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.     

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.     

Mathematical modeling and simulation of peristaltic activity in Ree-Eyring fluid flow through non-uniform complaint channel: Different varying conditions

The current study incorporates variable viscosity and thermal conductivity on modeling Ree-Eyring fluid flow inside a peristaltic non-uniform complaint channel. The small Reynolds number and long-wavelength approximations are employed for resolve the governing nonlinear differential equations. Temperature expression is obtained with the help of series solution method. The graphs are drawn on relevant parameters to investigate its effect on velocity, temperature, concentration, and streamlines through MATLAB 2020b. The results confer more velocity in the Newtonian fluid in comparison with non-Newtonian fluid. Also, the model discloses that the size of the bolus can be varied by varying the viscosity parameter. This result helps in understanding the thrombus formation in blood vessels.     

Electroosmosis-modulated bio-flow of nanofluid through a rectangular peristaltic pump induced by complex traveling wave with zeta potential and heat source

Electrokineticmicroperistaltic pumps are important biomechanical devices that help in targeted drugging of sick body parts. This article is focused on mathematical modeling and analysis of some important aspect of such flows in a rectangular duct with wall properties. Effects of zeta potential, heat source, and deby length are also studied. Carbon nanotubes (CNTs) in the Newtonian base fluid are assumed as drugging material. A comparison of single-walled CNTs and multiwalled CNTs is also presented. It is considered that the walls are flexible and encapsulating the region with limited permeability. The defined flow problem is modeled and analyzed analytically for the transport of CNT–water nanofluid. It is accepted that the flow is steady, nonturbulent, and propagating waves do have a considerably longer wavelength when compared to amplitude. The conditions and assumptions lead to a model of coupled partial differential equations of order two. The exact results using the eigenfunction expansion method are procured and shown accordingly. The predictions about the behavior of important parameters are displayed for single-walled CNT and multiwalled CNT—water nanofluidic behavior—using figures. The impact of sundry parametersis are analyzed. The application of the current study involved a transporting/targeted drug delivery system using peristaltic micropumps and magnetic fields in pharmacological engineering.     

On the Stagnation Point Flow of a Special Class of Non-Newtonian Fluids

Abstract

The two-dimensional boundary layer equations for a class of non-Newtonian fluids, for which the apparent viscosity can be expressed as a polynomial in the second scalar invariant of the rate of strain tensor, have been derived. These equations have been employed to analyse the flow near a stagnation point over a stationary impermeable wall. The non-Newtonian effects on the boundary layer velocity profile and the wall skin friction have been studied, and compared with the corresponding Newtonian fluid. The fluid velocity in the boundary layer has been shown to be retarded by the non-Newtonian effect while the skin friction increases proportionate to it.     

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.     

Experimental study on the rheological behavior of nanolubricant-containing MCM-41 nanoparticles with viscosity measurement

In this study, the rheological behavior and viscosity of a stable nanofluid, which is prepared with the suspension of MCM-41 nanoparticles in SAE40 engine oil as base fluid, would be presented. Two-step method has been used to stabilize the nanoparticles in engine oil. To obtain structural and morphological properties of the synthesized nanoparticles, small-angle X-ray scattering, N₂ adsorption/desorption analysis and scanning electron microscopy have been done. Then, viscosity of nanofluids has been measured in temperature range of 25–55 °C, shear rates up to 13,000 s^?1 and different concentrations (0 mass%, 0.5 mass%, 1 mass%, 3 mass% and 5 mass% of MCM-41 nanoparticles). For all the samples, the shear stress versus shear rate diagrams showed that SAE40 oil has Newtonian behavior, in which adding mesoporous silica nanoparticles causes non-Newtonian or pseudoplastic behavior. The results declared that viscosity decreases with increasing temperature and increases with an enhancement in concentration. Furthermore, based on experimental results, an accurate correlation has been proposed to predict the viscosity of SAE40/MCM-41 nanolubricants.

     

Experimental and modeling study of Newtonian and non-Newtonian fluid flow in pore network micromodels

The in situ rheology of polymeric solutions has been studied experimentally in etched silicon micromodels which are idealizations of porous media. The rectangular channels in these etched networks have dimensions typical of pore sizes in sandstone rocks. Pressure drop/flow rate relations have been measured for water and non-Newtonian hydrolyzed-polyacrylamide (HPAM) solutions in both individual straight rectangular capillaries and in networks of such capillaries. Results from these experiments have been analyzed using pore-scale network modeling incorporating the non-Newtonian fluid mechanics of a Carreau fluid. Quantitative agreement is seen between the experiments and the network calculations in the Newtonian and shear-thinning flow regions demonstrating that the 'shift factor,'alpha, can be calculated a priori. Shear-thickening behavior was observed at higher flow rates in the micromodel experiments as a result of elastic effects becoming important and this remains to be incorporated in the network model.     

Dynamic wetting of Boger fluids

The impact of fluid elasticity on the dynamic wetting of polymer solutions is important because many polymer solutions in technological use exhibit non-Newtonian behaviors in the high shear environment of the wedge-like flow near a moving contact line. Our former study [G.K. Seevaratnam, Y. Suo, E. Ramé, L.M. Walker, Phys. Fluids 19 (2007) Art. No. 012103] showed that shear thinning induced by a semi-flexible high molecular weight polymer reduces the viscous bending near a moving contact line as compared to a Newtonian fluid having the same zero-shear viscosity. This results in a dramatic reduction of the dependence of the effective dynamic contact angle on contact line speed. In this paper, we discuss dynamic wetting of Boger fluids which exhibit elasticity-dominated rheology with minimal shear thinning. These fluids are prepared by dissolving a dilute concentration of high molecular weight polymer in a "solvent" of the oligomer of the polymer. We demonstrate that elasticity in these fluids increases curvature near the contact line but that the enhancement arises mostly from the weakly non-Newtonian behavior already present in the oligomeric solvent. We present evidence of instabilities on the liquid/vapor interface near the moving contact line.     

Peristaltic activity in blood flow of Casson nanoliquid with irreversibility aspects in vertical non-uniform channel

Due to the illuminating function of nanoliquids in several technological and medicinal domains, particularly in liquid transport processes known as peristalsis, inquisitive researchers have investigated the flow of peristaltic nanofluids. Consequently, the current study investigates the entropy production and magnetic influence on the peristaltic transport of heat and mass transport of Casson nanofluid in a non-uniform channel under convective circumstances. Utilizing the perturbation approach, fields of concentration, temperature, and velocity are derived from non-linear coupled partial differential equations (PDE). Entropy generation studies have been done. In addition, the influence of associated factors via specific physical terms, including the Sherwood number, the skin-friction coefficient, and the Nusselt number, for both Casson and Newtonian liquids, as well as the trapping phenomena, is visually examined.     

A study on dual solutions for water-based hybrid nanofluids flowing through convergent channel with dissipative heat transport

Over the years, the fluid flows in conjunction with thermal transport between non-parallel surfaces having converging nature is of great significance due to their broad spectrum of applications, which include fluid flows through nozzles in petroleum engineering, blood flow in arteries, lubrication systems, automobile radiators, thermal pumps, and water purification processes. Additionally, hybrid nanofluid is a prolific topic because of its thermal properties and potentials which provide a better performance even compared with common nanofluid in optimizing heat transfer. Therefore, this article presents a numerical simulation to investigate the heat transport characteristics of hybrid nanofluids in Jeffery-Hamel flow through a convergent channel. The considered hybrid nanofluids are composed of Copper (Cu) and Graphene-oxide (Go) as suspended nanoparticles and water as base fluid. This analysis further includes the impacts of viscous dissipation and magnetic field. A mathematical model for fluid flow and heat transfer are constructed with the help of cylindrical polar coordinates. The governing equations are converted into a system of ordinary differential equations (ODEs) by Lie symmetry group transformation. A MATLAB code is exercise to get the numerical solutions for flow and thermal distributions. An interesting phenomenon is that dual solutions are obtained in the computation. Thus, a comprehensive discussion is included on the dual solutions for various involved variables. The current findings may be employed in petroleum science, r biomedical scientists, polymer industry, etc.     

煤灰在高温下的流变特性研究

为了研究煤灰在高温下的流变特性,以陕西神木煤、内蒙纳林沟煤、宁夏羊肠湾煤和山东南屯煤四种煤灰为样品,利用高温旋转黏度计,研究了高温下煤灰渣黏度和剪切应力随剪切速率的变化。实验结果表明,当实验温度高于煤灰的液相线温度时,其流型表现为牛顿流体;当温度低于液相线温度时,其流型逐渐由牛顿流体转变为非牛顿流体。其中,陕西神木煤和宁夏羊肠湾煤的煤灰样品在高温下表现为剪切增稠,随着温度的降低,由牛顿流体转变为屈服涨塑性流体;内蒙纳林沟煤和山东南屯煤的煤灰样品在高温下表现为剪切变稀,随着温度的降低,由牛顿流体转变为屈服假塑性流体。另外,随着温度的降低,由于液态煤灰中晶体的不断析出,使屈服应力逐渐增大,降低了煤灰的流动性。     

茂金属聚乙烯和低密度聚乙烯共混物的流变行为

研究了茂金属催化乙烯丁烯1共聚物mPE和LDPE共混物的流变行为.测定了一系列共混物的稳态剪切粘度和动态粘弹性,用改进Cross模型拟合实验数据.mPE的零切粘度η₀较小,从牛顿型转变为非牛顿型所需的剪切速率较大,转变应力较高,在挤出加工剪切速率范围内熔体粘度高,对剪切敏感性差,这是由于它有较低的重均分子量、窄的分子量分布(M_w/M_n=21)所致.对于对数加和规律,共混物η₀在mPE/LDPE为50/50和25/75时有强烈的正偏差,这是由于共混物自由体积减小所致.共混物的转变应力τ^*和非牛顿指数n随LDPE加入量增大而降低,表明共混物对剪切的敏感性提高,加工性得到改善.G'和G”的一致性说明mPE和LDPE共混是相容的.     

Effect of viscous dissipation on MHD water-Cu and EG-Cu nanofluids flowing through a porous medium

This paper provides a comparative analysis of two different types of nanofluids for Stokes second problem. Additional effects of MHD, porosity and viscous dissipation are also considered. Two types of Newtonian liquids (water and ethylene glycol) are considered as base fluids with suspended nanosized Cu particles. A homogenous model of Newtonian nanofluids over a flat plate is used to describe this phenomenon with Stokes boundary conditions such that the ambient fluid is static and with uniform temperature. The problem is first written in terms of nonlinear partial differential equations with physical conditions; then after non-dimensional analysis, the Laplace transform method is used for its closed-form solution. Exact expressions are determined for the dimensionless temperature, velocity field, Nusselt number and skin friction coefficient and arranged in terms of exponential and complementary error functions satisfying the governing equations and boundary conditions. They are also reduced to the known solutions of Stokes second problem for Cu-water nanofluids. Results are computed using Maple software. The results showed that both skin friction and rate of heat transfer increase with increasing solid volume fraction of nanoparticles. MHD and porosity had an opposite effect on velocity for both types of nanofluids. The dimensionless temperature increases by increasing the Eckert and Hartmann numbers.

     

Green synthesis,crystal growth,and some physicochemical studies on an inter-molecular compound of anthranilic acid and <Emphasis Type="Italic">m</Emphasis>-nitro-benzoic acid system

Nanofluids are prepared by suspending the nanoparticles in the base fluid and can be substantially enhanced the heat transfer rate compared to the pure fluids. In this paper, experimental investigation of the effects of volume concentration and temperature on dynamic viscosity of the hybrid nanofluid of multi-walled carbon nanotubes and aluminum oxide in a mixture of water (80%) and ethylene-glycol (20%) has been presented. The nanofluid was prepared with solid volume fractions between 0.0625 and 1%, and experiments were performed in the temperature range of 25–50 °C. The measurement results at different shear rates showed that the base fluid and nanofluid samples with solid volume fractions of less than 0.5% had Newtonian behavior, while those with higher solid volume fractions (0.75 and 1%) exhibit a pseudoplastic rheological behavior with a power law index of less than unity. The results showed that viscosity has a direct relationship with solid volume fraction of the nanofluid. The value of maximum enhancement is which occurred in 25 °C. Moreover, the consistency index and power law index have been obtained by accurate curve fitting for samples with non-Newtonian behavior of nanofluids. The results also revealed that the apparent viscosity generally increases with an increase in the solid volume fraction.     

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.     

Electrophoresis in a Carreau fluid at arbitrary zeta potentials

The electrophoresis of colloidal particles has been studied extensively in the past. Relevant analyses, however, are focused mainly on the electrophoretic behavior of a particle in a Newtonian fluid. Recent advances in science and technology suggest that the electrophoresis conducted in a non-Newtonian fluid can play a role in practice. Here, the electrophoresis of a concentrated colloidal dispersion in a Carreau fluid is investigated under the conditions of arbitrary electrical potential where the effect of double-layer polarization may be significant. A pseudo-spectral method coupled with a Newton-Raphson iteration scheme is used to solve the governing equations, which describe the electric, the flow, and the concentration fields. The results of numerical simulation reveal that, due to the effect of shear thinning, the electrophoretic mobility for the case of a Carreau fluid is greater than for that of a Newtonian fluid. Also, the higher the surface potential of a particle, the more significant the non-Newtonian nature of a Carreau fluid on its electrophoretic mobility.     

Effect of EM propagation medium on electrorheological characteristics of dielectric nanofluids

The effect of dielectric loss on the electrorheological (ER) characteristic of dielectric nanofluids under shear was studied. When nanofluids are activated by an applied electric field, it behaves like a non-Newtonian fluid under ER effect by creating the chains of nanoparticles. ER characteristics of ZnO and Al₂O₃ nanofluids with various nanoparticles concentration (0.1, 0.05, 0.01 wt%) were measured. For this purpose, a solenoid-based electromagnetic (EM) transmitter was used under different propagation media including air, tap water, and salt water. The result shows that all the nanofluids exhibit pseudo-plastic behavior, while the electric field causes a significant increase in viscosity in the presence of tap water, followed by salt water. Additionally, the viscosity of nanofluid shows a high dependence on particle loading. A possible mechanism was also proposed to describe the effect of dielectric properties on the ER behavior of dielectric nanofluids.     

Rheometry-PIV of shear-thickening wormlike micelles

The shear-thickening behavior of an equimolar semidilute aqueous solution of 40 mM/L cetylpyridinium chloride and sodium salicylate was studied in this work by using a combined method of rheometry and particle image velocimetry (PIV). Experiments were conducted at 27.5 degrees C with Couette, vane-bob, and capillary rheometers in order to explore a wide shear stress range as well as the effect of boundary conditions and time of flow on the creation and destruction of shear-induced structures (SIS). The use of the combined method of capillary rheometry with PIV allowed the detection of fast spatial and temporal variations in the flow kinematics, which are related to the shear-thickening behavior and the dynamics of the SIS but are not distinguished by pure rheometrical measurements. A rich-in-details flow curve was found for this solution, which includes five different regimes. Namely, at very low shear rates a Newtonian behavior was found, followed by a shear thinning one in the second regime. In the third, shear banding was observed, which served as a precursor of the SIS and shear-thickening. The fourth and fifth regimes in the flow curve were separated by a spurtlike behavior, and they clearly evidenced the existence of shear-thickening accompanied by stick-slip oscillations at the wall of the rheometer, which subsequently produced variations in the shear rate under shear stress controlled flow. Such a stick-slip phenomenon prevailed up to the highest shear stresses used in this work and was reflected in asymmetric velocity profiles with spatial and temporal variations linked to the dynamics of creation and breakage of the SIS. The presence of apparent slip at the wall of the rheometer provides an energy release mechanism which leads to breakage of the SIS, followed by their further reformation during the stick part of the cycles. In addition, PIV measurements allowed the detection of apparent slip at the wall, as well as mechanical failures in the bulk of the fluid, which suggests an extra contribution of the shear stress field to the SIS dynamics. Increasing the residence time of the fluid in the flow system enhanced the shear-thickening behavior. Finally, the flow kinematics is described in detail and the true flow curve is obtained, which only partially fits into the scheme of existing theoretical models for shear-thickening solutions.     

Experimental investigation toward obtaining a new correlation for viscosity of WO3 and Al2O3 nanoparticles-loaded nanofluid within aqueous and non-aqueous basefluids

In this study, the effect of temperature and mass fraction of Al₂O₃ and WO₃ nanoparticles dispersed in deionized water and liquid paraffin was investigated on dynamic viscosity of nanofluid. The results of the TEM tests showed that the size of Al₂O₃ and WO₃ nanoparticles was ranged from 10 to 60 nm, and the results showed that nanoparticles were semi-spherical. Also the results of DLS and zeta potential tests, respectively, exhibited the uniform size and high stability of the nanoparticles in the basefluid environment. The findings showed that adding a certain amount of nanoparticles to water and liquid paraffin increases dynamic viscosity, and in the case of various shear rates, the viscosity is constant for the water-based nanofluids, which indicates the Newtonian behavior of the nanofluid. In addition, for those prepared by liquid paraffin as a basefluid, the viscosity does not remain constant at different shear rates and at low amount of shear rate the viscosity achieves higher value, indicating non-Newtonian behavior of liquid paraffin-based nanofluids. The results showed that by increasing the temperature in liquid paraffin-based nanofluid the uniformity and linearity of the viscosity curve at various shear rates could be observed, which represents an approach for Newtonian behavior of nanofluid at higher temperatures. These results also showed that with increasing the mass fraction of nanoparticles in water and liquid paraffin, the viscosity increases at different shear rates. Finally, the correlation presented in this study shows that for nanofluid viscosity as a function of nanoparticles load and temperature, the deviation of correlated data from experimental values is less than 10%.