Pressure-viscosity Coefficient Research Articles

Streaming potential of viscoelastic fluids with the pressure-dependent viscosity in nanochannel

The plane Poiseuille flow of viscoelastic fluids with pressure-dependent viscosity is analyzed through a narrow nanochannel, combining with the electrokinetic effect. When the fluid viscosity depends on pressure, the common assumption of unidirectional flow is unsuitable since the secondary flow may exist. In this case, we must solve the continuity equation and two-dimensional (2D) momentum equation simultaneously. It is difficult to obtain the analytical electrokinetic flow characteristics due to the nonlinearity of governing equations. Based on the real applications, we use the regular perturbation expansion method and give the second-order asymptotic solutions of electrokinetic velocity field, streaming potential, pressure field, and electrokinetic energy conversion (EKEC) efficiency. The result reveals a threshold value of Weissenberg number (Wi) exists. The strength of streaming potential increases with the pressure-viscosity coefficient when Wi is smaller than the threshold value. An opposite trend appears when Wi exceeds this threshold value. Besides, the Weissenberg number has no effect on the zero-order flow velocity, but a significant effect on the velocity deviation. A classical parabolic velocity profile transforms into a wavelike velocity profile with the further increase in Wi. Finally, the EKEC efficiency reduces when pressure-dependent viscosity is considered. Present results are helpful to understand the streaming potential and electrokinetic flow in the case of the fluid viscosity depending on pressure.

Effects of a typical shear dependent viscosity on analytical elastohydrodynamic lubrication film thickness predictions: A critical issue for the classical approach

Many engineering estimates of the film thickness in the concentrated contacts of real machines have come from extrapolations of measurements of elastohydrodynamic lubrication film thickness performed in glass on steel elastohydrodynamic rigs. Such estimates are likely to have large errors due to shear dependence of viscosity. The classical film thickness formulas employed have not been validated except for some Newtonian reference liquids at room temperature because the real pressure-viscosity response measured in viscometers has been ignored. A blend of polyalpha olefin base oils with mild shear-thinning has been employed in a line contact calculation to assess the effects of shear-dependent viscosity on the power-law exponents of the classical film thickness formula. The exponents on the pressure-viscosity coefficient and on the elastic modulus of the solids are not sensitive to the non-Newtonian effect. The exponents on ambient pressure viscosity and velocity are slightly reduced by shear-thinning. The exponents on pressure and scale are substantially increased by the shear dependence. The usual practice of measuring film thickness in an elastohydrodynamic rig to obtain an effective “[Formula: see text]-value” to use in a classical Newtonian film thickness formula will overstated the film thickness of a liquid which is shear dependent in the elastohydrodynamic lubrication inlet.

Measurement Techniques and Methods for the Pressure Coefficient of Viscosity of Polymer Melts

Viscosity is a prominent rheological property of polymer, which is affected by temperature, pressure, shear rate, molecular structure, and other factors. Despite the importance of the pressure effect, there remains a paucity of investigations on the dependence of pressure on viscosity compared with other factors, such as shear rate and temperature. Previous research has established that the correlation between pressure and viscosity is usually expressed by the pressure coefficient. In this paper, different measurement techniques and methods for the pressure coefficient of viscosity of polymer melts are reviewed and evaluated on the basis of published experimental data. The capillary rheometer with a pressurized exit chamber is widely employed because of its accuracy and simple use. Besides, the accuracy and relationship of pressure coefficients determined by different methods are discussed.

Rheological Characterization and Tribological Evaluation of Water-Based Lubricants in AISI 52100 Bearing Steel

This study explores the rheological and tribological behavior of water-based lubricants (WBLs) as potential alternatives for electric vehicle (EV) applications. As the transportation sector increasingly shifts towards EVs to reduce carbon emissions, the demand for efficient lubricants becomes critical. WBLs here are defined as fluids containing a minimum of 50 wt% water mixed with glycerol, ethylene glycol (MEG), polyethylene glycol (PEG), or one of two polyalkylene glycols (PAGs). Rheological properties were investigated and compared with traditional lubricating oils. Results demonstrate distinctive rheological characteristics in WBLs, with viscosity–temperature responses resembling traditional oils with lowered pressure–viscosity coefficients. Nevertheless, WBLs exhibit promising film-forming capabilities in highly loaded contacts. Additionally, in sliding contacts, WBLs generally display lower friction coefficients compared to traditional oils, with PEG exhibiting the lowest value near 0.1. These findings suggest that WBLs may offer advantages in reducing friction and energy loss in EV applications. Furthermore, sliding wear tests indicate low wear rates in WBLs such as PEG, PAG, and glycerol, supporting their potential as viable lubrication options. The study highlights the importance of high-pressure rheology and tribochemistry in wear mechanisms among the different lubricants.

Unraveling the pressure-viscosity behavior and shear thinning in glycerol using atomic scale molecular dynamics simulations

In order to increase the usage and explore new applications of glycerol as a replacement for fossil-based lubricants its properties needs to be known at the fundamental level. In this study, the viscosity of pure glycerol at high pressures and strain rates has been investigated using of molecular dynamics (MD) simulations, utilizing both the Green-Kubo (GK) formalism and the SLLOD algorithm. Although the viscosity acquired by the GK method is in agreement with the corresponding experimental values at low pressure, a significant distinction was identified between the viscosity obtained by the GK method and the experimental values at higher pressures (P > 0.5 GPa). This results in a clear difference between the viscosity-pressure coefficient attained by the GK method and the corresponding experimental value. The SLLOD method using a non-equilibrium MD (NEMD) platform was exploited to take into account the simultaneous effects of strain rate and pressure on viscosity. As a result, the pressure-viscosity coefficient acquired by the SLLOD algorithm approaches the experimental value. By combining the experimental outputs for viscosity at low strain rates (γ̇ < 104 s−1) with the SLLOD outputs at higher rates (γ̇ > 105 s−1), the evolutions of glycerol viscosity with pressure and strain rate were ultimately achieved. Implementing this computational platform depicts the shear thinning process in pure glycerol in a wide range of pressures and strain rates.

Post-impact squeeze-out behavior of oils with different pressure-dependent rheological properties

The rapid approach of surfaces significantly increases pressure and viscosity of lubrication oil, trapping it in a dimple at the contact zone that requires time to be squeezed out. In this study, a measuring system was developed that utilized a ball-disk impact device and light interference technology to investigate the post-impact squeeze-out behavior of oils. Dimple shape evolution varied depending on the pressure-dependent rheological properties of the oils. Specifically, higher pressure–viscosity coefficients resulted in greater reduction in dimple radius, whereas lower pressure–viscosity coefficients led to quicker collapse in dimple height, providing a qualitative criterion for comparing pressure-dependent rheological properties of oils. Additionally, effect of initial dimple height and external load on the squeeze-out behavior were investigated.

Correlation between Lubricating Oil Characteristic Parameters and Friction Characteristics

In order to help one to judge the friction properties of lubricating oils without tests, this paper intends to establish the correlation between the characteristic parameters of lubricating oils and the friction properties. The elastohydrodynamic and boundary friction properties of poly alpha olefin (PAO) synthetic oil, polyol ester oil and paraffin-based mineral oil were tested using a Mini-Traction Machine. Fourier transform infrared microscopy is used to identify material changes before and after friction tests. The kinematic and dynamic viscosities of the three lubricating oils were measured using a petroleum product viscosity tester and a rotating rheometer. The results show that the kinematic viscosity does not directly determine the COF (coefficient of friction) of the lubricating oil, but the higher the dynamic viscosity, the higher the COF of the lubricating oil. The higher the viscosity-pressure coefficient, the lower the viscosity index (the worse the viscosity-temperature performance), and the higher the COF of the lubricating oil, which is related to the adaptability of the molecular structure of lubricating oils to pressure and temperature. PAO synthetic oils and polyol ester oils have excellent friction properties resulting from their strong adaptability to temperature and pressure variations due to the presence of linear chains and flexible groups.

Thickening Properties of Carboxymethyl Cellulose in Aqueous Lubrication

Increasingly restricted availability and environmental impact of mineral oils have boosted the interest in sustainable lubrication. In this study, the thickening properties of sodium carboxymethyl celluloses (CMCs) were investigated in order to assess their potential as viscosity modifiers in aqueous gear and bearing fluids. The pressure, temperature and shear dependence of viscosity was studied at different concentrations and molecular weights MW. The tribological properties were investigated at different viscosity grades in both sliding and rolling contact, and compared to rapeseed oil and polyethylene glycol 400. The viscosity of the CMC solutions was adjustable to all application-relevant viscosity grades. Viscosity indices were similar or higher compared to the reference fluids and mineral oil. Temporary and permanent viscosity losses increased with MW. Permanent viscosity loss was highest for high MW derivatives, up to 70%. The pressure-viscosity coefficients α were low and showed a high dependency on shear and concentration. In rolling contact, low MW CMC showed up to 35% lower friction values compared to high MW, whereas no improvement of lubricating properties was observed in sliding contact. The results suggest that low MW CMC has great potential as bio-based thickener in aqueous lubrication.

Quantifying the inlet pressure and shear stress of elastohydrodynamic lubrication

Central film thickness in elastohydrodynamic lubrication is governed by lubricant properties in the low-pressure contact inlet. A relevant definition of pressure-viscosity coefficient would require knowledge of the maximum inlet pressure. The maximum inlet shear stress determines if the Newtonian assumption is valid. Using numerical simulations, the maximum inlet pressure is found, wherein changes in viscosity continue to influence film thickness. It is found to depend on operating conditions, and it ranges from 50 to 185 MPa. The maximum inlet shear stress is found to reach up to 2 MPa. Analytical formulas are offered for predicting maximum inlet pressure and shear stress. These allow for a refined definition of the pressure-viscosity coefficient, restricted to a clearly-defined contact inlet.

A Comparison of the High-Pressure Viscometry and Optical Inference Methods Used to Determine the Pressure-Viscosity Coefficient

Abstract Pressure-viscosity coefficients (PVC) are used in the predictions of elastohydrodynamic lubricated (EHL) componentry. These coefficients are obtained by either viscometry or optical EHL inference. The literature indicates that each method differs in its conclusion. Those who favor viscometry believe optical methods yield a misleading coefficient. Those who favor optical methods suggest low shear viscometric results over-predict the high shear-influenced film thickness. This work compares each method relative to di-(ethylhexyl) sebacate (DEHS), and five MIL and DOD spec lubricants. PVC results from viscometry and two optical methods are presented. Comparisons are made relative to other published measurements. Conclusions show PVCs inferred from optical film thickness measurements, differ from those obtained by viscometry. Viscometry methods are demonstrated as being consistent. Optically inferred results have uncertainty and require ample data to align with classical dimensionless speed exponents. While the optical measurements are truly EHL, the test conditions fall outside the fitted window of classical algebraic film equations, like that of Hamrock and Dowson. The PVC discrepancies, between optical inference and viscometry and for the studied fluids, cannot be explained by the proper account of the refractive index, shear thinning models, and/or film thickness correction models.

High-Pressure Thermophysical Properties of Eight Paraffinic, Naphthenic, Polyalphaolefin and Ester Base Oils

In this work, the thermophysical properties of four mineral (paraffinic and naphthenic) and four synthetic (polyalphaolefin and ester) base oils are measured. Knowledge of these properties is of vital importance for the correct and optimal formulation and design of lubricants, and for the development of equations of state and transport models that adequately represent their properties. Density, isothermal compressibility, thermal expansion coefficient, dynamic viscosity, pressure–viscosity coefficient, and contact angle were determined. To carry out this work, a pρT apparatus, a rotational viscometer, a falling body viscometer, and a contact angle analyzer were used. Highest densities were found for the polyalphaolefin and ester synthetic oils, increasing around 5% from 0.1 to 100 MPa for all the base oils. The density of the synthetic oils is less dependent on temperature changes. For the expansivity and compressibility of all the base oils, decreases with pressure of up to 35% and 45% were observed. From the contact angle measurements, it was observed that base oils with a higher viscosity grade have a worse wetting. The greatest effect of pressure on the dynamic viscosity was obtained for the naphthenic mineral oil and the lowest effect for the polyalphaolefin oil. Paraffinic and naphthenic oils present the highest universal pressure–viscosity coefficients.

Electrokinetic energy conversion of high pressure-driven flow with pressure-viscosity effect at high zeta potential

In this study, the electrokinetic energy conversion efficiency is investigated theoretically in high pressure-driven flow with the pressure-viscosity effect. Calculations of the electrokinetic flow in a straight nanochannel are based on the Poisson-Boltzmann equation and modified fluid momentum equation. Once the viscosity of fluid is dependent on the pressure, the strongly non-linear governing equation should be solved simultaneously due to the unknown fluid viscosity. Thus, the domain perturbation method is used to solve the distributions of flow velocity and pressure. Based on obtained velocity and pressure, the maximum conversion efficiency is calculated by thermodynamic analysis. Results show the maximum efficiency increases with the decrease of salt concentration and the peak efficiency can be obtained at sufficiently low salt concentration. For a given salt concentration, the maximum efficiency decreases monotonously with the increase of pressure-viscosity coefficient. Besides, the maximum energy conversion efficiency of ignoring the pressure-viscosity effect is larger than that of considering the pressure-viscosity effect.

ANALYTICAL AND NUMERICAL SOLUTIONS FOR SOME

Oscillatory motions of incompressible viscous fluids with exponential dependence of viscosity on the pressure between infinite horizontal parallel plates are analytically and numerically studied. The fluid motion is generated by the lower plate that oscillates in its plane and exact expressions are established for the steady-state solutions. The convergence of starting solutions to the corresponding steady-state solutions is graphically proved. The steady solutions corresponding to the simple Couette flow of the same fluids are obtained as limiting cases of the previous solutions. As expected, the fluid velocity diminishes for increasing values of the pressure-viscosity coefficient and ordinary fluids flow faster. The time required to reach the steady-state is graphically approximated. The spatial profiles of the starting solutions are presented both for oscillatory motions and the simple Couette flow.

The electrokinetic energy conversion analysis of Newtonian fluids with pressure-dependent viscosity in rectangular nanotube

In this work, a theoretical analysis for the streaming potential and the electro-kinetic energy conversion (EKEC) efficiency of Newtonian fluids with pressure-dependent viscosity in rectangular nanotube was developed. Accordingly, the dimensionless velocity, dimensionless streaming potential, dimensionless pressure and the electrokinetic energy conversion (EKEC) efficiency are obtained by using the perturbation method expanded in terms of the pressure-viscosity coefficient based on a linear dependent relationship between viscosity and pressure. The results indicate that with pressure-viscosity coefficient, the pressure required to drive the flow increases sharply. Also as pressure-viscosity coefficient increases, the streaming potential and EKEC efficiency decreases gradually, contrary to velocity. It is worth noting that within the given parameter range, the maximum efficiency obtained by present analysis is about 0.19% when pressure viscosity coefficients is 0.001. Moreover, appropriately adjusting ratio of channel width to height and the geometrical aspect ratio of the nanotube can improve effectively the streaming potential and the EKEC efficiency.

Viscosity and Density Measurements of Poly(ethyleneglycol) 200 and Poly(ethyleneglycol) 600 at High Pressures

New measurements for the viscosity and density of poly(ethyleneglycol) 200 [PEG 200] and of poly(ethyleneglycol) 600 [PEG 600], at pressures up to 50 MPa, are presented. The temperature range of the measurements performed for PEG 200 was from 293 to 348 K and for PEG 600 was from 303 to 348 K. A vibrating wire viscometer operated in the steady-state mode was used to carry out the measurements with an estimated overall uncertainty less than U(η) = 0.02·η, for viscosities up to 68 mPa s, and less than U(η) = 0.026·η, for higher viscosities with a confidence level of 0.95 (k = 2). Complementary density measurements for both PEGs were performed in the same ranges of temperature and pressure as for the viscosity measurements, using an Anton Paar HP vibrating tube densimeter, with an estimated overall uncertainty of about U(ρ) = 0.002·ρ with a confidence level of 0.95 (k = 2). Moreover, pressure–viscosity coefficients were obtained for both PEGs. A method based on a dense hard-sphere fluid theory was used to correlate the viscosity data with the density, for both PEGs, with a deviation of the experimental results less than 1%. A modified Tait equation was used to correlate the density results with temperature and pressure.

A Proposed Pressure–Viscosity Coefficient Model Through Processing of Falling Body Viscometry Data for Di-(Ethylhexyl) Sebacate

Abstract The relative volume and falling body viscosity of a common high-pressure rheology reference lubricant, di-(2-ethylhexyl) sebacate (DEHS), are presented. Relative volume measurements up to 300 MPa are completed with a piezo-bellows relative volume cartridge. Viscosity measurements up to 1 GPa are completed with a pressurized falling body viscometer. Digital signal-processing routines used for viscosity and relative volume measurements are discussed. The viscosity data are then fit into the modified Yasutomi model. Integration of this fit, as well as that of other models found in the literature, is used to propose a pressure–viscosity coefficient model. Comparisons are first made to DEHS, followed by the application of the study results to 17 other well-documented fluids. The validity of this method is investigated using the integrated viscosity model of DEHS as well as other available datasets presented in literature. The authors perform a comparison between the calculated pressure–viscosity coefficient α* and those presented for the mentioned datasets created with the signal-processing routines. The analysis shows that the proposed pressure–viscosity coefficient model is able to accurately capture the inverse of the asymptotic isoviscous pressure response of the majority of data when compared to other calculation methods.

High-Temperature Superlubricity Realized with Chlorinated-Phenyl and Methyl-Terminated Silicone Oil and Hydrogen-Ion Running-in.

Ceramic friction pairs lubricated with chlorinated-phenyl and methyl-terminated silicone oil (CPSO) systems have potential applications in the aerospace industry. In this study, the effects of the running-in process and temperature on the lubricating performance of CPSO were investigated. The superlubricity of Si3N4/sapphire lubricated with CPSO was realized at >190 °C after H+-ion running-in. The mechanism of this high-temperature superlubricity was investigated by determining the stable adsorption configurations and adsorption energies of CPSO on different surfaces using density functional theory calculations. Compared with that on the Si3N4 surface, the adsorption capacity of CPSO on the hydroxylated SiO2 surface generated by H+-ion running-in increased, whereas the steric hindrance decreased. The viscosity-temperature curve of CPSO was measured, wherein the viscosity and pressure-viscosity coefficient of CPSO considerably decreased with increasing temperature, leading to high-temperature superlubricity in a wide speed/load range. This is the first paper to report oil-based superlubricity at temperatures of 190 °C, or even higher-temperature conditions. Furthermore, it provides guidance for the use of ceramic-CPSO systems in high-temperature conditions, including in the aerospace industry.

Long-time solutions for some mixed boundary value problems depicting motions of a class of Maxwell fluids with pressure dependent viscosity

Closed-form expressions are established for dimensionless long-tome solutions of some mixed initial-boundary value problems. They correspond to three isothermal unsteady motions of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure. The fluid motion, between infinite horizontal parallel flat plates, is induced by the lower plate that applies time-dependent shear stresses to the fluid. As a check of the obtained results, the similar solutions corresponding to the classical incompressible Maxwell fluids performing same motions are recovered as limiting cases of present solutions. Finally, some characteristics of fluid motion as well as the influence of pressure-viscosity coefficient on the fluid motion are graphically presented and discussed.

Study on Factors Influencing Film Formation of Grease and Calculation Model for Grease Film Thickness

The grease film thickness was measured in fully flooded elastohydrodynamic lubrication, and the influence of rolling speed, load, consistency, base oil type and thickener type on grease film thickness was analyzed. A new calculation model for grease film thickness was established. The results show that the grease film thickness increases with the increasing rolling speed, and then levels off with the amount of thickener in the contact region reaching an equilibrium. The degree of grease film enhancement comparing to its base oil will depend on thickener type and consistency. The larger the atmospheric viscosity and pressure-viscosity coefficient of the base oil, the higher the film thickness of the greases with the same thickener. The grease film thicknesses with the same base oil and different thickeners are determined by the size of thickener particles at the same consistency or concentration. The larger the consistence of the grease, the larger the effective viscosity of the grease at the contact and the thicker the grease film thickness whose base oil has the same type and viscosity along with the same type of thickener. The calculated values by the new model are in good agreement with the measured values.

The rheological model of biodiesels at elevated pressures and temperatures

Abstract In the present study, an approximation is used to study viscosity as a function of pressure at different temperatures. The correlation so obtained is applied to study the viscosity of biodiesels extracted from soybean, Vistive soybean, canola, used canola, coconut and rapeseed. The computed values of viscosity from the proposed model were found to be in good agreement with experimental data throughout the range of pressure and temperature studied. The maximum average absolute relative deviation (AARD%) and mean AARD% are found to be 0.52 and 0.20, respectively, over the entire range of pressure (0.1–140 MPa) and temperature (283.15–373.15 K) for all biodiesels except rapeseed biodiesel, for which the values are 1.1 and 0.62, respectively. Furthermore, this work includes the very first investigation conducted so far on the variation of the pressure–viscosity coefficient (PVC) with pressure at different temperatures for biodiesels. The variation in PVC with the temperature is more sensitive at elevated pressures as compared to atmospheric pressure whereas the variation in PVC with pressure is more sensitive at elevated temperatures as compared to room temperature.