Viscosity Equation Research Articles

Aspects of nonflat FRW bouncing models with quadratic equation of state

In this paper, we investigate the possibility of a nonsingular model of universe in the framework of general relativity in nonflat FRW geometries with quadratic equation of state and bulk viscosity. We study whether a nonsingular bounce requires violation of energy conditions. We discuss the thermodynamical aspects of the resulting models with equilibrium description. In particular, we discuss the validity of the generalized second law of thermodynamics for resulting cosmologies.

Analysing dissipative effects in the ΛCDM model

In the present paper, the effects of viscous dark matter are analysed within the ΛCDM model. Here we consider bulk viscosity through the Israel-Stewart theory approach, leading to an effective pressure term in the continuity equation that accomplishes for the dissipative effects of the dark matter fluid. Then, the corresponding equation for viscosity is solved and a general equation for the Hubble parameter is obtained with the presence of a cosmological constant. The existence of de Sitter solutions is discussed, where a wider range of solutions is found in comparison to the ΛCDM model. Also the conditions for the near thermodynamical equilibrium of the fluid is analysed. Finally, a qualitative analysis provides some constraints on the model by using Supernovae Ia data which reveals the possible importance of causal thermodynamics in cosmology.

Model for the prediction of drag torque characteristics in wet clutch with radial grooves

Drag torque can cut down the efficiency of the vehicle transmission system. So it should be reduced on the premise of normal vehicle lubrication and heat dissipation. The purpose of this paper is to analyze the variation rule of drag torque in single-plate wet clutch from the perspective of flow rate, density, and viscosity. In the theoretical model of drag torque, the flow field is divided into oil film area and cavitation zone. Based on the mass flow conservation and viscosity–pressure equation, the equivalent density and viscosity of each node in each region are obtained. Then the total drag torque is calculated through the sum of each node’s torque. Finally, the curves of drag torque with rotational speed under different working conditions are obtained by numerical calculation, and they have been tested and verified. Through this research, the following conclusions can be reached: the rotational speed of the peak of drag torque is near the maximum speed where full oil film lubrication is realized. While temperature declines, it will lead to higher viscosity, then the speed of the lubricant along the radial direction will decrease, resulting in the increase in maximum speed of full oil film lubrication under the same oil supply; accordingly, the peak of drag torque will rise. If the flow rate of oil supply is increased, the maximum speed where full oil film lubrication is realized will be higher; consequently, the maximum drag torque will be improved. When clearance becomes wider, the cross-sectional area of the radial flow will be larger, then the maximum speed of full oil film lubrication under the same oil supply will be decreased, thus the peak of drag torque will decline.

Properties of a Terpolymer-Treated Soil: A 13C NMR Study

The Young’s modulus and the secant modulus of a terpolymer-treated soil as a function of the polymer’s characteristics are discussed in the context of a more general inelastic property known as the toughness parameter. The soil chosen was a sample of the State of Qatar subsoil. The terpolymer, designated TPAM, was characterized by a backbone structure of acrylamide, anionic carboxylate, and cationic (3-acrylamidopropyl-trimethylammonium chloride) repeat units. The backbone unit ratio was estimated from 13C NMR analyses. TPAM was synthesized by straightforward NaOH hydrolyses of an acrylamide/cationic copolymer. The correlations between the NaOH molarity of the hydrolysis solution, with the corresponding ratio of the anionic and cationic units, were shown to have a significant influence on the value of the toughness parameter. It is speculated that controlling the anionic and cationic ratio of a terpolymer is a general approach to optimize the toughness parameter of treated soils. Measurements of the molecular weight of TPAM were made, and comments on the importance of this feature are given. The equivalent viscosity was also recorded. It is pointed out that the work is particularly relevant to the practical problem of subsoil pavement stabilization in which the terpolymer acts as a soil binder. Suggestions on further work are given.

Analysis of velocity slipping at wall boundary under rarefied gas condition based on the effect of viscosity

PurposeVelocity slipping model, based on the stratification theory (the film in inflatable support area of aerostatic guide way was divided into near wall layer, thin layer and continuous flow layer in the direction of height), was established, and the model was combined with viscosity changes in each layer.Design/methodology/approachSimulated and analyzed by LAMMPS and two-dimensional molecular dynamics method, some relevant conclusions were drawn.FindingsAt a high temperature, viscosity is low, velocity slipping is large and velocity gaps in near-wall layer and thin layer are large. When the temperature is constant, the dimensionless slipping length and Kn number are linear.Research limitations/implicationsThe effect of the equivalent viscosity on gas slipping model is proposed. viscosity is smaller, gas velocity slipping is greater, temperature is higher, gas velocity slipping is greater, velocity gap of near wall layer and thin layer is larger. When the temperature is constant, the dimensionless slipping length ls and Kn number are linear.Originality/valueThe global model of lubricating film velocity slipping between plates was established, and mathematical expression of slipping model in each layer, based on the stratification theory, was presented.

New insights into chelator recycling by a chelating resin: From molecular mechanisms to applicability

As part of the project of developing a “green” and highly feasible soil remediation process, recycling an eco-friendly chelating agent, glycine, using Chelex-100 chelating resin, was studied. Two model complexes, copper and nickel glycinates, were tested under various conditions, including equivalent viscosity but different temperature conditions. Two similar complexes demonstrated very different reactivity towards Chelex-100. An in-depth study led to the discovery of unusual metal-dependent mechanisms of the complex-to-resin metal transfer. Particularly, nickel transfer proceeds via a dissociative mechanism, whereas copper transfer does not require pre-dissociation of the complexes, and proceeds via the associative ligand-exchange mechanism. Both processes result in the recovery of the used chelator. The glycine solution was applied on the spiked soil, then recovered on Chelex-100 resin and successfully reused, thus demonstrating a proof of the concept. These findings contribute to the science, strategies, and methodology of both water purification and chelator recycling fields.

Investigation of Pressure Drop of Trapped Oil in Capillaries with Circular Cross-Sections

An investigation is performed to determine the cause of the pressure drop for mobilizing a trapped oil slug in capillaries with circular cross-sections. This research is focused on pressure drop across the tube at different stages of oil mobilization and the physics behind the rapid decrease during slug separation. Pressure drop decease in the hold-up stage, which is too small to be observed experimentally, and the severe change of pressure drop during the slug detachment process are observed and quantitatively analyzed using computational fluid dynamics. The method used for the analysis is the equivalent viscosity model. For different slug lengths and multislug cases, the role of the capillary pressure difference in the process of trapped oil migration is well-recognized. The influence of oil dispersion in porous media on pressure drop when saturation is constant is also discussed. Compared with multislug pressure drops, the relative error of the equivalent viscosity model and computational fluid dynamic...

Modeling of delayed elasticity in glass

We have developed a numerical model based on finite element analysis (FEA) with a viscoelastic material model coupling stress relaxation and structural relaxation, using the Mauro-Allan-Potuzak (MAP) non-equilibrium viscosity equation as the shift function. A modeling study of the delayed elasticity behavior in glass under different equilibrium viscosity and non-equilibrium viscosity conditions is conducted. The delayed elastic response is found to be well described by a stretched exponential function with three parameters: the maximum delayed elasticity response, the retardation time of delayed elasticity response, and the stretching exponent of delayed elasticity response. The delayed elasticity magnitude is seen to increase with lower values of the stretching exponent bstress. At equilibrium viscosity, the retardation time shows a linear relationship with the stress relaxation time. However, when the temperature drops sharply in the non-equilibrium viscosity cases, the delayed elastic response may be frozen resulting in a lower magnitude for the delayed elasticity and the retardation time is not linear any more with the stress relaxation time. The delayed elasticity stretching exponent is seen to vary slightly at different relaxation times and normalized delayed elasticity response can roughly be collapsed into a single master curve. The impact of liquid fragility is also studied.

Study on Hydration of Illite in K+, Na+, Ca2+, Mg2+, and Al3+ Electrolyte Solutions

Abstract The hydration of clay particles in aqueous solutions plays an important role in the scientific and industrial fields. In this study, the hydration properties of fine illite particles in K+, Na+, Ca2+, Mg2+, and Al3+ electrolyte solutions were investigated through the relative viscosity method based on Einstein’s viscosity equation. During the experiments, the hydration index (I) was measured using a rheometer to analyze the hydration layers formed on the illite surfaces in different aqueous electrolyte solutions, and it was found that the index I was the highest in Al3+ followed by that in Mg2+, Ca2+, Na2+, and K+ in descending order. It was also observed that the index increased as the electrolyte concentration increased until the solution reached an adsorption equilibrium. When electrolytes were added, the effect of electroviscosity on the calculated value of I became weaker until it could eventually be neglected. Based on these results, we concluded that the electroviscosity should be considered when calculating the hydration index of a suspension of fine charged particles with low conductivity.

Determination of the Dynamic Viscosity of Liquid Alloys from the Phase Diagram

That viscosity and fluidity are equilibrium processes may be established on the basis of the Boltzmann distribution in terms of randomized particles. Specifically, the virtual presence of three classes of particles— with crystal mobility, liquid mobility, and vapor mobility—is assumed. Accordingly, the viscosity and fluidity of solutions—in particular, molten metallic alloys—may be considered in terms of the equilibrium contributions of each component to the total viscosity and fluidity, despite the kinetic interpretation of the usual expressions for these liquid properties. A linear additive equation for the viscosity is only possible for perfect solutions; for present purposes, that corresponds to alloys with unlimited mutual solubility of the components. Alloys with eutectics, chemical compounds, and other singularities in the phase diagram are characterized by viscosity equations that reproduce the shape of the liquidus curve over the whole range of alloy composition at different temperatures. Greater smoothness and closeness of the curves is observed at higher temperatures. These aspects of the temperature dependence of the viscosity may be explained on the basis of randomized particles and the visual cluster model of viscosity, with calculation of the proportions of the clusters that determine the alloy viscosity. Such viscosity is determined from a formula in which the thermal barrier to randomization is the thermal energy RTcr at the liquidus temperature, which is characterized by the temperature of melt crystallization Tcr, analogously to the melting point of the pure materials. On that basis, we propose a method of calculating the alloy viscosity from the phase diagram. From the temperature dependences of the viscosity of the pure components, the alloy viscosity may be determined from the proportion of clusters at any temperature above the liquidus curve and the viscosities of the pure components, taking account of the mole fraction of each component. The result is a trifactorial model of the viscosity of a liquid alloy. In this model, the variable is the thermal barrier RTcr to randomization, which determines the proportion of clusters both for pure materials (at RTcr = RTm) and for alloys. Overall, this model corresponds to the virtual cluster theory of viscosity and is consistent with the concept of randomized particles.

Rheological Behavior of Mixture of Carbonyl Iron Powder (CIP) and High Density Polyethylene (HDPE)

Rheological study has been performed experimentally by using melt flow index (MFI) tester on a mixture of CI (Carbonyl Iron) powder and HDPE (High-Density Polyethylene) polymer. The rheological properties such as volume flow rate (cm3/s), shear strain rate (s-1) and viscosity (Pa.s) are investigated for varying conditions of temperature and weight (pressure). This also includes experimental determination of viscosity dependence over parameters like temperature, shear strain rate and CI powder loading by weight added in HDPE. For this experimental conditions selected are temperatures 4480K-5230K in steps of 250K, weights in MFI tester (ultimately converted to shear strain rate) 0.325, 1.20, 2.16, 3.80, 5.00Kg and carbonyl iron powder loading in binder HDPE (by weight) 80%-92% in steps of 6%. A constitutive equation for viscosity is formulated which considers all factors affecting viscosity with the maximum percentage error of about 4% between experimental value and value predicted by the formulated equation is obtained.

Optimum formulation derivation for the ultimate packing fraction using monodispersed particle sizes when optimizing suspension viscosities

PurposeThe importance of maximizing the particle packing fraction in a suspension by maximizing average particle size ratio of D5/D1 has been adequately shown to be important as previously reported in the literature. This study aims to extend that analysis to include the best formulation approach to maximize the packing fraction with a minimum number of monodisperse particle sizes.Design/methodology/approachAn existing model previously developed by this author was modified theoretically to optimize the ratio used between consecutive monodisperse particle sizes. This process was found to apply to a broad range of particle configurations and applications. In addition, five different approaches for maximizing average particle size ratio D̅5/D̅1 were addressed for blending several different particle size distributions. Maximizing average particle size ratio D̅5/D̅1 has been found to result in an optimization of the packing fraction. Several new concepts were also introduced in the process of maximizing the packing fraction for these different approaches.FindingsThe critical part of the analysis to maximize the packing fraction with a minimum number of particles was the theoretical optimization of the ratio used between consecutive monodisperse particle sizes. This analysis was also found to be effectively independent of the maximum starting particle size. This study also clarified the recent incorrect claim in the literature that Furnas in 1931 was the first to generate the maximum theoretical packing fraction possible for n different particles that was actually originally developed in conjunction with the Sudduth generalized viscosity equation. In addition, the Furnas generated equation was also shown to give significantly different results from the Sudduth generated equation.Research limitations/implicationsExperimental data involving monodisperse particles of different blends with a minimum number of particle sizes that are truly monodisperse are often extremely difficult to obtain. However, the theoretical general concepts can still be applicable.Practical implicationsThe expanded model presented in this article provides practical guidelines for blending pigments using a minimum number of monodisperse particle sizes that can yield much higher ratios of the particle size averages D̅5/D̅1 and thus potentially achieve significantly improved properties such as viscosity.Originality/valueThe model presented in this article provides the first apparent guidelines to control the blending of pigments in coatings by the optimization of the ratio used between consecutive monodisperse particle sizes. This analysis was also found to be effectively independent of the maximum starting particle size.

PENGARUH KONSENTRASI SUBSTRAT PADA PEMBUATAN MALTODEKSTRIN DARI SUBSTRAT PATI SAGU

The aims of this research were to examine the effect of the optimal sago substrate concentration to produce maltodextrin. This research consists of two factors. First factor was sago concentration that consists of 4 levels (20%, 25%, 30% and 35%) and the second was time of liquefaction that consisting of 7 levels (0 minutes, 20 minutes, 40 minutes, 60 minutes, 80 minutes, 100 minutes, and 120 minutes). Parameters of observation were reducing sugar levels, total solid, the values equivalent dextrose, residual starch and viscosity. Data were analyzed using a completely randomized design if treatment had real effect on parameter then continued with Duncan test. The result of the research was the best concentration in maltodextrin hydrolysis was in concentration of 35% in terms of reducing sugar levels, total solids, equivalent dextrose and viscosity with each value 138.69 g / L, 39.41%, 35.37% and 5021.43 cP. While the he best reaction time liquefaction of maltodextrin at 120 minutes with reducing sugar levels, total solid, the values dextrose equivalent and viscosity with each value of 158.25 g / L, 41.28%, 38.35% and 1701.42 Cp

Vanishing vertical limit of the incompressible combined viscosity and magnetic diffusion magnetohydrodynamic system

In this paper, we consider the incompressible combined viscosity and magnetic diffusion magnetohydrodynamic system with Dirichlet boundary condition in a half space of . We establish the asymptotic expansions of this system by multiscale analysis and obtain the horizontal alone viscosity and magnetic diffusion magnetohydrodynamic equations and the boundary layer equations. And then we study the well‐posedness of the 2 equations. At last, we get the vanishing limit when the vertical viscosity and magnetic diffusion coefficient tends to zero.

Volumetric, Viscosity and Conductance Studies of Solute–Solute and Solute–Solvent Interactions of Some Alkali Metal Chlorides in Aqueous Citric Acid at Different Temperatures

Abstract The present study aims for the structure-making and structure-breaking behavior of some electrolytes in aqueous citric acid solution. The density, viscosity and conductance of some alkali metal chlorides lithium chloride (LiCl), sodium chloride (NaCl) and potassium chloride (KCl) in 0.01 m aqueous citric acid have been measured in the concentration range 0.01–0.12 m at 303.15, 308.15, 313.15 and 318.15 K. From these measurements, molar volume, viscosity parameters and molar conductance have been deliberated. Debye Hückel limiting law is used for the assessment of the contributions of various types of solute–solvent interactions. Jones–Dole viscosity equation is used to calculate viscosity B-coefficient for these salts in aqueous citric acid, which is known to provide information concerning the solvation of ions and their effects on the structure of the solvent in the near environment of the solute particles. The free energies of activation of viscous flow per mole of solvent, Δ μ 1 0 ‡ $\Delta \mu _1^{0\ddagger }$ and solute, Δ μ 2 0 ‡ , $\Delta \mu _2^{0\ddagger },$ have also been evaluated by using viscosity data. Using molar volume, the transfer volume Фv o tr has also been computed. The structure making/ breaking behavior of LiCl, NaCl and KCl is inferred from the sign of second derivative of partial molar volume with respect to temperature at constant pressure (d2φv o/dT2)p, Temperature coefficient of B. dB/dT and temperature coefficient of Walden product i.e. d(Λm oηo)/dT values. It has been found from these studies that LiCl, NaCl and KCl behave as structure-breaker in 0.01 m aqueous citric acid solution. The results have been qualitatively used to explain the molecular interaction and structural changes between the components of these mixtures.

A note on Stokes’ problem in dense granular media using the -rheology

The classical Stokes’ problem describing the fluid motion due to a steadily moving infinite wall is revisited in the context of dense granular flows of mono-dispersed beads using the recently proposed$\unicode[STIX]{x1D707}(I)$-rheology. In Newtonian fluids, molecular diffusion brings about a self-similar velocity profile and the boundary layer in which the fluid motion takes place increases indefinitely with time$t$as$\sqrt{\unicode[STIX]{x1D708}t}$, where$\unicode[STIX]{x1D708}$is the kinematic viscosity. For a dense granular viscoplastic liquid, it is shown that the local shear stress, when properly rescaled, exhibits self-similar behaviour at short time scales and it then rapidly evolves towards a steady-state solution. The resulting shear layer increases in thickness as$\sqrt{\unicode[STIX]{x1D708}_{g}t}$analogous to a Newtonian fluid where$\unicode[STIX]{x1D708}_{g}$is an equivalent granular kinematic viscosity depending not only on the intrinsic properties of the granular medium, such as grain diameter$d$, density$\unicode[STIX]{x1D70C}$and friction coefficients, but also on the applied pressure$p_{w}$at the moving wall and the solid fraction$\unicode[STIX]{x1D719}$(constant). In addition, the$\unicode[STIX]{x1D707}(I)$-rheology indicates that this growth continues until reaching the steady-state boundary layer thickness$\unicode[STIX]{x1D6FF}_{s}=\unicode[STIX]{x1D6FD}_{w}(p_{w}/\unicode[STIX]{x1D719}\unicode[STIX]{x1D70C}g)$, independent of the grain size, at approximately a finite time proportional to$\unicode[STIX]{x1D6FD}_{w}^{2}(p_{w}/\unicode[STIX]{x1D70C}gd)^{3/2}\sqrt{d/g}$, where$g$is the acceleration due to gravity and$\unicode[STIX]{x1D6FD}_{w}=(\unicode[STIX]{x1D70F}_{w}-\unicode[STIX]{x1D70F}_{s})/\unicode[STIX]{x1D70F}_{s}$is the relative surplus of the steady-state wall shear stress$\unicode[STIX]{x1D70F}_{w}$over the critical wall shear stress$\unicode[STIX]{x1D70F}_{s}$(yield stress) that is needed to bring the granular medium into motion. For the case of Stokes’ first problem when the wall shear stress$\unicode[STIX]{x1D70F}_{w}$is imposed externally, the$\unicode[STIX]{x1D707}(I)$-rheology suggests that the wall velocity simply grows as$\sqrt{t}$before saturating to a constant value whereby the internal resistance of the granular medium balances out the applied stresses. In contrast, for the case with an externally imposed wall speed$u_{w}$, the dense granular medium near the wall initially maintains a shear stress very close to$\unicode[STIX]{x1D70F}_{d}$which is the maximum internal resistance via grain–grain contact friction within the context of the$\unicode[STIX]{x1D707}(I)$-rheology. Then the wall shear stress$\unicode[STIX]{x1D70F}_{w}$decreases as$1/\sqrt{t}$until ultimately saturating to a constant value so that it gives precisely the same steady-state solution as for the imposed shear-stress case. Thereby, the steady-state wall velocity, wall shear stress and the applied wall pressure are related as$u_{w}\sim (g\unicode[STIX]{x1D6FF}_{s}^{2}/\unicode[STIX]{x1D708}_{g})f(\unicode[STIX]{x1D6FD}_{w})$where$f(\unicode[STIX]{x1D6FD}_{w})$is either$O(1)$if$\unicode[STIX]{x1D70F}_{w}\sim \unicode[STIX]{x1D70F}_{s}$or logarithmically large as$\unicode[STIX]{x1D70F}_{w}$approaches$\unicode[STIX]{x1D70F}_{d}$.

Mathematical model and sensitivity analysis for describing emulsification in ASP flooding

Alkali-surfactant polymer flooding has become an important technique to improve oil recovery following the development of oil fields while the function of emulsification in enhanced oil recovery is rarely considered in the existing mathematical model for numerical simulation. In this paper, the mechanism of improving the recovery of the emulsification was analyzed in ASP flooding, and a relatively perfect mathematical model with deep filtration-theory was established, in which oil–water volume equation, saturation equation, viscosity equation, and permeability reduction equation are included. The new model is used to simulate the actual block of an oil field; the simulated results of the new model and an old model without considering the emulsification are compared with the actual well history. It is found that new model which is easy to be realized in numerical simulation has a high precision fitting, and the effect of adding oil and decreasing water is obvious. The sensitivity of emulsification was analyzed, and the results show that the water reducing funnel becomes wider and the rate of water cut decreases rapidly with the increase of emulsifying capacity, and then the rate of recovery slows down. The effect of increasing oil and decreasing water is better, and the degree of recovery increases. The emulsification of the ASP flooding is maintained at a moderate level, which corresponds to Φ = 0.2 in the new model, and the emulsification is applied to realize the general mathematical quantitative description, so as to better guide the oilfield development.

An equivalent single-phase flow for oil-water two-phase flow and its potential application in well test

In this work an equivalent single-phase flow model is proposed based on the oil-water two-phase flow equation with saturation-dependent parameters such as equivalent viscosity and equivalent formation volume factor. The equivalent viscosity is calculated from the oil-water relative permeability curves and oil-water viscosity. The equivalent formation volume factor is obtained by the fractional flow of the water phase. In the equivalent single-phase flow model, the equivalent viscosity and phase saturation are interdependent when the relative permeability curves are known. Four numerical experiments based on PEBI grids show that equivalent single-phase flow has a good agreement with the oil-water two-phase flow, which shows that the equivalent single-phase flow model can be used to interpret oil-water two-phase pressure data measured in the wellbore during the buildup period. Because numerical solution of single-phase flow model is several times faster than that of the two-phase flow model, whether the new model interprets the pressure data directly or offers good initial values for the true oil-water two-phase pressure data interpretation, it will obviously improve the efficiency of the interpretation of oil-water pressure data and decrease the burden of engineers.

Viscosity of Structured Disperse Systems

A generalized viscosity equation has been proposed for structured disperse systems with their peculiar rheological properties. Some characteristic features of the viscosity curve have been revealed at the beginning of structuration. Different variants of viscosity equations for structured disperse systems have been considered, and their comparison with the experimental data has been performed. The possibilities of estimating the porosity and shear viscosity of structured media with a fixed layer of particles have been demonstrated.

Measurement and correlation of the liquid viscosity of trans-1-chloro-3,3,3-trifluoropropene (R1233zd(E))

Abstract In 2015, many nations have reached the agreement to limit greenhouse gas emissions in the Paris Agreement on climate change. New working fluids with low global warming potential (GWP) has thus caused extensive interest, which can protect the environment and meet engineering performance requirements. trans-1-Chloro-3,3,3-trifluoropropene (R1233zd(E)) is one of the new working fluids that has potential applications in refrigeration systems. In this work, viscosity data of trans-1-chloro-3,3,3-trifluoropropene were reported. The viscosity was meausred over the temperature range of (243–373) K and at pressures up to 40 MPa using a vibrating-wire viscometer. The combined expanded uncertainty of the reported viscosity is 2% with a confidence level of 0.95 (k = 2). These experimental data were used to correlate a viscosity equation that covers a wide temperature and pressure range, with an estimated uncertainty at a 95% confidence level of 2% for the liquid phase from (240 to 400) K at pressures up to 40 MPa.