Pressure Dependence Of Viscosity Research Articles

Measurement of the pressure dependence of viscosity of polymer melts using a back pressure‐regulated capillary rheometer

AbstractThe effect of pressure on the melt viscosity was experimentally investigated for five polymers: polycarbonate (PC), acrylonitrile‐butadiene‐styrene (ABS), polystyrene (PS), polypropylene (PP), and low‐density polyethylene (LDPE). Measurements were carried out using capillary rheometer modified to allow regulation of back pressure. To enable correction for the entrance pressure drop, two round‐hole dies were used: a 1‐mm diameter die of length 10 mm and an orifice die of the same diameter. For determining the pressure coefficient from the experimental viscosity data, time‐pressure superposition was applied to generate a master curve to which the Carreau‐Yasuda model was fitted. The resulting pressure coefficients revealed that for the polymers studied the order of the degree of the pressure dependence is as follows: PS > ABS > PC > PP > LDPE. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010

A note on the flow of a fluid with pressure-dependent viscosity in the annulus of two infinitely long coaxial cylinders

The dependence of the viscosity of fluids on pressure has been well established by experiments and it needs to be taken into consideration in problems where there is a large variation of pressure in the flow domain. In this paper we consider the flow of a fluid in the annulus between two cylinders whose viscosity depends on the pressure. First we consider the steady flow in the annulus due to the rotation of one cylinder with respect to the other. Then we study the problem of flow in the annular region due to torsional and longitudinal oscillations of one cylinder with respect to the other. In both the problems considered the flow is found to be markedly different from that for the incompressible Navier–Stokes fluid with constant viscosity.

Determination of the heat transfer coefficient from short‐shots studies and precise simulation of microinjection molding

AbstractThe filling process of a micro‐cavity was analyzed by modeling the compressible filling stage by using pressure‐dependent viscosity and adjusted heat transfer coefficients. Experimental filling studies were carried out at the same time on an accurately controlled microinjection molding machine. On the basis of the relationship between the injection pressure and the filling degree, essential factors for the quality of the simulation can be identified. It can be shown that the flow behavior of the melt in a micro‐cavity with a high aspect ratio is extremely dependent on the melt compressibility in the injection cylinder. This phenomenon needs to be considered in the simulation to predict an accurate flow rate. The heat transfer coefficient between the melt and the mold wall that was determined by the reverse engineering varies significantly even during the filling stage. With increasing injection speed and increasing cavity thickness, the heat transfer coefficient decreases. It is believed that the level of the cavity pressure is responsible for the resulting heat transfer between the polymer and the mold. A pressure‐dependent model for the heat transfer coefficient would be able to significantly improve the quality of the process simulation. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers

A bulk cloud parameterization in a Venus General Circulation Model

A condensing cloud parameterization is included in a super-rotating Venus General Circulation Model. A parameterization including condensation, evaporation and sedimentation of mono-modal sulfuric acid cloud particles is described. Saturation vapor pressure of sulfuric acid vapor is used to determine cloud formation through instantaneous condensation and destruction through evaporation, while pressure dependent viscosity of a carbon dioxide atmosphere is used to determine sedimentation rates assuming particles fall at their terminal Stokes velocity. Modifications are described to account for the large range of the Reynolds number seen in the Venus atmosphere. Two GCM experiments initialized with 10 ppm-equivalent of sulfuric acid are integrated for 30 Earth years and the results are discussed with reference to “Y” shaped cloud structures observed on Venus. The GCM is able to produce an analog of the “Y” shaped cloud structure through dynamical processes alone, with contributions from the mean westward wind, the equatorial Kelvin wave, and the mid-latitude/polar Mixed Rossby/Gravity waves. The cloud top height in the GCM decreases from equator to pole and latitudinal gradients of cloud top height are comparable to those observed by Pioneer Venus and Venus Express, and those produced in more complex microphysical models of the sulfur cycle on Venus. Differences between the modeled cloud structures and observations are described and dynamical explanations are suggested for the most prominent differences.

Existence Theory for Steady Flows of Fluids with Pressure and Shear Rate Dependent Viscosity, for Low Values of the Power-Law Index

We deal with a system of partial differential equations describing a steady flow of a homogeneous incompressible non-Newtonian fluid with pressure and shear rate dependent viscosity subject to the homogeneous Dirichlet (no-slip) boundary condition. We establish a global existence of a weak solution for a certain class of such fluids in which the dependence of the viscosity on the shear rate is polynomiallike, characterized by the power-law index. A decomposition of the pressure and Lipschitz approximations of Sobolev functions are considered in order to obtain almost everywhere convergence of the pressure and the symmetric part of the velocity gradient and thus obtain new existence results for low value of the power-law index.

An experimental study on the pressure dependence of viscosity in silicate melts

The effect of pressure on melt viscosity was investigated for five compositions along the join An(CaAl(2)Si(2)O(8))-Di(CaMgSi(2)O(6)) and four alkali silicates containing lithium, sodium, and potassium in constant ratio of approximately 1:1:1, but alkali-silica ratios are varying. The experiments were performed in an internally heated gas pressure vessel at pressures from 50 to 400 MPa in the viscosity range from 10(8) to 10(11.5) Pas using parallel plate viscometry. The polymerized An composition shows a negative pressure dependence of viscosity while the other, more depolymerized compositions of the join An-Di have neutral to positive pressure coefficients. The alkali silicates display neutral to slightly positive pressure coefficients for melt viscosity. These findings in the high viscosity range of 10(8)-10(11) Pas, where pressure appears to be more efficient than in low viscous melts at high temperature, are consistent with previous results on the viscosity of polymerized to depolymerized melts in the system NaAlSi(3)O(8)-CaMgSi(2)O(6) by Behrens and Schulze [H. Behrens and F. Schulze, Am. Mineral. 88, 1351 (2003)]. Thus we confirm that the sign of the pressure coefficient for viscosity is mainly related to the degree of melt polymerization in silicate and aluminosilicate melts.

Relaxation of Libyan desert glass: Evidence for negative viscosity–pressure dependence in silica?

Libyan desert glass (LDG) with silica content >99 mol% was examined to obtain evidence for negative viscosity–pressure dependence in silica. Calorimetric scanning experiments under ambient pressure revealed a shift of ∼22 K in glass transition temperature ( T g ) from pristine to relaxed LDG, respectively. While the endothermic overshot in the isobaric heat capacity at T g remains practically unaffected, the shift occurs due to a decrease in the onset of relaxation. Because in silicate glasses, caloric and kinetic glass transition are strongly coupled, this finding indicates that kinetic freezing of LDG originally occurred at lower temperature than it does in glasses of equivalent composition under normal conditions. Considering the most probable origin of LDG – a meteoritic impact – and assuming that at least some compression is preserved in natural LDG samples, this observation is interpreted as evidence for decreasing viscosity with increasing pressure, and is related to decreasing Si–O–Si bond angle in the pressure-regime below 1 GPa.

Relaxation and Prigogine–Defay ratio of compressed glasses with negative viscosity-pressure dependence

Differential scanning calorimetry and density measurements were employed to study relaxation processes in compressed NaAlSi(3)O(8) and Na(0.34)Ca(0.31)Al(0.96)Si(3.04)O(8) glasses with negative dependence of viscosity (eta) on pressure (p). Isobaric configurational heat capacities, coefficients of thermal expansion and compressibility of the melts, and real and apparent fictive temperatures are reported for the pressure regime from 0.1 to 700 MPa and cooling rates from 0.1 to 400 K/min. The onset of glass transition, measured on the compressed glass under normal pressure, is found to shift with increasing pressure of freezing in accordance with in situ viscosity data. Based on the pressure-derivative of the compression-induced excess enthalpy (or apparent fictive temperature), a condition for which a negative dependence of fictive temperature on pressure occurs is developed. It is further shown that in this case, also d eta/d p is negative. We suggest that in the region of glass transition, glasses with large Prigogine-Defay (PD) ratio have a high probability to also exhibit a negative dependence of viscosity on pressure. However, the criterion cannot be applied inversely: particularly glasses with a high sensitivity of short-range structural parameters to pressure may exhibit a relatively low PD ratio, but negative d eta/d p.

A new approach to description of the pressure dependence of viscosity

Abstract Based on more precise description of the temperature-pressure dependence of entropy, we expand the Avramov’s model. In this way, viscosity or relaxation time are described with better accuracy. It is demonstrated that there is a strong relation between the fragility parameter F, described here, and the fragility parameter m, introduced by Angell, m ≈ ( 13 ± 10 % ) F . Analyses of experimental data on dielectric relaxation of phenylphthalein-dimethylether (PDE) are in agreement with the proposed model.

Pressure dependence of viscosity of rhyolitic melts

Viscosity of silicate melts is a critical property for understanding volcanic and igneous processes in the Earth. We investigate the pressure effect on the viscosity of rhyolitic melts using two methods: indirect viscosity inference from hydrous species reaction in melts using a piston cylinder at pressures up to 2.8 GPa and direct viscosity measurement by parallel-plate creep viscometer in an internally-heated pressure vessel at pressures up to 0.4 GPa. Comparison of viscosities of a rhyolitic melt with 0.8 wt% water at 0.4 GPa shows that both methods give consistent results. In the indirect method, viscosities of hydrous rhyolitic melts were inferred based on the kinetics of hydrous species reaction in the melt upon cooling (i.e., the equivalence of rheologically defined glass transition temperature and chemically defined apparent equilibrium temperature). The cooling experiments were carried out in a piston-cylinder apparatus using hydrous rhyolitic samples with 0.8–4 wt% water. Cooling rates of the kinetic experiments varied from 0.1 K/s to 100 K/s; hence the range of viscosity inferred from this method covers 3 orders of magnitude. The data from this method show that viscosity increases with increasing pressure from 1 GPa to 3 GPa for hydrous rhyolitic melts with water content ⩾0.8 wt% in the high viscosity range. We also measured viscosity of rhyolitic melt with 0.13 wt% water using the parallel-plate viscometer at pressures 0.2 and 0.4 GPa in an internally-heated pressure vessel. The data show that viscosity of rhyolitic melt with 0.13 wt% water decreases with increasing pressure. Combining our new data with literature data, we develop a viscosity model of rhyolitic melts as a function of temperature, pressure and water content.

Stability analysis of the Rayleigh–Bénard convection for a fluid with temperature and pressure dependent viscosity

The classical problem of thermal-convection involving the classical Navier–Stokes fluid with a constant or temperature dependent viscosity, within the context of the Oberbeck–Boussinesq approximation, is one of the most intensely studied problems in fluid mechanics. In this paper, we study thermal-convection in a fluid with a viscosity that depends on both the temperature and pressure, within the context of a generalization of the Oberbeck–Boussinesq approximation. Assuming that the viscosity is an analytic function of the temperature and pressure we study the linear as well as the non-linear stability of the problem of Rayleigh–Benard convection. We show that the principle of exchange of stability holds and the Rayleigh numbers for the linear and non-linear stability coincide.

Pressure-dependent viscosity and free volume of atactic and syndiotactic polystyrene

The effect of pressure on viscosity is an important but often overlooked aspect of the flow properties of polymeric materials. In this work, two polymers (an atactic and a syndiotactic Polystyrene) were characterized to determine the effect of pressure on viscosity. In particular, a device was adopted to increase the exit pressure of a standard capillary rheometer, thus obtaining data of viscosity under high pressure and high shear rates. The Simha-Somcynsky equation of state was applied to the pressure–volume–temperature experimental data of both materials to obtain the dependence of free volume on temperature and pressure. The Doolittle equation was eventually employed to verify the dependence of viscosity on free volume. It was found that, for both materials, a linear relationship holds between the logarithm of zero-shear-rate viscosity (at several temperatures and pressures) and the inverse of free volume.

Implications of large elastic thicknesses for the composition and current thermal state of Mars

The martian elastic lithosphere thickness T e has recently been constrained by modeling the geodynamical response to loading at the martian polar caps and T e was found to exceed 300 km at the north pole today. Geological evidence suggests that Mars has been volcanically active in the recent past and we have reinvestigated the martian thermal evolution, identifying models which are consistent with T e > 300 km and the observed recent magmatic activity. We find that although models satisfying both constraints can be constructed, special assumptions regarding the concentration and distribution of radioactive elements, the style of mantle convection and/or the mantle's volatile content need to be made. If a dry mantle rheology is assumed, strong plumes caused by, e.g., a strongly pressure dependent mantle viscosity or endothermic phase transitions near the core–mantle boundary are required to allow for decompression melting in the heads of mantle plumes. For a wet mantle, large mantle water contents of the order of 1000 ppm are required to allow for partial mantle melting. Also, for a moderate crustal enrichment of heat producing, elements the planet's bulk composition needs to be 25 and 50% sub-chondritic for dry and wet mantle rheologies, respectively. Even then, models resulting in a globally averaged elastic thicknesses of T e > 300 km are difficult to reconcile with most elastic thickness estimates available for the Hesperian and Amazonian periods. It therefore seems likely that large elastic thicknesses in excess of 300 km are not representative for the bulk of the planet and that T e possibly shows a large degree of spatial heterogeneity.

Mathematical Analysis of Unsteady Flows of Fluids with Pressure, Shear-Rate, and Temperature Dependent Material Moduli that Slip at Solid Boundaries

In Bridgman's treatise [The Physics of High Pressures, MacMillan, New York, 1931], he carefully documented that the viscosity and the thermal conductivity of most liquids depend on the pressure and the temperature. The relevant experimental studies show that even at high pressures the variations of the values in the density are insignificant in comparison to that of the viscosity, and it is thus reasonable to assume that the liquids in question are incompressible fluids with pressure dependent viscosities. We rigorously investigate the mathematical properties of unsteady three-dimensional internal flows of such incompressible fluids. The model is expressed through a system of partial differential equations representing the balance of mass, the balance of linear momentum, the balance of energy, and the equation for the entropy production. Assuming that we have Navier's slip at the impermeable boundary we establish the long-time existence of a (suitable) weak solution when the data are large.

Effect of mantle compressibility on the thermal and flow structures of the subduction zones

The heat generated by viscous dissipation is consistently evaluated using a 2‐D compressible subduction model with variations of mantle rheology (constant as well as pressure and temperature dependent viscosity), dip, age, and velocity of the subducting slab. For comparison, we also conduct 2‐D incompressible subduction calculations with the same conditions and parameters used in the compressible formulation. The effect of compressibility on the thermal and flow structures of the subduction zones is relatively small and concentrated along the base of the mantle wedge, with temperature differences <100°C and differences in kinematic energy of the mantle wedge <1% between compressible and incompressible models. Mantle rheology has a stronger effect on thermal and flow structures than mantle compressibility as well as the variations of dip, age, and velocity of the subducting slab. The heat from viscous dissipation in the compressible model increases the slab temperatures over the incompressible model (<70°C), as a result of additional conduction across the slab surface (constant viscosity) and thinning of the thermal boundary layer caused by viscosity reduction (pressure‐ and temperature‐dependent viscosity).

Study of a variant of Stokes’ first and second problems for fluids with pressure dependent viscosities

In this paper we extend the seminal work of Stokes concerning the flow due to a suddenly accelerated plate and an oscillating plate for the Navier–Stokes fluid, to a fluid with pressure dependent viscosity. The viscosity of many fluids varies significantly with pressure, a fact recognized by Stokes, and Barus in fact conducted experiments that showed that the variation of the viscosity with pressure was exponential. Given such a tremendous variation, it would be interesting to see how this change in viscosity affects the nature of the solution to these problems. We find that the velocity field, and hence the structure of the vorticity and the shear stress at the walls for fluids with pressure dependent viscosity are markedly different from those for the classical Navier–Stokes fluid.

Numerical model of heat flow in back-arc regions

We numerically modeled mantle wedge flow driven by subducting plates and its consequences to surface heat flow in back-arc regions, where an increase in surface heat flow has been observed in almost all subduction zones. In order to calculate the steady state temperature and velocity field in a generic subduction zone model we utilized a new technique which does not require a priori assumptions about the position of the slab–wedge boundary. We demonstrated that calculated surface heat flow is very sensitive to the thermal boundary condition prescribed at the base of the model for a simple temperature-dependent viscosity. Since an increase of surface heat flow is a common feature of many back-arc regions, it should be rather independent on various thermal conditions applied at the bottom. We showed that such a robust behavior can be reproduced if, moreover, a strong pressure-dependence of viscosity is taken into account. The pattern of increased surface heat flow is then stable for a wide range of settings including various dip angles and age of the subducting slab. The temperature- and pressure-dependent viscosity resulted in a nearly isothermal mantle wedge, where temperatures exceeded 1200 °C even in relatively shallow depths, and, consequently, elevated surface heat flow is consistent with recent hot back-arcs evidence. Circulation in the wedge was obtained since the employed viscosity law resulted in creation of a zone of substantially reduced viscosity in shallow depths below the continental crust.

A Combined Analysis of PVT and Rheological Measurements: Novel Results for Three Amorphous Polymers

AbstractThe fractional free volume f of polycarbonate (PC), polystyrene (PS) and poly(methyl methacrylate) (PMMA) is determined by pressure–volume–temperature (PVT) measurements using the Simha–Somcynsky equation of state. Results are compared with the free volume obtained by viscoelastic measurements. Temperature and pressure dependent viscosity and free volume results are correlated using the characteristic ratio C∞ and the parameter B of the monomeric friction factor ζ = ζexp B/f. This leads to obtain new results on the temperature and pressure dependence of C∞, as well as on the pressure dependence of B parameter.magnified image

Stability of plane Poiseuille–Couette flows of a piezo-viscous fluid

We examine stability of fully developed isothermal unidirectional plane Poiseuille–Couette flows of an incompressible fluid whose viscosity depends linearly on the pressure as previously considered in Hron et al. [J. Hron, J. Málek, K.R. Rajagopal, Simple flows of fluids with pressure-dependent viscosities, Proc. R. Soc. Lond. A 457 (2001) 1603–1622] and Suslov and Tran [S.A. Suslov, T.D. Tran, Revisiting plane Couette–Poiseuille flows of a piezo-viscous fluid, J. Non-Newtonian Fluid Mech. 154 (2008) 170–178]. Stability results for a piezo-viscous fluid are compared with those for a Newtonian fluid with constant viscosity. We show that piezo-viscous effects generally lead to stabilisation of a primary flow when the applied pressure gradient is increased. We also show that the flow becomes less stable as the pressure and therefore the fluid viscosity decrease downstream. These features drastically distinguish flows of a piezo-viscous fluid from those of its constant-viscosity counterpart. At the same time the increase in the boundary velocity results in a flow stabilisation which is similar to that observed in Newtonian fluids with constant viscosity.

Flow of fluids with pressure dependent viscosities in an orthogonal rheometer subject to slip boundary conditions

We consider slow steady flows of Navier–Stokes-like fluids with pressure dependent viscosities between rotating infinite parallel plates with Navier slip boundary conditions. We derive exact solutions which correspond to flows in orthogonal and torsional rheometers, and investigate the effect of the slip coefficient and the material parameters on the solutions. We find that even when inertial effects are ignored, vorticity boundary layers develop at the upper boundary due to the pressure dependence of the viscosity. These boundary layers diminish and eventually disappear with increased slippage.