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Temperature- and pressure-dependent elastic properties (static and dynamic shear and bulk moduli) of porous rocks are investigated in terms of the characteristics of pore microstructures (i.e., crack density, crack porosity, and crack aspect-ratio distribution). Based on the Mori–Tanaka (MT) and David–Zimmerman (DZ) models, we correlated elastic properties with these microstructural characteristics and indicated that these microstructural properties can be estimated from dynamic and static moduli that are measured by considering the joint effect of thermal stress and confining pressure. Experiments with a tight sandstone under the saturated condition show that the cumulative crack density and porosity obtained from static moduli are higher than those from dynamic moduli. We demonstrated that the MT and DZ models can be used to describe the temperature- and pressure-dependent microstructures using static and dynamic properties. The dynamic bulk compressibility and shear compliance decrease with increasing confining pressures and decreasing temperatures, whereas the corresponding static values experience complex variations due to the joint effect of thermal stress and confining pressure. For the domination of thermal stress exerted by an increase in temperature, the widening of earlier formed micro-cracks during heating reduces the static moduli. However, during the domination by confining pressure, pre-existing micro-cracks will be closed with increasing temperatures, which increases the static moduli. These static elastic properties (Young’s modulus, bulk modulus, and Poisson’s ratio) share a similar exponential trend with the ratio of thermal stresses to confining pressures, which can be used to correlate dynamic and static moduli.HighlightsWe illustrate temperature- and pressure-dependent pore microstructures jointly using static and dynamic moduli based on the Mori-Tanaka and David-Zimmerman models.Experiments with a saturated tight sandstone show that the cumulative crack density and porosity obtained from static moduli are higher than those from dynamic moduli.Static moduli share a similar exponential trend with the ratio of thermal stresses to confining pressures based on which we propose an approach to estimate static moduli from dynamic moduli.

A three-dimensional nonlinear strength criterion for rocks considering both brittle and ductile domains is proposed through the combination of the segmented meridian function and a generalized deviatoric function with one parameter. The segmented meridian function is composed of the Hoek–Brown criterion, the smoothing transition surface, and the modified Drucker–Prager cap model. Besides, two deviatoric functions characterizing the smoothness and convexity based on the Matsuoka–Nakai criterion are suggested to describe the initial yield stage (brittle domain) and compaction yield cap stage (ductile domain). To verify the accuracy of the proposed strength criterion, six representative sets of true triaxial experimental data were selected from the existing literature, including two types of rocks, namely Dunham dolomite, KTB amphibolite, Mizuho trachyte, and Westerly granite that are independent of hydrostatic pressure in the brittle domain, and Bentheim sandstone and Castlegate sandstone which are dependent on hydrostatic pressure in the brittle–ductile domain. The results show that the experimental data are evenly distributed on the surface of the failure envelope in the three-dimensional principal stress space, demonstrating that the proposed strength criterion can accurately describe and predict the strength change of rocks in both brittle and ductile domains.HighlightsA three-dimensional nonlinear strength criterion for rocks considering both brittle and ductile domains is proposed.The segmented meridian function is composed of the Hoek–Brown criterion, the smoothing transition surface, and the modified Drucker–Prager cap model.Two deviatoric functions characterizing the smoothness and convexity based on the Matsuoka–Nakai criterion are suggested to describe the initial yield stage (brittle domain) and compaction yield cap stage (ductile domain).

This work addresses spreading pressure dependence of real adsorbed solution theory (RAST) for mixed-gas adsorption equilibria using generalized Langmuir (gL) isotherm. Considering vacant sites as an integral part of competitive multicomponent adsorption on a constant adsorbent surface area, the gL isotherm properly accounts for surface heterogeneity and loading, adsorbate composition, and temperature dependence. We show the spreading pressure dependence of adsorbate activity coefficient expression in the RAST framework can be generated from the gL isotherm. The procedure is illustrated with a spreading pressure dependent adsorption nonrandom two-liquid activity coefficient model, and the results are validated for ten binary mixed-gas adsorption equilibria systems including two highly nonideal azeotropic systems.

Electrically induced bearing failure is a reoccurring problem in modern drive train designs. To predict this damage, electrical models of bearings are required. In these models, the permittivity of lubricants is often assumed to be constant. However, the permittivity is dependent on pressure and temperature. For operating temperatures and pressures of journal bearings, no investigation of the permittivity of the lubricant exists. For this purpose, this study investigates the pressure and temperature dependence of lubricant permittivity using specially fabricated model bodies with layered structures of steel, ceramic insulating layers and copper in a parallel plate capacitor setup. Tests were performed applying temperatures between 20 °C and 100 °C and pressures between 1 and 250 bar. A mineral oil and a polyalkylene glycol (PAG) oil were examined. Results show a clear dependence of the permittivity on pressure and temperature. The mineral oil exhibits stronger pressure sensitivity, while the PAG oil shows more pronounced temperature dependence. Empirical equations to describe the permittivity as a function of temperature and pressure are derived. These findings provide relevant input for the selection of lubricants used in electrical environments. They also support the development of predictive models for modern electrical and tribological systems.

Ninety years of high-pressure measurements with many different types of viscometers have shown that faster-than-exponential (super-Arrhenius) pressure dependence of viscosity is universal for glass-forming liquids and, therefore, all typical liquid lubricants. Dielectric spectroscopy at elevated pressure also yields super-Arrhenius response in the dependence on pressure of the primary relaxation time. In contrast, classical elastohydrodynamic lubrication (EHL) has gone to great lengths to ignore this phenomenon, including fictional accounts of the results of viscometry. As a result of this, classical EHL is unable to quantitatively account for one of the most important properties affecting friction at low sliding velocity, the low-shear viscosity. Differences in friction between similar liquids at low sliding velocity can be explained by their different inflection pressures. Some observed liquid response to shear stress at high pressure can be explained with the measured super-Arrhenius pressure dependence. It should be clear that, had classical EHL employed realistic pressure dependence of viscosity from its beginning, the field would have been in a better position today to solve engineering problems which involve the differences among molecular structures.

That classical elastohydrodynamic lubrication (EHL) is not a quantitative field can be illustrated by its failure to provide a consistent and rigorous definition of the viscosity-pressure coefficient. Indeed, if the pressure dependence of viscosity cannot be accurately described, then the viscosity-pressure coefficient cannot be defined. Classical EHL has employed fictional narratives to justify the pressure dependences that have been utilized. In this context, the purpose of this perspective article is to review specific and real needs from EHL and to show that data and models describing the viscosity-pressure dependence are already available and how they can properly be used. The final aim is to encourage researchers to change their philosophy of classical EHL to a quantitative approach, in which every hypothesis and every result, whether experimental or numerical, would be justified on the basis of acceptable physics.

Topology optimization (TopOpt) is a mathematical-driven design procedure to realize optimal material architectures. This procedure is often used to automate the design of devices involving flow through porous media, such as micro-fluidic devices. TopOpt offers material layouts that control the flow of fluids through porous materials, providing desired functionalities. Many prior studies in this application area have used Darcy equations for primal analysis and the minimum power theorem (MPT) to drive the optimization problem. But both these choices (Darcy equations and MPT) are restrictive and not valid for general working conditions of modern devices. Being simple and linear, Darcy equations are often used to model flow of fluids through porous media. However, two inherent assumptions of the Darcy model are: the viscosity of a fluid is a constant, and inertial effects are negligible. There is irrefutable experimental evidence that viscosity of a fluid, especially organic liquids, depends on the pressure. Given the typical small pore-sizes, inertial effects are dominant in micro-fluidic devices. Next, MPT is not a general principle and is not valid for (nonlinear) models that relax the assumptions of the Darcy model. This paper aims to overcome the mentioned deficiencies by presenting a general strategy for using TopOpt. First, we will consider nonlinear models that take into account the pressure-dependent viscosity and inertial effects, and study the effect of these nonlinearities on the optimal material layouts under TopOpt. Second, we will explore the rate of mechanical dissipation, valid even for nonlinear models, as an alternative for the objective function. Third, we will present analytical solutions of optimal designs for canonical problems; these solutions not only possess research and pedagogical values, but also facilitate verification of computer implementations. Graphical Abstract We have considered a pressure-driven problem with axisymmetry and got optimal material layouts using topology optimization by maximizing the total rate of dissipation. The left figure shows unphysical finger-like design patterns when the primal analysis does not enforce explicitly the underlying radial symmetry. The right figure shows that one can avoid such numerical pathologies if the primal analysis invokes axisymmetry conditions.

Nanoporous aerogels are excellent thermal insulation materials with thermal conductivities down to about 0.012 W m −1  K −1 at ambient conditions. So far, it was assumed that the total thermal conductivity of aerogels can be described by a simple superposition of the different individual heat transport contributions. However, recent investigations reveal that thermal coupling effects can result in a gas pressure dependent contribution that may be up to three times higher than expected from just a gas phase thermal conductivity, which is predicted by the Knudsen equation at given porosity and pore size. In this study, we use data from previous publications covering a gas pressure range from 10 −5 to 10 MPa and analyze systematically the impact of pore size as well as solid phase and gas phase thermal conductivity on the coupling effect. The goal is to evaluate the data with respect to practical implications for aerogels in general. This means using the gas pressure dependence of the thermal conductivity of aerogels to determine their average pore size as well as allowing for a targeted optimization of aerogel-based insulations for applications at given gas pressure and temperature. Graphical Abstract

Use has been made of the Pitzer ion-interaction or virial coefficient approach to estimate the pressure dependence of the osmotic and activity coefficients of aqueous solutions of sodium nitrate (NaNO3) up to 423.15 K and 6.0 mol·kg−1 using published volumetric data on NaNO3(aq). In particular, volumetric Pitzer ion-interaction parameters have been evaluated from a mathematical fit of published apparent molar volume data with the appropriate Pitzer equation. The Pitzer parameters were then fitted as a function of temperature and pressure. These results were then used to calculate the change in the osmotic and activity coefficients in going from the state of an initial pressure p1 to one of a final pressure p2. These pressure dependences have been combined with the osmotic and activity coefficient values of NaNO3(aq) at 0.1 MPa or vapor-saturation pressures (psat) obtained from the model of Archer to yield a comprehensive set of thermodynamic parameters for NaNO3(aq) at temperatures from 293.15 K through 423.15 K, at pressures of (5, 10, 15, 20) MPa, and molalities to 6.0 mol·kg−1.

The flammable propane–air mixtures raise specific safety and environmental issues in the industry, storage, handling and transportation; therefore dilution of such mixtures has gained significant importance from the viewpoint of fire safety, but also due to nitrogen oxide’s emission control through flameless/mild combustion. In this paper, the propagation of the flame in C3H8-air-diluent stoichiometric gaseous mixtures using Ar, N2 and CO2 as diluents was investigated. Data were collected from dynamic pressure-time records in spherical propagating explosions, centrally ignited. The experiments were done on stoichiometric C3H8-air + 10% diluent mixtures, at initial pressures within 0.5–2.0 bar and initial temperatures within 300–423 K. The flame velocity was determined from laminar burning velocities obtained using the pressure increase in the incipient stage of flame propagation (when the pressure increase is lower than the initial pressure). The experimental propagation velocities were compared with computed ones obtained from laminar burning velocities delivered by kinetic modeling made using the GRI mechanism (version 3.0) with 1D COSILAB package. The thermal and baric coefficients of propagation velocity variation against the initial temperature and pressure are reported and discussed.