Viscosity Equation Research Articles

Oblique Collision of Two Power-Law Fluid Jets at Low Speed

The present study focuses on characteristics of a liquid sheet resulting from the oblique collision of two power-law fluid jets at low speed. Liquid expands radially from the impact point, forming a bay-leaf-shaped sheet bounded by a thicker rim. A theoretical model for two power-law impinging jets is established. Sheet velocity distribution is deduced through energy conservation during impingement; other sheet features are predicted by solving conservation equations for mass and momentum of the sheet rim where equivalent viscosity is proposed. The predicted sheet shape and rim diameter are compared to experiments, and they share good consistency. Based on the model, the effects of rheological parameters ( and ) on sheet characteristics, such as shape, velocity, and thickness distribution, are discussed.

Phase change alloy viscosities down to Tg using Adam-Gibbs-equation fittings to excess entropy data: A fragile-to-strong transition

A striking anomaly in the viscosity of Te85Ge15 alloys noted by Greer and coworkers from the work of Neumann et al. is reminiscent of the equally striking comparison of liquid tellurium and water anomalies documented long ago by Kanno et al. In view of the power laws that are used to fit the data on water, we analyze the data on Te85Ge15 using the Speedy-Angell power-law form, and find a good account with a singularity Ts only 25 K below the eutectic temperature. However, the heat capacity data in this case are not diverging, but instead exhibit a sharp maximum like that observed in fast cooling in the Molinero-Moore model of water. Applying the Adam-Gibbs viscosity equation to these calorimetric data, we find that there must be a fragile-to-strong liquid transition at the heat capacity peak temperature, and then predict the "strong" liquid course of the viscosity down to Tg at 406 K (403.6 K at 20 K min−1 in this study). Since crystallization can be avoided by moderately fast cooling in this case, we can check the validity of the extrapolation by making a direct measurement of fragility at Tg, using differential scanning calorimetric techniques, and then comparing with the value from the extrapolated viscosity at Tg. The agreement is encouraging, and prompts discussion of relations between water and phase change alloy anomalies.

Modeling Sensitivity Using Constant Eddy Viscosity and Zero Equation Turbulence models (Case Study: 60 km Length of Ibrahimia Channel, Egypt)

Modeling Sensitivity Using Constant Eddy Viscosity and Zero Equation Turbulence models (Case Study: 60 km Length of Ibrahimia Channel, Egypt)

Two-Phase Analysis of A Helical Microchannel Heat Sink Using Nanofluids

A three-dimensional helical microchannel heat sink (HMCHS) model is developed to investigate the heat transfer characteristics using Al2O3–water-based nanofluid. The two-phase mixture model with modified effective thermal conductivity and viscosity equations is employed for solving the problem numerically. The model developed is validated by comparing the results of Nusselt number with available experimental and numerical data for a wide range of Reynolds number. The detailed results of the thermal field are reported for the effects of helix radius (0.15–0.30 mm), pitch (0.5–2.0 mm), number of turns (7–10), and aspect ratio (1.5–3.0). The analysis presents a unique fundamental insight into the complex secondary flow pattern in the channel due to curvature effects.

Density and viscosity of aqueous mixtures of N-methyldiethanolamines (MDEA), piperazine (PZ) and ionic liquids

The density and viscosity measurements of aqueous mixtures of N-methyldiethanolamine (MDEA), piperazine (PZ) and the ionic liquids (ILs) 1-n-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]), 1-butyl-3-methylimidazolium dicyanamide ([bmim][DCA]), and 1-ethyl-3-methylimidazolium trifluoromethanesulfonate ([emim][OTf]) were conducted in this work. It was found that an increase in IL concentration resulted in an increase in the densities and viscosities of the aqueous mixtures. The density and viscosity equations for MDEA, PZ and IL aqueous mixtures as a function of temperature and concentration of ILs were derived as well. The density and viscosity equations obtained adequate accuracies with less than 0.34% and 4.013% of deviation from experimental data respectively.

Effect of starting time on hydro-viscous drive speed regulating start

Purpose– The purpose of this paper is to reveal the effect of starting time on hydro-viscous drive speed regulating start.Design/methodology/approach– The modified transient Reynolds equation, thermal energy equation and temperature–viscosity equation were solved simultaneously by using finite element method. And then variations of the oil film load capacity, variations of temperature and variations of the torque generated by the oil film during the starting process were obtained.Findings– The results show that during the starting process, both the oil film load capacity and the temperature show an upward trend, the torque increases during the beginning period and then decreases during the latter part of the starting process. When the starting time is less than 60 s, variations of the oil film load capacity and temperature show fluctuations, which decrease with the starting time. For any output speed, the corresponding oil film load capacity, temperature and torque decrease with the starting time, and the decreasing amplitude also decreases with the starting time.Originality/value– This paper indicates that the starting time can be set to 60-90 s to obtain a perfect starting process. The simulation results are verified by the speed regulating start experiments. Research findings of this work provide theoretical basis for the design and practical application of the hydro-viscous drive equipments.

Experimental research and numerical analysis in thin film lubrication of point contact

Purpose – The purpose of this paper is to establish a rapid and effective numerical model of thin film lubrication with clear physical conception, in which viscosity variation along the direction of film thickness was used instead of average viscosity, and continuous Reynolds equation was used in the calculation of thin film lubrication. Design/methodology/approach – Based on rheology and thin film lubrication with point contact and considering features of shear thinning and like-solidification of lubricant oil in the thin film lubrication state, a modified formula with overall average equivalent viscosity was proposed by combining numerical calculation and experiment data. Findings – It is a fast and efficient method for film lubrication state simulation. Research limitations/implications – Thin film lubrication research on a nanoscale is very popular, and a variety of thin film lubrication models are proposed. Due to the complexity of thin film lubrication, it is still in the stage of revealing law and establishing calculation model. Originality/value – The key issue is how to obtain the viscosity correction formula derived from engineering practice, also considered the lubricating oil class solidification and shear-thinning properties on thin film lubrication, while based on the system experiment, the viscosity modified formula for the gap, speed changes are proposed to obtain the overall average equivalent viscosity which makes the thin film lubrication micro to macro, so that a clear physical meaning for thin-film lubrication numerical calculation model is established.

Investigation on characteristics of liquid self-diffusion in slit nanopores using simple quasicrystal model of liquid

Dynamical properties of liquid in nano-channels attract much interest because of their applications in engineering and biological systems. The transfer behavior of liquid confined within nanopores differs significantly from that in the bulk. Based on the simple quasicrystal model of liquid, analytical expressions of self-diffusion coefficient both in bulk and in slit nanopore are derived from the Stokes–Einstein equation and the modified Eyring's equation for viscosity. The local self-diffusion coefficient in different layers of liquid and the global self-diffusion coefficient in the slit nanopore are deduced from these expressions. The influences of confinement by pore walls, pore widths, liquid density, and temperature on the self-diffusion coefficient are investigated. The results indicate that the self-diffusion coefficient in nanopore increases with the pore width and approaches the bulk value as the pore width is sufficiently large. Similar to that in bulk state, the self-diffusion coefficient in nanopore decreases with the increase of density and the decrease of temperature, but these dependences are weaker than that in bulk state and become even weaker as the pore width decreases. This work provides a simple method to capture the physical behavior and to investigate the dynamic properties of liquid in nanopores.

РІВНЯННЯ ДЛЯ РОЗРАХУНКУ В'ЯЗКОСТІ ТА ТЕПЛОПРОВІДНОСТІ ХОЛОДОАГЕНТУ R134а

Equations for alternative refrigerant R134a viscosity and thermal conductivity calculation expressed in terms of independent variables, such as temperature and density are worked out. Equation coefficients are determined by the least square technique according to the experimental data. The equations describe viscosity at temperature ranging from 248 to 439 K at a pressure up to 6,0 MPa and thermal conductivity at temperature ranging from 248 to 533 K at a pressure up to 60,9 MPa. The composed equations accuracy is quite acceptable for the engineering calculations.

A novel theoretical approach to the temperature–viscosity relation for fluidic fuels

Viscosity is a first and foremost function both for theory and application. By approximating the interaction potential of molecule in fluidic fuel as constant and proposing a new method to calculate the momentum transfer by means of the radius of averaged volume per molecule, an equation of viscosity versus temperature was derived, which were found in good agreement with a lot of data from gaseous to liquid fuels by the curve fit. The equation also predicted that the viscosity initially decreased with temperature and then slowly increased in the high temperature region. When using it as correlation equation for the dependence of viscosity on temperature, it was able to cover more fluids from gaseous to liquid fuels.

Hydrophilic Nanoparticles Facilitate Wax Inhibition

A new class of hybrid pour point depressants (PPDs) are developed on the basis of poly(octadecyl acrylate) (POA) functionality and POA/nanosilica hybrid particles. Activity performance is demonstrated using a model waxy oil system consisting of 10 wt % macrocrystalline wax dissolved in dodecane, effectively emulating the essential characteristics of waxy petroleum fluids. Differential scanning calorimetry (DSC) evidence confirms that POA molecules enhance the solubility of wax in the continuous oil phase, reducing the wax appearance temperature. The presence of POA also serves effectively to modulate the crystal morphology to a more regular spherical-like shape, instead of the disc-like morphologies common to pristine paraffin wax crystals, affecting reduced gelation temperatures in accordance with percolation theory predictions. In addition, rheometric yield stresses decrease with increasing dosage rates of POA. A solvent-blending protocol is followed to subsequently prepare POA/nanosilica hybrid particles. Optimal PPD performance of the hybrid particle system is attained at a dosage rate of 100 ppm. At dosages higher than the optimal dose, the gel strength increases in an analogous manner to the directionality of the Einstein equation for viscosity. The POA/nanosilica hybrid particle system provides spherical templates for wax precipitation, resulting in a compact precipitate structure, which suppresses gelation and improves the flowability of the model waxy oil by several orders of magnitude. DSC data confirm that a vast majority of the POA molecules become solubilized in the continuous oil phase upon dispersion of the hybrid nanoparticle system. As such, the free POA molecules enhance wax solubility in the continuous oil phase. Hydrophobic nanoparticles retain a more robust ability to modulate waxy oil rheology at low-dosage rates, as compared to purely polymeric functionality. The primary mechanism of hybrid particle PPDs involves heterogeneous nucleation activity. The hybrid particles effectively provide solid–liquid interface sites as wax precipitation templates, which result in spherical-like spherical wax morphologies. The compact morphologies hinder and suppress the percolation process necessary to form a volume-spanning network of wax crystals. As such, the hybrid nanoparticles constitute effective and economic PPD additives and may serve as the basis for next-generation environmentally friendly wax inhibition agents, by reducing the amount of additives needed.

Numerical analysis of non-Newtonian rheology effect on hydrocyclone flow field

Abstract In view of the limitations of the existing Newton fluid effects on the vortex flow mechanism study, numerical analysis of non Newton fluid effects was presented. Using Reynolds stress turbulence model (RSM) and mixed multiphase flow model (Mixture) of FLUENT (fluid calculation software) and combined with the constitutive equation of apparent viscosity of non-Newtonian fluid, the typical non-Newtonian fluid (drilling fluid, polymer flooding sewage and crude oil as medium) and Newton flow field (water as medium) were compared by quantitative analysis. Based on the research results of water, the effects of non-Newtonian rheology on the key parameters including the combined vortex motion index n and tangential velocity were analyzed. The study shows that: non-Newtonian rheology has a great effect on tangential velocity and n value, and tangential velocity decreases with non-Newtonian increasing. The three kinds of n values (constant segment) are: 0.564(water), 0.769(polymer flooding sewage), 0.708(drilling fluid) and their variation amplitudes are larger than Newtonian fluid. The same time, non-Newtonian rheology will lead to the phenomenon of turbulent drag reduction in the vortex flow field. Compared with the existing formula calculation results shown, the calculation result of non-Newtonian rheology is most consistent with the simulation result, and the original theory has large deviations. The study provides reference for theory research of non-Newtonian cyclone separation flow field.

Rough Soft-EHL with Non-Newtonian Lubricant

This paper presents the effect of surface roughness on soft elastohydrodynamic lubrication in circular contact with non-Newtonian lubricant. The time independent modified Reynolds equation, elastic equation and lubricant viscosity equation were formulated for compressible fluid. Perturbation method, Newton-Raphson method, finite different method and full adaptive multigrid method were implemented to obtain the film pressure, film thickness profiles and friction coefficient in the contact region at various the amplitude of surface roughness, surface speed of sphere, modulus of elasticity and radius of sphere. The simulation results showed that the film thickness in contact region depended on the profile of surface roughness. The minimum film thickness decreased but maximum film pressure and friction coefficient increase when the amplitude of surface roughness and modulus of elasticity increased. For increasing surface speeds, the minimum film thickness and friction coefficient increase but maximum film pressure decreases. When radius of sphere increases, the minimum film thickness increases but maximum film pressure and friction coefficient decrease.

Density, viscosity, and saturated vapor pressure of ethyl trifluoroacetate

The properties of ethyl trifluoroacetate (CF3COOCH2CH3) were measured as a function of temperature: density (278.08 to 322.50)K, viscosity (293.45 to 334.32)K, saturated vapor pressure (293.35 to 335.65)K. The density data were fitted to a quadratic polynomial equation, and the viscosity data were regressed to the Andrade equation. The correlation coefficient (R2) of equations for density and viscosity are 0.9997 and 0.9999, respectively. The correlation between saturated vapor pressures and temperatures was achieved with a maximum absolute relative deviation of 0.142%. In addition, the molar evaporation enthalpy in the range of T=(293.35 to 335.65)K was estimated by the Clausius–Clapeyron equation.

Numerical study of water entry supercavitating flow around a vertical circular cylinder influenced by turbulent drag-reducing additives

This paper attempts to introduce a numerical simulation procedure to simulate water-entry problems influenced by turbulent drag-reducing additives in a viscous incompressible medium. Firstly we performed a numerical investigation on water-entry supercavities in water and turbulent drag-reducing solution at the impact velocity of 28.4 m/s to confirm the accuracy of the numerical method. Based on the verification, projectile entering water and turbulent drag-reducing solution at relatively high velocity of 142.7 m/s (phase transition is considered) is simulated. The cross viscosity equation was adopted to represent the shear-thinning characteristic of aqueous solution of drag-reducing additives. The configuration and dynamic characteristics of water entry supercavity, flow resistance were discussed respectively. It was obtained that the numerical simulation results are in consistence with experimental data. Numerical results show that the supercavity length in drag-reducing solution is larger than one in water and the velocity attenuates faster at high velocity than at low velocity; the influence of drag-reducing solution is more obvious at high impact velocity. Turbulent drag-reducing additives have the great potential for enhancement of supercavity.

Floppy Mode Degeneracy and Decoupling of Constraint Predictions in Super-Cooled Borate and Silicate Liquids

The theory of temperature-dependent topological constraints has been used to successfully explain the compositional dependence of glass properties for oxide and non-oxide compositions. It relates the number of topological degrees of freedom with the glass transition temperature through the configurational entropy of the system. Based on this, we estimated the number of degrees of freedom directly from viscosity measurements of binary alkali borate and silicate glasses. Both approaches exhibit a strong decoupling, which we suggest can be traced to the presence of medium- and long-range constraints that are not taken into account by bond constraint counting. The observed variation of the energy barrier for structural rearrangement and floppy mode degeneracy also corroborate our interpretation. We provide evidence that the degeneracy of floppy modes changes with chemical composition and that the parameter K(x) of the MYEGA viscosity equation could be used to assess changes in the medium-range order.

Unveiling the relationships among the viscosity equations of glass liquids and colloidal suspensions for obtaining universal equations with the generic free volume concept.

The underlying relationships among viscosity equations of glass liquids and colloidal suspensions are explored with the aid of free volume concept. Viscosity equations of glass liquids available in literature are focused and found to have a same physical basis but different mathematical expressions for the free volume. The glass transitions induced by temperatures in glass liquids and the percolation transition induced by particle volume fractions in colloidal suspensions essentially are a second order phase transition: both those two transitions could induce the free volume changes, which in turn determines how the viscosities are going to change with temperatures and/or particle volume fractions. Unified correlations of the free volume to both temperatures and particle volume fractions are thus proposed. The resulted viscosity equations are reducible to many popular viscosity equations currently widely used in literature; those equations should be able to cover many different types of materials over a wide temperature range. For demonstration purpose, one of the simplified versions of those newly developed equations is compared with popular viscosity equations and the experimental data: it can well fit the experimental data over a wide temperature range. The current work reveals common physical grounds among various viscosity equations, deepening our understanding on viscosity and unifying the free volume theory across many different systems.

Understanding empirical powder flowability criteria scaled by Hausner ratio or Carr index with the analogous viscosity concept

The viscosity concept is introduced to granular powders after the analogous granular temperature is defined, and the viscosity equations are derived with the Eyring's rate process theory and free volume concept.

Viscosity Measurements of Dilute Poly(2-ethyl-2-oxazoline) Aqueous Solutions Near Theta Temperature Analyzed within the Joint Rouse-Zimm Model

The steady-state shear viscosity of low-concentrated Poly(2-ethyl-2-oxazoline) (PEOX) aqueous solutions is measured near the presumed theta temperature using the falling ball viscometry technique. The experimental data are analyzed within the model that joins the Rouse and Zimm bead-spring theories of the polymer dynamics at the theta condition, which means that the polymer coils are considered to be partially permeable to the solvent. The polymer characteristics thus depend on the draining parameterhthat is related to the strength of the hydrodynamic interaction between the polymer segments. The Huggins coefficient was found to be 0.418 at the temperature 20°C, as predicted by the theory. This value corresponds toh= 2.92, contrary to the usual assumption of the infiniteh. This result indicates that the theta temperature for the PEOX water solutions is 20°C rather than 25°C in the previous studies. The experimental intrinsic viscosity is well described coming from the Arrhenius equation for the shear viscosity.

Particle spectra and HBT radii for simulated central nuclear collisions of C + C, Al + Al, Cu + Cu, Au + Au, and Pb + Pb from $$\sqrt{s}=62.4$$ s = 62.4 – $$2760$$ 2760 GeV

We study the temperature profile, pion spectra, and HBT radii in central, symmetric, and boost-invariant nuclear collisions, using a super hybrid model for heavy-ion collisions (SONIC), combining pre-equilibrium flow with viscous hydrodynamics and late-stage hadronic rescatterings. In particular, we simulate Pb + Pb collisions at \(\sqrt{s}=2.76\) TeV, Au + Au, Cu + Cu, Al + Al, and C + C collisions at \(\sqrt{s}=200\) GeV, and Au + Au and Cu + Cu collisions at \(\sqrt{s}=62.4\) GeV. We find that SONIC provides a good match to the pion spectra and HBT radii for all collision systems and energies, confirming earlier work that a combination of pre-equilibrium flow, viscosity, and QCD equation of state can resolve the so-called HBT puzzle. For reference, we also show p + p collisions at \(\sqrt{s}=7\) TeV. We make tabulated data for the 2 + 1 dimensional temperature evolution of all systems publicly available for the use in future jet energy loss or similar studies.