Pressure Dependence Of Viscosity Research Articles

Mathematical models for fluids with pressure-dependent viscosity flowing in porous media

In this paper we study three filtration problems through porous media, assuming that the viscosity of the fluid depends on pressure. After showing that in this case Darcy’s law is “formally” preserved (meaning that the formal relation remains unchanged except for viscosity that now depends on pressure), we focus on the following problems: Green–Ampt infiltration through a dry porous medium; the Dam problem; the Muskat problem. For each model (free boundary problems) we obtain explicit solutions that allow to quantify the detachment from the classical case, where with the word “classical” we mean that viscosity is taken constant.

Numerical solutions of Williamson fluid with pressure dependent viscosity

In the present paper, we have examined the flow of Williamson fluid in an inclined channel with pressure dependent viscosity. The governing equations of motion for Williamson fluid model under the effects of pressure dependent viscosity and pressure dependent porosity are modeled and then solved numerically by the shooting method with Runge Kutta Fehlberg for two types of geometries i.e., (i) Poiseuille flow and (ii) Couette flow. Four different cases for pressure dependent viscosity and pressure dependent porosity are assumed and the physical features of pertinent parameters are discussed through graphs.

Asymptotic solutions of weakly compressible Newtonian Poiseuille flows with pressure-dependent viscosity

We consider both the axisymmetric and planar steady-state Poiseuille flows of weakly compressible Newtonian fluids, under the assumption that both the density and the shear viscosity vary linearly with pressure. The primary flow variables, i.e. the two non-zero velocity components and the pressure, as well as the mass density and viscosity of the fluid are represented as double asymptotic expansions in which the isothermal compressibility and the viscosity–pressure-dependence coefficient are taken as small parameters. A standard perturbation analysis is performed and asymptotic, analytical solutions for all the variables are obtained up to second order. These results extend the solutions of the weakly compressible flow with constant viscosity and those of the incompressible flow with pressure-dependent viscosity. The combined effects of compressibility and the pressure dependence of the viscosity are analyzed and discussed.

A note on the unbounded creeping flow past a sphere for Newtonian fluids with pressure-dependent viscosity

We investigate theoretically isothermal, incompressible, creeping Newtonian flows past a sphere, under the assumption that the shear viscosity is pressure-dependent, varying either linearly or exponentially with pressure. In particular, we consider the three-dimensional flow past a freely rotating neutrally buoyant sphere subject to shear at infinity and the axisymmetric flow past a sedimenting sphere. The method of solution is a regular perturbation scheme with the small parameter being the dimensionless coefficient which appears in the expressions for the shear viscosity. Asymptotic solutions for the pressure and the velocity field are found only for the simple shear case, while no analytical solutions could be found for the sedimentation problem. For the former flow, calculation of the streamlines around the sphere reveals that the fore-and-aft symmetry of the streamlines which is observed in the constant viscosity case breaks down. Even more importantly, the region of the closed streamlines around the sphere is absent. Last, it is revealed that the angular velocity of the sphere is not affected by the dependence of the viscosity on the pressure.

A depth-averaged -rheology for shallow granular free-surface flows

AbstractThe $\mu (I)$-rheology is a nonlinear viscous law, with a strain-rate invariant and pressure-dependent viscosity, that has proved to be effective at modelling dry granular flows in the intermediate range of the inertial number, $I$. This paper shows how to incorporate the rheology into depth-averaged granular avalanche models. To leading order, the rheology generates an effective basal friction, which is equivalent to a rough bed friction law. A depth-averaged viscous-like term can be derived by integrating the in-plane deviatoric stress through the avalanche depth, using pressure and velocity profiles from a steady-uniform solution to the full $\mu (I)$-rheology. The resulting viscosity is proportional to the thickness to the three halves power, with a coefficient of proportionality that is angle dependent. When substituted into the depth-averaged momentum balance this term generates second-order derivatives of the depth-averaged velocity, which are multiplied by a small parameter. Its inclusion therefore represents a singular perturbation to the equations. It is shown that a granular front propagating down a rough inclined plane is completely unaffected by the rheology, but, discontinuities, which naturally develop in inviscid roll-wave solutions, are smoothed out. By comparison with existing experimental data, it is shown that the depth-averaged $\mu (I)$-rheology accurately predicts the growth rate of spatial instabilities to steady-uniform flow, as well as the dependence of the cutoff frequency on the Froude number and inclination angle. This provides strong evidence that, in the steady-uniform flow regime, the predicted decrease in the viscosity with increasing slope is correct. Outside the range of angles where steady-uniform flows develop, the viscosity becomes negative, which implies that the equations are ill-posed. This is a signature of the ill-posedness of the full $\mu (I)$-rheology at both high and low inertial numbers. The depth-averaged $\mu (I)$-rheology therefore cannot be used outside the valid range of angles without additional regularization.

Effect of temperature-dependent viscosity on mantle convection

Two-dimensional numerical calculations in cylindrical shell geometry have been carried out to investigate the effect of the temperature-dependent viscosity on the pattern and the characteristic parameters of the thermal convection occurring in the Earth’s mantle. Systematic model runs established that the viscosity decreasing with the temperature is reduced around the hot core-mantle boundary (CMB) which facilitates ‘the heat transport’ from ‘the core to the mantle’. On the other hand, the viscosity increases near the cold surface which hinders the heat outcome and results in higher mantle temperature and lower surface velocity. A power law relation was revealed between the strength of the temperature-dependence and the observed parameters, such as the velocity, surface mobility, heat flow, average temperature and viscosity. Two additional ‘mantle-like’ models were built up with extra strong temperature-dependent viscosity to imitate the flow in the Earth’s mantle. In model 1, in which the viscosity decreases seven orders of magnitude with the temperature increase, a highly viscous stagnant lid evolves along the cold surface which does not participate in the convection. The existence of the stagnant surface lid reduces the surface heat flow and generates a low viscosity asthenosphere beneath the lid with vigorous small-scale convection. In model 2, in which the viscosity decreases only six orders of magnitude with the temperature and the pressure-dependent viscosity is stronger, does not form a surface stagnant lid, highly viscous ‘slabs’ submerge to the CMB and effectively influence the hot upwelling plumes. Based on our numerical results it is necessary to implicate the yield stress into the simulations in order to obtain a highly viscous, ‘rigid’ surface lid, the lithosphere which can be broken up and subduct down to the mantle.

The pressure and temperature dependence of volume and viscosity of four Diesel fuels

The relative volumes and the viscosities of four Diesel fuels have been measured experimentally to pressures up to 350MPa and temperatures to 160°C. The experimental liquids were an extra low viscosity reference fuel, an ethanol based blend, neat biodiesel and 20% biodiesel. The Tait and Murnaghan equations of state represented the pressure–volume–temperature response equally well. The improved Yasutomi model for supercooling liquids, which accurately represents the temperature and pressure dependence of the viscosity of lubricating oils, did not fit the data well except for neat biodiesel. Surprisingly, the Doolittle free-volume equation was accurate only for the low viscosity reference fuel. The reason for the correlation difficulties may be illuminated by the behavior of the thermodynamic scaling of the viscosities. The Stickel analysis of the normalized Ashurst–Hoover parameter indicates that, for all liquids except the reference fuel, the measured viscosities lie across the transition in the response of viscosity to temperature and pressure. Consequently, only the comprehensive normalized Ashurst–Hoover scaling model successfully fits all data.

Viscosity of ionic liquids: an extensive database and a new group contribution model based on a feed-forward artificial neural network.

A knowledge of various thermophysical (in particular transport) properties of ionic liquids (ILs) is crucial from the point of view of potential applications of these fluids in chemical and related industries. In this work, over 13 000 data points of temperature- and pressure-dependent viscosity of 1484 ILs were retrieved from more than 450 research papers published in the open literature in the last three decades. The data were critically revised and then used to develop and test a new model allowing in silico predictions of the viscosities of ILs on the basis of the chemical structures of their cations and anions. The model employs a two-layer feed-forward artificial neural network (FFANN) strategy to represent the relationship between the viscosity and the input variables: temperature, pressure, and group contributions (GCs). In total, the resulting GC-FFANN model employs 242 GC-type molecular descriptors that are capable of accurately representing the viscosity behavior of ILs composed of 901 distinct ions. The neural network training, validation, and testing processes, involving 90, 5, and 5% of the whole data pool, respectively, gave mean square errors of 0.0334, 0.0595, and 0.0603 log units, corresponding to squared correlation coefficients of 0.986, 0.973, and 0.972 and overall relative deviations at the level of 11.1, 13.8, and 14.7%, respectively. The results calculated in this work were shown be more accurate than those obtained with the best current GC model for viscosity of ILs described in the literature.

Flows of Carreau fluid with pressure dependent viscosity in a variable porous medium: Application of polymer melt

The present work concerns the pressure dependent viscosity in Carreau fluid through porous medium. Four different combinations of pressure dependent viscosity and pressure dependent porous medium parameters are considered for two types of flow situations namely (i) Poiseuille flow and (ii) Couette flow. The solutions of non-linear equations have been evaluated numerically by Shooting method along with Runge-Kutta Fehlberg method. The physical features of pertinent parameters have been discussed through graphs.

Anomalous properties of water predicted by the BK3 model

Recently, we proposed a new model for water [P. T. Kiss and A. Baranyai, J. Chem. Phys. 138, 204507 (2013)]. We presented a detailed description of the development of this classical, polarizable model, and a large number of calculated properties. The model provided excellent estimates for ambient liquid properties and reasonably good results from high-pressure solids to gas-phase clusters. In this paper we present results of extensive calculations for temperature-dependent water anomalies in terms of the pressure. The calculated isobars of the temperature-density and the self-diffusion diagrams provide excellent estimates of the experimental values. The estimated compressibility isobars perfectly match the experimental ones if we shift our numbers by ∼10 K upwards. The calculated pressure-dependent viscosity values are excellent at higher temperatures and qualitatively correct at lower temperatures.

Classical EHL Versus Quantitative EHL: A Perspective Part I—Real Viscosity-Pressure Dependence and the Viscosity-Pressure Coefficient for Predicting Film Thickness

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.

Conditional stability for thermal convection in a rotating couple-stress fluid saturating a porous media with temperature- and pressure-dependent viscosity using a thermal non-equilibrium model

Abstract. A nonlinear stability threshold for convection in a rotating couple-stress fluid saturating a porous medium with temperature- and pressure-dependent viscosity using a thermal non-equilibrium model is found to be exactly the same as the linear instability boundary. This optimal result is important because it shows that linear theory has completely captured the physics of the onset of convection. The effects of couple-stress fluid parameter F, temperature- and pressure-dependent viscosity Γ, interface heat transfer coefficient H, Taylor number TA , Darcy–Brinkman number D ˜ a $\tilde{D}a$ , and porosity modified conductivity ratio γ on the onset of convection have been investigated. Asymptotic analysis for both small and large values of interface heat transfer coefficient H is also presented. An excellent agreement is found between the exact solutions and asymptotic solutions.

Effect of Surface Roughness and Viscosity-Pressure Dependency on the Couple Stress Squeeze Film Characteristics of Parallel Circular Plates

Combined effects of surface roughness and viscosity-pressure dependency on the couple stress squeeze film characteristics of parallel circular plates are presented. On the basis of Christensen’s stochastic theory, two types of one-dimensional roughness structures, namely, the radial roughness and azimuthal roughness patterns, are considered and the stochastic modified Reynolds equation for these two types of roughness patterns is derived for Stokes couple stress fluid by taking into account variation of viscosity with pressure. The standard perturbation technique is employed to solve the averaged Reynolds equation and closed form expressions for the mean fluid film pressure, load carrying capacity, and squeeze film time are obtained. It is found that the effects of couple stresses and viscosity-pressure dependency are to increase the load carrying capacity, and squeeze film time for both types of roughness patterns. The effect of azimuthal (radial) roughness pattern is to increase (decrease) these squeeze film characteristics as compared to the corresponding smooth case.

On the helical pipe flow with a pressure-dependent viscosity

We address the flow of incompressible fluid with a pressure-dependent viscosity through a pipe with helical shape. The viscosity-pressure relation is defined by the Barus law. The thickness of the pipe and the helix step are assumed to be of the same order and considered as the small parameter. After transforming the starting problem, we compute the asymptotic solution using curvilinear coordinates and standard perturbation technique. The solution is provided in the explicit form clearly showing the influence of viscosity-pressure dependence and pipe's geometry on the effective flow.

The motion of a piezoviscous fluid under a surface load

Using a variant of a spectral collocation method we numerically solve the problem of the motion of a highly viscous fluid with pressure dependent viscosity under a surface load, which is a problem relevant in many applications, in particular in geophysics and polymer melts processing. We compare the results with the results obtained by the classical Navier–Stokes fluid (constant viscosity). It turns out that for a realistic parameter values the two models give substantially different predictions concerning the motion of the free surface and the velocity and the pressure fields beneath the free surface.As a byproduct of the effort to test the numerical scheme we obtain an analytical solution—for the classical Navier–Stokes fluid—of the surface load problem in a layer of finite depth.

Investigation of temperature and pressure dependent equilibrium and transport properties of liquid acetone by molecular dynamics simulation

In this paper, equilibrium thermodynamic and transport properties of liquid acetone were studied by classical molecular dynamics simulation at P=1atm and T=280–330K, using OPLS force field. The simulated densities are quite in agreement with experiment (%AAD=2.0). Simulated viscosities based on Stokes–Einstein and Green–Kubo methods are agree with experiment with %AAD=13 and 4.1, respectively, which is reasonably good for OPLS force field. Also, the pressure dependent density and viscosity was simulated at low (320K) and high (398K) temperature in the range P=7.53–34.95MPa. The simulated density are comparable with experiment (%AAD=2.9 and 0.8 at 320K and 398K, respectively). Simulated viscosities by Green–Kubo formulism with respect to experiment (%AAD=2.9 and 4.8 at 320K and 398K, respectively) are much more accurate than by Stokes–Einstein method (%AAD=5.9 and 9.6 at 320K and 398K, respectively). Simulated viscosity versus pressure at 398K increases rather smoothly, however, at 323K it increases nonmonotonically with a marked inflection point characteristic of acetone and astonishingly maps an exact trend, mimicking the trend of experimental data accurately. These anomalous behaviors of the viscosities are a first report of such rend.

GLOBAL STABILITY FOR THERMAL CONVECTION IN A COUPLE-STRESS FLUID WITH TEMPERATURE AND PRESSURE DEPENDENT VISCOSITY

Abstract We show that the global nonlinear stability threshold for convection in a couple-stress fluid with temperature and pressure dependent viscosity is exactly the same as the linear instability boundary. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It has also been found that the couplestress fluid is more stable than the ordinary viscous fluid and then the effect of couple-stress parameter (F) and variable dependent viscosity (Γ) on the onset of convection is also analyzed.

Towards a complete numerical description of lubricant film dynamics in ball bearings

In this article, we propose a framework for a detailed finite element analysis of elastohydrodynamic lubrication in ball bearings. Our contribution to this field is twofold. First, we present a fully monolithic ALE method for the treatment of fluid---structure interaction. For the lubricant, we use the full Navier---Stokes equations in combination with a pressure-dependent viscosity law and include thermal effects. Second, we introduce a novel method for a fully implicit treatment of the evolution of the lubricants' free surface using Nitsches method. This allows for arbitrarily large time steps independent of the spatial discretization. Despite the variety of numerical challenges present in this application, such as anisotropy and extreme values of pressure, our approach for the first time shows robustness up to high rotational speeds as required in industrial applications. We describe the numerical ingredients we use in detail and present numerical results that validate our approaches and demonstrate its capabilities.

Conditional stability for thermal convection in a rotating couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity

A nonlinear stability threshold for rotation in a couple-stress fluid heated from below saturating a porous medium with temperature and pressure dependent viscosity is exactly the same as the linear instability boundary. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. The effects of couple-stress parameter, variable dependent viscosity, medium permeability, Taylor number and Darcy–Brinkman number on the onset of convection are also analysed.

An evaluation of the pressure-dependent melt viscosity of polyphenylsulfone

A method for the determination of pressure-affected viscosity from capillary rheometry and pressure–volume–temperature (PVT) data was tested on polyphenylsulfone melt. Shear viscosity data evaluated at selected temperatures (345–375°C) were interlinked to the PVT data at pressures ranging from 1 to 200 MPa. According to the recently proposed correlation approach, a pressure-dependent shear viscosity is derived from the relationship (verified on several commodity polymers) between temperature-dependent viscosity and a free volume parameter computed using the Simha–Somcynsky equation of state. Finally, the predicted pressure-viscosity coefficient was compared with the value obtained experimentally on a modified single piston rheometer. POLYM. ENG. SCI., 54:711–715, 2014. © 2013 Society of Plastics Engineers