonequilibrium molecular-dynamics simulations

The shear viscosity of molten NaCl and KCl was calculated through equilibrium (EMD) and nonequilibrium molecular-dynamics (NEMD) simulations in the canonical (N,V,T) ensemble. Two rigid-ion potentials were investigated, namely, the Born-Mayer-Huggins-Tosi-Fumi potential and the Michielsen-Woerlee-Graaf-Ketelaar potential with the parameters proposed by Ladd. The NEMD simulations were performed using the SLLOD equations of motion [D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984)] with a Gaussian isokinetic thermostat and the results are compared with those obtained from Green-Kubo EMD (N,V,T) simulations and experimental shear viscosity data. The NEMD zero strain rate shear viscosity, eta(0), was obtained by fitting a simplified Carreau-type equation and by application of mode-coupling theory, i.e., a eta-gamma(1/2) linear relationship. The values obtained from the first method are found to be significantly lower than those predicted by the second. The agreement between the EMD and NEMD results with experimental data is satisfactory for the two potentials investigated. The ion-ion radial distribution functions obtained with the two rigid-ion potentials for both molten salts are discussed in terms of the differences between the two models.     

Shear small-angle light scattering studies of shear-induced concentration fluctuations and steady state viscoelastic properties

We aimed at elucidating the influence of shear-induced structures (shear-enhanced concentration fluctuations and/or shear-induced phase separation), as observed by rheo-optical methods with small-angle light scattering under shear flow (shear-SALS) and shear-microscopy, on viscoelastic properties in semidilute polystyrene (PS) solutions of 6.0 wt % concentration using dioctyl phthalate (DOP) as a Theta solvent and tricresyl phosphate (TCP) as a good solvent. In order to quantify the effects of the shear-induced structures, we conducted a numerical analysis of rheological properties in a homogeneous solution based on the constitutive equation developed by Kaye-Bernstein, Kearsley, and Zapas (K-BKZ). In the low-to-intermediate shear rate gamma region between tau(w) (-1) and tau(e) (-1), where tau(w) and tau(e) are, respectively, terminal relaxation time and the relaxation time for chain stretching, the steady state rheological properties, such as shear stress sigma and the first normal stress difference N(1), for the PS/DOP and PS/TCP solutions are found to be almost same and also well predicted by the K-BKZ equation, in spite of the fact that there is a significant difference in the shear-induced structures as observed by shear-SALS and shear-microscopy. This implies that the contribution of the concentration fluctuations built up by shear flow to the rheological properties seems very small in this gamma region. On the other hand, once gamma exceeds tau(e) (-1), sigma and N(1) for both PS/DOP and PS/TCP start to deviate from the predicted values. Moreover, when gamma further increases and becomes higher than gamma(a,DOP) (sufficiently higher than tau(e) (-1)), above which rheological and scattering anomalies are observed for PS/DOP, sigma and N(1) for PS/DOP and PS/TCP are significantly larger than those predicted by K-BKZ. Particularly, a steep increase of sigma and N(1) for PS/DOP above gamma(a,DOP) is attributed to an excess free energy stored in the system via the deformation of interface of well-defined domains, which are aligned into the stringlike structure developed parallel to the flow axis, and stretching of the chains connecting the domains in the stringlike structures. Thus, we advocate that the effect of shear-induced structures should be well considered on the behavior of sigma and N(1) at the high gamma region above tau(e) (-1) in semidilute polymer solutions.     

Structural, topographical, and shear characteristics of milk protein and monoglyceride monolayers spread at the air-water interface

In this contribution we are concerned with the study of structure, topography, and surface rheological characteristics under shear conditions of monoglyceride (monopalmitin and monoolein) and milk protein (beta-casein, kappa-casein, caseinate, and WPI) spread monolayers at the air-water interface. Combined surface chemistry (surface film balance and surface shear rheometry) and microscopy (Brewster angle microscopy: BAM) techniques have been applied in this study to pure emulsifiers (proteins and monoglycerides) spread at the air-water interface. To study the shear characteristics of spread films, a homemade canal viscometer was used. The experiments have demonstrated the sensitivity of the surface shear viscosity (eta(s)) of protein and monoglyceride films at the air-water interface, as a function of surface pressure (or surface density). The surface shear viscosity was higher for proteins than for monoglycerides. In addition, eta(s) was higher for the globular WPI than for disordered beta-casein and caseinate due to the strong forces acting on spread globular proteins. This technique makes it possible to distinguish between beta-casein and caseinate spread films, with the higher eta(s) values for the later due to the presence of kappa-casein. The eta(s) value varies greatly with the surface pressure (or surface density). In general, the greater the surface pressure, the greater the values of eta(s). Finally, the eta(s) value is also sensitive to the monolayer structure, as was observed for monoglycerides with a rich structural polymorphism (i.e., monopalmitin).     

Abnormal viscosity increment observed for an ionic liquid by dissolving lithium chloride

The effect of adding an inorganic salt, lithium chloride, and water on the viscosity of an ionic liquid, 1-n-butyl-3-methylimidazolium chloride (BmimCl), was investigated by shear stress measurements with a rheometer. The shear rate dependence of the viscosity showed shear thinning behavior, which implies that some structure should exist in the liquid and the structure should change at high shear rates. Addition of LiCl enhances the viscosity of BmimCl. The logarithmic value of zero-shear viscosity, eta(0), of BmimCl increases linearly and largely with increasing added salt content. The increasing rate of the viscosity by addition of LiCl was about 10 times larger than that for an aqueous solution of LiCl. When water is added into BmimCl, viscosity decreased. The increasing rate of the viscosity by addition of LiCl for BmimCl with about 5 wt % of water was almost the same as that for BmimCl without addition of water.     

High solids content latexes with low viscosity

The effect of particle size distribution (PSD) on the solids content and viscosity of the multi-sized latex was investigated by blending mono-sized latexes and measuring their rheological properties. The results showed that the maximum packing (highest solids content) was observed at a weight fraction 80% of large particles with respect to total solids content for both bi-modal and tri-modal latexes, and the lowest viscosity was obtained when the ratio of large to medium to small particles was approximately 80/10/10 (by weight). A two-stage technique to prepare high solids multi-sized polymer latex was developed by using a polymer latex previously made as seed and by adding small amount of additional surfactants and/or second group of polymer particles. The PSD of the latex was optimized by varying the amount of the seed, the additional surfactants, and the second group of particles. Film forming latexes with high solids (>65%) and low viscosity were obtained. Received: 18 February 2000 Accepted: 30 September 2000     

Solid colloidal particles inducing coalescence in bitumen-in-water emulsions

Silica particles are dispersed in the continuous phase of bitumen-in-water emulsions. The mixture remains dispersed in quiescent storage conditions. However, rapid destabilization occurs once a shear is applied. Observations under the microscope reveal that the bitumen droplets form a colloidal gel and coalesce upon application of a shear. We follow the kinetic evolution of the emulsions viscosity, eta, at constant shear rate: eta remains initially constant and exhibits a dramatic increase after a finite time, tau. We study the influence of various parameters on the evolution of tau: bitumen droplet size and volume fraction, silica diameter and concentration, shear rate, etc.     

Generalized rheological characteristic of plastic disperse systems with polymeric and low-molecular dispersion media (matrices)

Analysis of literature data on the flow of polymeric and oligomeric compositions as well as on systems of low viscous dispersion media containing a high-disperse filler (carbon black, silica, high-disperse chalk) has been carried out. As the basic idea, a proposal is made that their viscosity anomaly is due not to the matrix viscosity anomaly, but to the gradual breakdown of the filler structural skeleton with increasing shear stress and shear rate . The viscosity anomaly of those compositions is determined by the zeroshear but not by the apparent matrix viscosity. A general relationship has been found to describe the flow of such systems depending on the zero-shear matrix viscosity values, ₀, their yield stress, _y , and filler volume concentration , whereK=4.9 andn=0.69 are constants.     

Rheological characterization of two viscosity grades of methylcellulose: an approach to the modeling of the thixotropic behaviour

The rheological behavior of two viscosity grades of methylcellulose (MC) (M-0262 and M-0512) was determined based on the dispersions of different polymer concentrations (from 0.1 to 5% w/w). In order to analyze the possible thixotropic character of the dispersions, the up and down curves of rheograms for several agitation times were plotted. In all cases, the Ostwald-De Waele rheological model (or Power Law model) was used. For both grades of MC, preparations of concentrations in the range of 0.1–1.0% (w/w) exhibited Newtonian behavior, while at polymer concentrations from 2–5% (w/w), pseudoplastic behavior was observed. The lower viscosity grade MC (M-0262) showed no thixotropy, while the higher viscosity grade MC (M-0512) exhibited thixotropic behavior from 2–5% (w/w). To analyze and define thixotropic behavior, we propose an equation model obtained from the values of consistence, m, determined for each of the curves in a flow diagram The results obtained from the proposed equation model showed good correlation to those obtained with the thixotropic areas method, and thus could be used as an alternative model for analyzing thixotropy.     

Alternative view of self-diffusion and shear viscosity

By performing an elementary transformation, the conventional velocity autocorrelation function expression for the temperature and density dependent self-diffusion constant D(T,rho) has been reformulated to emphasize how initial particle momentum biases final mean displacement. Using collective flow variables, an analogous expression has been derived for 1/eta(T,rho), the inverse of shear viscosity. The Stokes-Einstein relation for liquids declares that D and T/eta should have a fixed ratio as T and rho vary, but experiment reveals substantial violations for deeply supercooled liquids. Upon analyzing the self-diffusion and viscous flow processes in terms of configuration space inherent structures and kinetic transitions between their basins, one possible mechanism for this violation emerges. This stems from the fact that interbasin transitions become increasingly Markovian as T declines, and though self-diffusion is possible in a purely Markovian regime, shear viscosity in the present formulation intrinsically relies on successive correlated transitions.     

Sound attenuation, shear viscosity, and mutual diffusivity behavior in the nitroethane-cyclohexane critical mixture

The shear viscosity eta(s), mutual diffusion coefficient D, and ultrasonic attenuation spectra of the nitroethane-cyclohexane mixture of critical composition have been measured at various temperatures near the critical temperature T(c). The relaxation rate of order parameter fluctuations resulting from a combined evaluation of the eta(s) and D data follows power law behavior with the theoretical exponent and with the large amplitude Gamma(o)=(156+/-2)x10(9) s(-1). The ultrasonic spectra have been evaluated in terms of a critical contribution and a noncritical background contribution. The amplitude of the former exhibits a temperature dependence, in conformity with a temperature dependence in the adiabatic coupling constant (|g| = 0.064 near T(c) and 0.1 at T-T(c)=3 K). If the variation of the critical amplitude with T is taken into account the experimental attenuation coefficient data display a scaling function which nicely fits to the theoretical prediction from the Bhattacharjee-Ferrell dynamic scaling model [R. A. Ferrell and J. K. Bhattacharjee, Phys. Rev. A 31, 1788 (1985)].