Pressure Dependence Of Viscosity Research Articles

Falkner–Skan boundary layer flow of a fluid with pressure-dependent viscosity past a stretching wedge with suction or injection

In this paper we study the boundary layer flow of a particular class of non-Newtonian fluids, namely piezo-viscous fluids, past a stretching wedge (Falkner–Skan flow). These fluids are essentially Navier–Stokes fluids with pressure-dependent viscosity. We consider the two-dimensional steady flow and introduce some similarity variables, so that the problem is reduced to a third-order nonlinear BVP. We solve the problem numerically by means of a shooting procedure combined with Newton’s method, and we find local similarity solutions. We investigate the behaviour of the velocity field, of the drag and of the thickness of the boundary layer for different values of the involved parameters, making a comparison between the piezo-viscous and the Newtonian case. We find that, depending on some material parameters, the effect of pressure is that of reducing or increasing the boundary layer with respect to the Newtonian case.

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.

Relation between rheological properties and the stress state in subducting slabs

The distribution of different stress states in the subducting slab indicated by centroid moment tensor solutions for intra-slab earthquakes can help constrain the rheological properties of the slabs. A comparison of slabs in the western and eastern Pacific realms shows contrasting patterns in the stress states down to depths of ~ 350 km. The majority of slabs in the western Pacific show a pair of down-dip compression (DC) and down-dip tension (DT) domains in the upper and lower parts of the slab reflecting the effects of the slab unbending during progressive subduction. In contrast, slabs in the eastern Pacific show predominantly in-plane DT stress irrespective of slab geometry. Two-dimensional numerical simulations assuming constant slab thickness and viscosity indicate that the development of slabs with in-plane DT stress at depths of 100–300 km requires the slabs to be thin and have a low viscosity (1023 Pa s). Weak slabs bend easily and tend to fold when they encounter increased resistance to downward movement at the 660-km boundary. The associated DC stresses are not transmitted up the slab so negative buoyancy of the slab and DT stress dominates at intermediate depths for this type of slab. Most experimentally derived rheological parameters predict a high viscosity (> 1024 Pa s) for such slabs. However, two-dimensional numerical simulations using temperature- and pressure-dependent viscosity show that a relatively low activation energy (~ 110 kJ/mol) for diffusion creep is a possible explanation for the observed distribution of stresses in the slabs. Such low activation energies are compatible with recent experimental work on diffusion creep of polyphase mantle materials in which a low effective activation energy for creep results from a slow grain growth due to pinning effect of the secondary phase. The simulations provide a mechanical explanation for the observed dominantly DT stress state at 100–300 km depths for young slabs and paired DT and DC stress states at the same depth range for old slabs.Graphical

Toward a continuum description of lubrication in highly pressurized nanometer-wide constrictions: The importance of accurate slip laws.

The Reynolds lubrication equation (RLE) is widely used to design sliding contacts in mechanical machinery. While providing an excellent description of hydrodynamic lubrication, friction in boundary lubrication regions is usually considered by empirical laws, because continuum theories are expected to fail for lubricant film heights h0 ≪ 10 nm, especially in highly loaded tribosystems with normal pressures pn ≫ 0.1 GPa. Here, the performance of RLEs is validated by molecular dynamics simulations of pressurized (with pn = 0.2 to 1 GPa) hexadecane in a gold converging-diverging channel with minimum gap heights h0 = 1.4 to 9.7 nm. For pn ≤ 0.4 GPa and h0 ≥ 5 nm, agreement with the RLE requires accurate constitutive laws for pressure-dependent density and viscosity. An additional nonlinear wall slip law relating wall slip velocities to local shear stresses extends the RLE's validity to even the most severe loading condition pn = 1 GPa and h0 = 1.4 nm. Our results demonstrate an innovative route for continuum modeling of highly loaded tribological contacts under boundary lubrication.

Effect of variable viscosity, porous walls and mixed thermal boundary condition on the onset of Rayleigh-Bénard convective instability

In this paper, we have studied the criteria for the onset of instability in the Rayleigh-Bénard convection problem, by considering a fluid layer confined between two infinitely extended rough boundaries, which are subjected to mixed-type thermal boundary conditions, physically representing the imperfectly conducting boundaries. The rough boundaries are assumed to be shallow porous layers with different pore size, properties, and permeabilities. Mathematically, it is given by the Saffman type boundary condition. Therefore, we have two generalized forms of boundary conditions, one for the flow field and the other for the thermal field. The two limiting cases of the mixed-type thermal boundary condition correspond to a perfectly conducting boundary and to a perfectly insulating boundary, whereas the two limiting cases of the hydrodynamic boundary condition correspond to a no-slip condition and to a free-surface condition, depending upon the limiting values of the parameters involved in these two generalized boundary conditions. The linear and nonlinear energy stability analyses are performed, and the existence of the region of subcritical instability is checked. Through the principle of exchange of stability analysis, it is found that the instability occurs only in the stationary mode. The adiabatic boundary condition is found to be more restrictive than the isothermal boundary condition. Under given conditions, the instability is observed to be occurring in the infinite wavelength mode for the case of adiabatic boundaries. In the present work, the effect of temperature and pressure dependent viscosity on the stability of the system has been shown and found to be of destabilizing nature. However, the roughness of the boundaries is found to be of stabilizing nature.

Flow Governed by Generalised Brinkman’s Equation through an Inclined Porous Channel

The unidirectional flow of a fluid with pressure-dependent viscosity through a porous structure is considered when the viscosity–pressure relationship is an exponential function of a pressure power function in order to investigate effects of the viscosity–pressure relation on the flow characteristics. The flow is governed by the generalized Brinkman’s equation with constant permeability, and a model flow domain of flow down an inclined porous channel is chosen for the sake of studying flow behaviour. Although the current work considers flow in a constant permeability porous structure, it does represent the first step in studying the more general flow through a variable permeability porous channel. The arising governing equations are solved numerically using MATLAB (version R2022a) and the flow is simulated to illustrate the effects of fluid properties, as well as flow and medium parameters, on the velocity profiles and shear stress. The results obtained should represent a baseline and a benchmark with which future experimental and theoretical work can be compared.

Modelling of the porous medium flow with pressure-dependent viscosity and drag coefficient

Abstract In this paper we consider the porous medium flow through a corrugated channel where the viscosity of the fluid can significantly change with the pressure. Assuming the exponential dependence of the viscosity and drag coefficient on the pressure, we propose the higher-order approximation of the solution to the nonlinear boundary-value problem governing the flow. To accomplish that, we combine the concept of the transformed pressure with asymptotic techniques.

Influence of lubricant material in the point contact zone of rolling friction on fatigue life for friction bearing units

Although lubrication is necessary for the satisfactory operation of rolling bearings, the effect of lubricant on the fatigue life of the bearing has not been sufficiently studied. In recent times, the theory of elastohydrodynamic (EHD) lubrication [1] has been used to explain the different effects of lubricants. According to this theory, the thickness of the lubricating layer separating the moving elements of the bearing is determined by the viscosity-pressure dependence of the lubricant. The contact of surface micron irregularities does not occur if it is possible to maintain a sufficient thickness of the lubricating layer - in this case, the long-term durability of the bearing is ensured. If the film thickness is reduced to a level where surface irregularities are encountered, the fatigue life rapidly decreases with increasing contact frequency. In any case, a comprehensive calculation methodology is needed that would allow to take into account the influence of lubricant on the fatigue life of bearing units.

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.

On lower-dimensional models of thin film flow, Part C: Derivation of a Reynolds type of equation for fluids with temperature and pressure dependent viscosity

This paper constitutes the third part of a series of works on lower-dimensional models in lubrication. In Part A, it was shown that implicit constitutive theory must be used in the modelling of incompressible fluids with pressure-dependent viscosity and that it is not possible to obtain a lower-dimensional model for the pressure just by letting the film thickness go to zero, as in the proof of the classical Reynolds equation. In Part B, a new method for deriving lower-dimensional models of thin-film flow of fluids with pressure-dependent viscosity was presented. Here, in Part C, we also incorporate the energy equation so as to include fluids with both temperature and pressure dependent viscosity. By asymptotic analysis of this system, as the film thickness goes to zero, we derive a simplified model of the flow. We also carry out an asymptotic analysis of the boundary condition, in the case where the normal stress is specified on one part of the boundary and the velocity on the remaining part.

Three‐dimensional numerical simulation on fiber orientation of short‐glass‐fiber‐reinforced polypropylene composite thin‐wall injection‐molded parts simultaneously accounting for wall slip effect and pressure dependence of viscosity

AbstractOn account of the inherent features of the thin‐wall injection molding process, a three‐dimensional numerical model, which accounts for wall slip effect and pressure dependence of viscosity (PDoV), was proposed for a more accurate simulation of the fiber orientation in thin‐wall injection‐molded parts of short‐glass‐fiber‐reinforced polymer composites (SGFRPC). First, the fiber orientation was simulated using the three‐dimensional and mid‐plane models, respectively. The comparison between the simulated and experimental results verifies that the three‐dimensional numerical results were in better agreement with the experimental measurements. Secondly, the influences of wall slip effect and PDoV on fiber orientation in thin‐wall injection‐molded parts of SGFRPC were analyzed based on the three‐dimensional numerical model. The results show that the three‐dimensional numerical simulation simultaneously accounting for wall slip effect and PDoV can better predict the fiber orientation in thin‐wall injection‐molded parts of SGFRPC, suggesting the validation of the proposed model. Finally, five main processing parameters, that is, injection rate, melt temperature, mold temperature, packing pressure, and packing time, were also studied in terms of their influences on the fiber orientation in thin‐wall injection‐molded parts of SGFRPC.

An improved prediction of frictional pressure drop using an accurate shear rate equation for high-yield stress drilling fluids at the surface and downhole conditions

This paper evaluates a more accurate and relatively new shear rate equation based on the phenomenological model for the high yield stress drilling fluids to estimate frictional pressure drop in laminar and turbulent flow regimes under surface and downhole conditions. Fann viscometer readings are used to determine shear rates using the above phenomenological model that differ from the conventional shear rates, i.e., γ˙(s−1)=1.7N, where N = Fann viscometer rotor rpm. The new shear rates are used to predict model parameters of Bingham plastic (BP), power-law (PL), Herschel–Bulkley (HB), and Robertson-Stiff (RS) models, and corresponding frictional pressure drops. The efficacy of the above rheology models with improved model parameters is tested by validating the literature-reported experimental pressure drop data of low to high yield stress water-based drilling fluids. The validation results are consistent and accurately predict frictional pressure drops using HB and RS models with the lowest MSE-values. The above methodology is applied to predict frictional pressure drops in a pipe for ten test high-pressure, high-temperature (HPHT) drilling fluids of varying base fluids at the surface and HPHT conditions in laminar and turbulent flow regimes. For this, isothermal compressibility and thermal decomposition temperature of drilling fluids are measured to forecast the temperature- and pressure-dependent densities and shear viscosities. The proposed density model is experimentally validated and found to predict density at downhole conditions adequately with mean absolute- and standard-deviation, i.e., 1.67 and 1.36%, respectively. Temperature- and pressure-dependent viscosity and density have been used to predict pressure drop under downhole conditions using HB and RS models with improved model parameters from the phenomenological model. The HB model is found to be more accurate than the RS model for predicting pressure drop. The proposed frictional pressure drop estimation method in the present study is more general and accurate under the surface and downhole conditions than the conventional practice.

Numerical investigation of the effect of surface viscosity on droplet breakup and relaxation under axisymmetric extensional flow

In this study, we perform boundary-integral simulations to investigate the role of interfacial viscosity in the deformation and breakup of a single droplet suspended in an axisymmetric extensional flow under the Stokes flow regime. We model the insoluble surfactant monolayer using the Boussinesq–Scriven constitutive relationship for a Newtonian interface. We compare the deformation and breakup results from our boundary-element simulations with results from small deformation perturbation theories. We observe that the surface shear/dilational viscosity increases/decreases the critical capillary number beyond which the droplet becomes unstable and breaks apart by reducing/increasing the droplet deformation at a given capillary number compared with a clean droplet. We present the relative importance of surface shear and dilational viscosity on droplet stability based on their measured values reported in experimental studies on surfactants, lipid bilayers and proteins. In the second half of the paper, we incorporate the effect of surfactant transport by solving the time-dependent convection–diffusion equation and consider a nonlinear equation of state (Langmuir adsorption isotherm) to correlate the interfacial tension with the changes in surfactant concentration. We explore the coupled influence of pressure-dependent surface viscosity and Marangoni stresses on droplet deformation and breakup. In the case of a droplet with pressure-dependent surface shear viscosity, we find that a droplet with pressure-thinning/thickening surfactant is less/more deformed than a droplet with pressure-independent surfactant. We conclude by discussing the combined impact of surface viscosity and surfactant transport on the relaxation of an initially extended droplet in a quiescent external fluid.

The extrusion of EPDM using an external gear pump: experiments and simulations

Abstract External gear pumps are used in fluid transport systems because of their tight clearances and accurate flow control. These tight clearances are a challenge for numerical studies in terms of spatial discretization. In earlier work, the flow of a viscous fluid in an external gear pump is computed using the finite element method (FEM). An element size based on the respective distance between boundaries is proposed. In this study, results based on the earlier work are compared to extrusion experiments of EPDM. The aim of this study is not only to validate the numerical simulations, but also to determine what material characteristics need to be taken into account for an accurate output prediction of the external gear pump. Especially the introduction of shear-thinning behavior results in an improvement of the amplitude of the pressure difference fluctuation. Taking into account compressibility, alters the torque fluctuation in such a way that it mimics the experiments. Unfortunately, the fluctuation in torque still has a too high amplitude. Eventually, simulations are performed including shear-thinning behavior, a temperature- and pressure-dependent viscosity, and compressibility. The effect of measuring the material behavior using oscillatory or shear experiments is shown. Furthermore, the simulations are applied to a second EPDM. Finally, different processing conditions are tested. For the simulations, only qualitative agreement is found, possibly as a result of the no slip boundary condition.

Modelling the anomalous shock response of titanium diboride

In planar shock compression experiments, polycrystalline titanium diboride ( TiB 2 ) often exhibits double-yield phenomena, atypical among non-transforming ceramics, in particle velocity histories. A finite-strain phase-field theory, with order parameters accounting for fracture and dilatation, followed by limited plastic slip and compaction, is specialized to study the uniaxial shock response of TiB 2 . The model accurately depicts longitudinal stress up to 120 GPa on the Hugoniot from multiple published sources, as well as shear stress inferred elsewhere from experimental shock data. A novel phase-field analysis enables one-, two- or three-wave structures depending on impact stress. These results are observed in experimental data and have not been successfully captured by prior numerical models. Results support the conjecture that (i) fracture and dilatation, followed by (ii) plastic deformation and compaction, and then (iii) fragmentation to a comminuted, viscous granular medium is a plausible sequence of physical mechanisms as shock stress increases. The first break in the velocity profile always corresponds to micro-cracking in the model, which correlates with the first yield point on the Hugoniot. In the three-wave regime, two plastic waves correlate with two yield points, where the first plastic wave after the precursor is due to fracture and the second dominated by plasticity. When impact is severe enough such that the second plastic wave overtakes the first, a single plastic waveform with multiple kinks emerges in particle velocity histories, consistent with some experimental data. These kinks are well explained by pressure-dependent viscosity in crack kinetics and by small-magnitude plastic deformation, and corresponding stress perturbations need not precisely correspond to particular cusps on the stress–volume Hugoniot.

Approximate solutions of the Riemann problem for a two-phase flow of immiscible liquids based on the Buckley–Leverett model

The article proposes an approximate method based on the "vanishing viscosity" method, which ensures the smoothness of the solution without taking into account the capillary pressure. We will consider the vanishing viscosity solution to the Riemann problem and to the boundary Riemann problem. It is not a weak solution, unless the system is conservative. One can prove that it is a viscosity solution actually meaning the extension of the semigroup of the vanishing viscosity solution to piecewise constant initial and boundary data. It is known that without taking into account the capillary pressure, the Buckley–Leverett model is the main one. Typically, from a computational point of view, approximate models are required for time slicing when creating computational algorithms. Analysis of the flow of a mixture of two immiscible liquids, the viscosity of which depends on pressure, leads to a further extension of the classical Buckley–Leverett model. Some two-phase flow models based on the expansion of Darcy’s law include the effect of capillary pressure. This is motivated by the fact that some fluids, e.g., crude oil, have a pressure-dependent viscosity and are noticeably sensitive to pressure fluctuations. Results confirm the insignificant influence of cross-coupling terms compared to the classical Darcy approach.

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.

Combined effects of elastic deformation and piezo-viscous dependency on the performance of a journal bearing operating with a non-Newtonian fluid

A theoretical study of the effects of elastic deformation and the variation of viscosity with pressure on the performance characteristics of a circular journal bearing lubricated with non-Newtonian fluids. The Barus law and the power law model are used to express the viscosity-pressure variation and the non-Newtonian behavior of fluids respectively. To determine the displacement field at the fluid film bearing liner interface, the elastic thin liner model is used. The modified Reynolds equation accounting the viscosity pressure dependency in the non-Newtonian fluids is mathematically derived and solved using finite difference method, to obtain the fluid film pressure field. The static performance characteristics for finite-width journal bearing are evaluated for various values of pressure-viscosity coefficient, the power law index n, and the elastic deformation coefficient. According to the results obtained, it is found that the hydrodynamic pressure and non-dimensional load-carrying capacity increase as the power law index and pressure-viscosity coefficient increases especially for rigid and heavily loaded bearing case. In addition, the combined effects of the elastic deformation and the viscosity pressure dependency are found to be more pronounced on the performance characteristics of a heavily loaded journal bearing operating with a shear-thickening fluid.

Parallel Flow of a Pressure-Dependent Viscosity Fluid through Composite Porous Layers

Flow of a fluid with pressure-dependent viscosity through a composite of two porous layers is considered in this work in an attempt to validate velocity and shear stress continuity conditions at the interface, and are popular in the study of flow over porous layers and through composite layers when viscosity of the fluid is constant. For the current problem, conditions at the interface between the porous layers reflect continuity assumptions of velocity and shear stress, with additional continuity assumptions on pressure and viscosity. Viscosity is assumed to vary continuously and exponentially across the layers as a function of pressure. Analytical solutions are obtained to illustrate the effects of flow and media parameters (Darcy numbers, layer thicknesses, angle of inclination, and viscosity adjustment parameter) on the dynamic behaviour of pressure-dependent viscosity fluids in porous structures. All computations, simulations and graphs in this work have been carried out and obtained using Maple 2020 software package.

Volumetric and viscosity data of selected oils analyzed in the density scaling regime

In this paper, we have performed thorough analyses of volumetric and viscosity data for six oils. The volumetric data has been inspected by using two different equations of state, drawing a special attention to the intersection of the isothermal pressure dependences of the thermal volume expansivity, which were earlier reported for various materials in the liquid state. Each fluid is unique with respect to the other oils’ relative composition, with those being either a pure liquid (Sebacate), or mineral oil with a proprietary blend of branched paraffins, napthalenes and aromatic molecules (Normafluid) or are undisclosed composition of mineral oil (MIN-H01 and MIN-H02) or are composed of fatty acid methyl esters (soybean biodiesel and rapeseed biodiesel). We have confirmed that the intersection points evaluated for different isotherms constitute a nonlinear curve for a given tested oil, and not any single point or straight line. Consequently, we have determined the temperature–pressure areas important from the application viewpoint, within which the thermal volume expansivity behaves differently, either increasing or decreasing with increasing temperature at a constant pressure. In the viscosity analysis, the parametrizations of the temperature–pressure dependences of specific volume based on the equations of state enabled to employ the density scaling idea in its simplest form of a power law of densityγ/temperature, where γ related to an effective intermolecular potential is independent of thermodynamic conditions to a good approximation, which was successfully validated by various materials mainly in the supercooled liquid state, but also in the normal liquid and liquid crystal states in some cases. We have found that the scaling law giving prediction benefits relied on a linkage between macroscopic measurement quantities and effective molecular interactions is obeyed by the viscosity data of examined oils. Then, based on the prediction capabilities of the density scaling criterion, we have successfully explored the inflection points observed in some isothermal pressure dependences of viscosity measured for the oils in the temperature–pressure ranges that differ from those earlier reported for other materials. This intriguing finding observed in case of the experimental data for only some examined oils yields not only cognitive benefits, but it is also expected to exert an effect for instance on mechanical properties of the materials. Thus, our comparative discussion about the intersection and inflection curves provide a useful contribution to the further investigations of these thermodynamic and dynamic issues and other physicochemical properties of oils, which require gaining a better insight.