Multiparticle collision dynamics modeling of viscoelastic fluids

In order to investigate the rheological properties of viscoelastic fluids by mesoscopic hydrodynamics methods, we develop a multiparticle collision (MPC) dynamics model for a fluid of harmonic dumbbells. The algorithm consists of alternating streaming and collision steps. The advantage of the harmonic interactions is that the integration of the equations of motion in the streaming step can be performed analytically. Therefore, the algorithm is computationally as efficient as the original MPC algorithm for Newtonian fluids. The collision step is the same as in the original MPC method. All particles are confined between two solid walls moving oppositely, so that both steady and oscillatory shear flows can be investigated. Attractive wall potentials are applied to obtain a nearly uniform density everywhere in the simulation box. We find that both in steady and oscillatory shear flows, a boundary layer develops near the wall, with a higher velocity gradient than in the bulk. The thickness of this layer is proportional to the average dumbbell size. We determine the zero-shear viscosities as a function of the spring constant of the dumbbells and the mean free path. For very high shear rates, a very weak "shear thickening" behavior is observed. Moreover, storage and loss moduli are calculated in oscillatory shear, which show that the viscoelastic properties at low and moderate frequencies are consistent with a Maxwell fluid behavior. We compare our results with a kinetic theory of dumbbells in solution, and generally find good agreement.     

Magnetic field effects on natural convection flow of a non-Newtonian fluid in an L-shaped enclosure

The effect of magnetic field on natural convection heat transfer in an L-shaped enclosure filled with a non-Newtonian fluid is investigated numerically. The governing equations are solved by finite-volume method using the SIMPLE algorithm. The power-law rheological model is used to characterize the non-Newtonian fluid behavior. It is revealed that heat transfer rate decreases for shear-thinning fluids (of power-law index, n?<?1) and increases for shear-thickening fluids (n?>?1) in comparison with the Newtonian ones. Thermal behavior of shear-thinning and shear-thickening fluids is similar to that of Newtonian fluids for the angle of enclosure α?<?60° and α?>?60°, respectively.     

Preparation and rheological characterization of poly(n-butyl methacrylate)/montmorillonite composites

Intercalated nanocomposites constituted of poly(butyl methacrylate) (PBMA) as the matrix and an organically modified montmorillonite as the nanosize filler were prepared and rheologically characterized in detail. The rheological behavior of the composites showed dependence on both temperature and clay content. For composites of low clay contents, the steady shear viscosity showed a Newtonian plateau in the low shear rate region at low temperatures and the plateau was replaced by a shear-thinning curve when the temperature was raised. For composites of higher clay contents, strong shear-thinning behavior were observed at all shear rates and all temperatures. The viscoelastic data of the composites showed unusual terminal behavior of a decreasing terminal slope at low frequencies with increasing temperature and clay loading. X-ray diffraction spectra showed that annealing process at higher temperatures shifted the Bragg reflection peaks to a lower angle and broadened the peaks, which provided the evidence for the existence of a temperature-induced solid-like structure that was responsible for the shear thinning and the unusual terminal viscoelastic behavior.     

Transient molecular dynamics simulations of viscosity for simple fluids

A transient molecular dynamics (TMD) method has been developed for simulation of fluid viscosity. In this method a sinusoidal velocity profile is instantaneously overlaid onto equilibrated molecular velocities, and the subsequent decay of that velocity profile is observed. The viscosity is obtained by matching in a least-squares sense the analytical solution of the corresponding momentum transport boundary-value problem to the simulated decay of the initial velocity profile. The method was benchmarked by comparing results obtained from the TMD method for a Lennard-Jones fluid with those previously obtained using equilibrium molecular dynamics (EMD) simulations. Two different constitutive models were used in the macroscopic equations to relate the shear rate to the stress. Results using a Newtonian fluid model agree with EMD results at moderate densities but exhibit an increasingly positive error with increasing density at high densities. With the initial velocity profiles used in this study, simulated transient velocities displayed clear viscoelastic behavior at dimensionless densities above 0.7. However, the use of a linear viscoelastic model reproduces the simulated transient velocity behavior well and removes the high-density bias observed in the results obtained under the assumption of Newtonian behavior. The viscosity values obtained using the viscoelastic model are in excellent agreement with the EMD results over virtually the entire fluid domain. For simplicity, the Newtonian fluid model can be used at lower densities and the viscoelastic model at higher densities; the two models give equivalent results at intermediate densities.     

Rheology and high-temperature stability of novel viscoelastic gemini micelle solutions

To broaden the application of clean fracturing fluid based on surfactant, a gemini cationic C₂₅-tailed surfactant, called FL-25, was synthesized. FL-25 can form a wormlike viscoelastic fluid in aqueous solution without adding any organic or inorganic salts. The rheological properties and thermal stability of the novel gemini micelle solutions were further investigated. The results show that the gemini micelle solution possesses viscoelasticity, thixotropy, and shear-thinning properties. The apparent viscosity of the viscoelastic gemini micelle solution at a shear rate of 170?s^?1 remains approximately 69?mPa?·?s at 110°C for 90 minutes, showing good high-temperature-resistance property. FL-25 may be a novel gemini surfactant applied in clean viscoelastic surfactant fracturing fluids in the oil and gas field.     

Wall Effects on Spheres Settling Through Non-Newtonian Fluid Media in Cylindrical Tubes

Experimental study is performed to understand and quantify the wall and eccentric retardation effects on spheres settling in shear thinning and shear-thinning viscoelastic fluids over a wide range of diameter ratios (0.02 < λ < 0.9). The four-parameter Carreau viscosity equation has been chosen to represent the apparent viscosity-shear rate of polyacrylamide solutions. Two new wall factor corrections are presented with excellent agreement compared to experimental data.

The terminal settling velocity of a sphere in bounded fluid is significantly reduced by the presence of confining boundaries, named wall retardation effect that decreases due to the shear-thinning behavior of power law fluids, which is weaken further by the elastic effect of viscoelastic fluids. The wall factors of spheres settling in viscoelastic fluids increase at low ξ up to 50, followed by a horizontal confidence region (0.7 ≤ f ≤ 1) at high ξ. In this region, the wall factor is mainly dominated by fluids’ elasticity, which is more distinguished for small spheres. As the settling spheres approach to the wall (b/R → 1), the neighboring wall exert more intensive retardation that reduce the terminal settling velocity greatly when b/R > 0.6 in pure shear-thinning fluids, and the extra retardation effect of nearby wall increases at high concentration due to the enhanced non-Newtonian property. In contrast, the eccentric effect on settling velocity in viscoelastic fluids is cut down greatly by the fluid's elasticity, which is negligible.     

Insulator-based dielectrophoretic focusing and trapping of particles in non-Newtonian fluids

Insulator-based dielectrophoretic (iDEP) microdevices have been limited to work with Newtonian fluids. We report an experimental study of the fluid rheological effects on iDEP focusing and trapping of polystyrene particles in polyethylene oxide, xanthan gum, and polyacrylamide solutions through a constricted microchannel. Particle focusing and trapping in the mildly viscoelastic polyethylene oxide solution are slightly weaker than in the Newtonian buffer. They are, however, significantly improved in the strongly viscoelastic and shear thinning polyacrylamide solution. These observed particle focusing behaviors exhibit a similar trend with respect to electric field, consistent with a revised theoretical analysis for iDEP focusing in non-Newtonian fluids. No apparent focusing of particles is achieved in the xanthan gum solution, though the iDEP trapping can take place under a much larger electric field than the other fluids. This is attributed to the strong shear thinning-induced influences on both the electroosmotic flow and electrokinetic/dielectrophoretic motions.     

Fluid rheological effects on streaming dielectrophoresis in a post-array microchannel

Recent studies have demonstrated the strong influences of fluid rheological properties on insulator-based dielectrophoresis (iDEP) in single-constriction microchannels. However, it is yet to be understood how iDEP in non-Newtonian fluids depends on the geometry of insulating structures. We report in this work an experimental study of fluid rheological effects on streaming DEP in a post-array microchannel that presents multiple contractions and expansions. The iDEP focusing and trapping of particles in a viscoelastic polyethylene oxide solution are comparable to those in a Newtonian buffer, which is consistent with the observations in a single-constriction microchannel. Similarly, the insignificant iDEP effects in a shear-thinning xanthan gum solution also agree with those in the single-constriction channel except that gel-like structures are observed to only form in the post-array microchannel under large DC electric fields. In contrast, the iDEP effects in both viscoelastic and shear-thinning polyacrylamide solution are significantly weaker than in the single-constriction channel. Moreover, instabilities occur in the electroosmotic flow and appear to be only dependent on the DC electric field. These phenomena may be associated with the dynamics of polymers as they are electrokinetically advected around and through the posts.     

Electroosmotic flow of non‐Newtonian fluids in a constriction microchannel

Insulator‐based dielectrophoresis has to date been almost entirely restricted to Newtonian fluids despite the fact that many of the chemical and biological fluids exhibit non‐Newtonian characteristics. We present herein an experimental study of the fluid rheological effects on the electroosmotic flow of four types of polymer solutions, i.e., 2000 ppm xanthan gum (XG), 5% polyvinylpyrrolidone (PVP), 3000 ppm polyethylene oxide (PEO), and 200 ppm polyacrylamide (PAA) solutions, through a constriction microchannel under DC electric fields of up to 400 V/cm. We find using particle streakline imaging that the fluid elasticity does not change significantly the electroosmotic flow pattern of weakly shear‐thinning PVP and PEO solutions from that of a Newtonian solution. In contrast, the fluid shear‐thinning causes multiple pairs of flow circulations in the weakly elastic XG solution, leading to a central jet with a significantly enhanced speed from before to after the channel constriction. These flow vortices are, however, suppressed in the strongly viscoelastic and shear‐thinning PAA solution.     

Shear viscosity of liquid copper at experimentally accessible shear rates: application of the transient-time correlation function formalism

We report on nonequilibrium molecular dynamics (NEMD) simulations results on the shear viscosity of liquid copper, modeled by a many-body embedded-atoms model potential. Because conventional NEMD methods are restricted to very high shear rates (at least of the order of 10(10) s(-1), that is several orders of magnitude larger than those accessible by experiment), previous work only provided access to the response of the fluid in the shear-thinning regime. Using the transient-time correlation function formalism, we show how NEMD simulations can be extended to study the rheological properties of liquid copper subjected to low, experimentally accessible, shear rates. Our results provide a full picture of the rheology of the system, in the Newtonian regime as well as in the shear-thinning regime.     

Viscoelastic Drag of Particles Settling in Wormlike Micellar Solutions of Varying Surfactant Concentration

Wormlike micellar octadecyl trimethyl ammonium chloride (OTAC) solution is a self-assembled fracturing fluid used to carry proppants into fractures in oil recovery. Slow settling velocity of proppant is desirably resulted from the viscoelastic drag with low viscosity of fracturing fluids for fracturing work. Steel spheres, as a substitute for proppants, fall into three semi-dilute OTAC solutions. The steady rheology demonstrates that OTAC solutions are divided into shear-thickening and shear-thinning regimes by the critical shear rate. The applied steel spheres always lie in the shear-thickening regime of the 2.8 wt% OTAC solution with aggregated micelles as their characteristic shear rates are less than the critical shear rate of the solution. Strong shear-thickening viscous drag results in lower settling velocity of steel spheres. Most of the applied steel spheres, on the other hand, lie in the shear-thinning regime of the 4 wt% OTAC solution with orientated micelles. Although the latter solution has small dissipation coefficient, high Weissenberg number, and consequently high elastic effect, the shear-thinning viscosity results in higher settling velocity of steel spheres.     

Elastic instabilities in the electroosmotic flow of non-Newtonian fluids through T-shaped microchannels

Electroosmotic flow (EOF) has been widely used to transport fluids and samples in micro- and nanofluidic channels for lab-on-a-chip applications. This essentially surface-driven plug-like flow is, however, sensitive to both the fluid and wall properties, of which any inhomogeneity may draw disturbances to the flow and even instabilities. Existing studies on EOF instabilities have been focused primarily upon Newtonian fluids though many of the chemical and biological solutions are actually non-Newtonian. We carry out a systematic experimental investigation of the fluid rheological effects on the elastic instability in the EOF of phosphate buffer-based polymer solutions through T-shaped microchannels. We find that electro-elastic instabilities can be induced in shear thinning polyacrylamide (PAA) and xanthan gum (XG) solutions if the applied direct current voltage is above a threshold value. However, no instabilities are observed in Newtonian or weakly shear thinning viscoelastic fluids including polyethylene oxide (PEO), polyvinylpyrrolidone (PVP), and hyaluronic acid (HA) solutions. We also perform a quantitative analysis of the wave parameters for the observed elasto-elastic instabilities.     

Batch electrophoretic cells with Eyring fluids: analysis of the hydrodynamics

Mixing and dispersion phenomena caused by the carrier fluid in an electrophoretic cell is the main subject of this study. In particular, the effects of Joule heating on temperature and velocity profiles for Eyring-model fluids (EMF) are studied. The heat transfer is sequentially coupled with momentum transfer to derive an analytical expression for both the temperature and the velocity profiles. These results are then used to show the hydrodynamic behavior of the fluid in a batch electrophoretic cell. Furthermore, the results obtained are useful to compare with the fluid behavior of other carriers of different rheology, such as Newtonian fluids, power-law fluids, and viscoelastic fluids that obey the CEF model. The results show that EMF are potentially good carriers for relatively high Joule heat generation and therefore good candidates to control mixing inside the electrophoretic cell.     

Shear-dependent viscosity in simple fluids

Computer simulation results are used to examine the shear-dependent viscosity of simple fluids. The prime purpose of the investigation was to examine the possible non-newtonian effects when the particles in a fluid interact through central forces. A range of spherical interactions was examined, including both potentials with a barrier and simple colloidal models, and in all cases the fluids were shear-thinning. The non-equilibrium radial distribution function for a soft potential is considerably more sensitive to shear rate than is that for the strongly repulsive model. Calculations of the hydrostatic pressure show that it increases with shear rate, demonstrating that the phenomena of shear thickening and shear dilatency — used interchangeably in the literature — are separate phenomena.     

The links-nodes-blobs model for shear-thinning-yield-stress fluids

A new model based on fractal and percolation concepts is proposed to explain the rheological behavior of shear-thinning yield-stress fluids. Suspension particles of the fluids are described in terms of the links-nodes-blobs (L-N-B) model. The complex suspension rheology can be interpreted via the similarity of the L-N-B model to the Rouse chain model. Consequently, the empirically universal relationship between the dimensionless shear stress, T, and the dimensionless shear rate, Γ, which was recently suggested by Coussot as T = 1+KΓ ⁿ at Γ<0.3 and approaches Newtonian behavior at Γ>50, can be derived in terms of microscopic properties of a suspension of the force-free particles, fractal dimensions of the percolation system, and the critical lengths of the percolation system. According to our study, a more precise and more general universal relationship, which fits experimental data well over a wide range from Γ = 10⁻⁷10³, is proposed as T = 1+Γ+KΓ ⁿ . The parameter K in the universal equation can be expressed as a function of the dimensionless cross-section of the blobs, the distribution of links, and fractal dimensions of the percolation system, while the exponent n in the universal equation is a function of the fractal dimensions only. The transition point of a shear-thinning yield-stress fluid from shear-thinning to Newtonian behavior was explicitly interpreted. Received: 22 March 1999 Accepted in revised form: 1 June 1999     

Flow‐induced particle orientation and rheological properties of suspensions of organoclays in thermoplastic resins

The influence of nano‐scale particles on the viscoelastic properties of polymer suspensions is investigated. We have developed a simulation technique for the particle orientation and polymer conformation tensors to study various features of the suspensions. The nano‐particles are modeled as thin rigid oblate spheroid particles and the polymers as FENE‐P type viscoelastic and Newtonian fluid. Both interparticle and polymer‐particle interactions have been taken into account in our numerical computations. The nonlinear viscoelastic properties of nanocomposites of layered silicate particles in non‐Newtonian fluids are examined at the start‐up of shear flow and are interpreted using the model to examine the effects of model parameters as well as flow conditions on particle orientation, viscosity, and first normal stress difference of the suspensions. We have studied the microstructure of polymer‐clay nanocomposites using X‐ray diffraction (XRD) scattering and transmission electron microscopy (TEM). The rheology of these nanocomposites in step‐shear is shown to be fairly well predicted by the model. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 2003–2011, 2010     

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.     

Helmholtz-Smoluchowski velocity for viscoelastic electroosmotic flows

Many biofluids such as blood and DNA solutions are viscoelastic and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. However, the governing equations for viscoelastic flows are not easily solvable, especially for electroosmotic flows where the streamwise velocity varies rapidly from zero at the wall to a nearly uniform velocity at the outside of the very thin electric double layer. In the present investigation, we have devised a simple method to find the volumetric flow rate of viscoelastic electroosmotic flows through microchannels. It is based on the concept of the Helmholtz-Smoluchowski velocity which is widely adopted in the electroosmotic flows of Newtonian fluids. It is shown that the Helmholtz-Smoluchowski velocity for viscoelastic fluids can be found by solving a simple cubic algebraic equation. The volumetric flow rate obtained using this Helmholtz-Smoluchowski velocity is found to be almost the same as that obtained by solving the governing partial differential equations for various viscoelastic fluids.