Pressure dependence of viscosity

Abstract

We reanalyze the pressure dependence of viscosity of liquids of constant composition under isothermal conditions. Based exclusively on very general considerations concerning the relationship between viscosity and "free volume," we show that, at moderate values of pressure, viscosity increases, as a rule, with increasing pressure, provided the liquid is in stable or metastable (undercooled) equilibrium states. However, even if the behavior of the viscosity is governed by free volume effects, deviations from a positive pressure dependence are possible, when the liquid's thermal expansion coefficient is negative. We derive an equation that allows one to quantitatively determine the pressure dependence of viscosity, which requires, in the simplest case, only the knowledge of the temperature dependence of viscosity at constant pressure, the thermal expansion coefficient, and the isothermal compressibility of the liquid. As an example, the negative pressure dependence of water in the range of temperatures 0-4 degrees C and of several silicate liquids, such as albite, jadeite, dacite, basalts, etc., could be explained in such a way. Other glass-forming liquids initially (for moderate pressures) show a positive pressure dependence of viscosity that changes to a negative one when subjected to high (approximately GPa) isostatic pressure. A detailed analysis of water and already mentioned silicate melts at GPa pressures shows that, in addition to free volume effects, other pressure induced structural transformations may have to be accounted for in a variety of cases. By this reason, the theoretical analysis is extended (i) in order to describe the pressure dependence of viscosity for systems that are in frozen-in thermodynamic nonequilibrium states (glasses, i.e., undercooled liquids below the glass transition temperature Tg) and (ii) to systems which undergo, in addition to variations of the free volume, pressure induced changes of other structural parameters. In such cases a decrease of viscosity with increasing pressure may occur, in principle, even if the thermal expansion coefficient is positive. In this way, the present analysis grants a general tool to estimate the pressure dependence of viscosity and supposedly settles the controversy in the current literature.

Generation of billow-like wavy folds by fluidization at high temperature in Nojima fault gouge: microscopic and rock magnetic perspectives

“…We hypothesized that the fault slip zone was exposed to high temperature (>350 °C) and that the fault gouge formation depth was 3 km. Under such temperature and pressure conditions, Schmelzer et al (2005) showed that the viscosity of water [pore fluid (η m )] is 9.137 × 10 −5 Pa s, being approximately 1.0 × 10 −4 Pa s. Therefore, if micrometer-sized finely comminuted products approximate to an equivalent diameter spherical particle, total viscosity (η s ) is 1.0 × 10 −2 Pa s. Due to frictional heating, the pore fluid expands in volume (e.g., Lachenbruch 1980). If the permeability of the fault slip zone decreases, the volume fraction of fault gouge decreases; this suggests that the total fluid viscosity of the fault slip zone further reduces below 1.0 × 10 −2 Pa s. Although Woods (1969) has demonstrated that KH instability can be generated under high Reynolds number conditions, we cannot deduce the concrete Reynolds number due to the difficulty in the estimation of the flow velocity in fault gouge.…”

Group invariant solution for a pre-existing fluid-driven fracture in impermeable rock

“…The parameter values are given in Table 2. The pressure dependence of the viscosity of water is anomalous since it decreases with increase in pressure [22]. From (4.15), the fracture length increases as the breadth decreases.…”

Upward Gas-Liquid Flow in Concentric and Eccentric Annular Spaces

“…Dependency of density of water with pressure and temperature (Schmelzer et al, 2005). The relative difference calculation is shown on the side and it is graphically indicated by the bold black arrow.…”

“…The same can be said in respect to pressure. Figure 4 below reflects the small dependency of the density of water with pressure (given in MPa) and temperature (Schmelzer et al, 2005). In TowerLab, the pressure range varies from 0.1 to 1.0 MPa.…”