Viscosity of Fluids in the Diamond-Anvil Cell

Measurement and modeling of the viscosity of fluids under high pressures is necessary to an understanding of fluid processes within the Earth and other planets. Areas of interest include terrestrial vulcanism, the flow of supercritical fluids which may induce metasomatism over large regions of Earth's upper mantle, and the dynamics of the fluid envelopes of the larger planets. We report here the application of rolling ball viscometry to supercritical fluids within the diamond-anvil cell. Recent results and the accuracies and potentials of the technique are discussed. For many fluids, viscosity as a function of pressure seems to follow Doolittle's empirical equation, roughly justified on the basis of free-volume theory. However, based on a survey of published data it has also been hypothesized that above twice the critical density the viscosities of simple, supercritical fluids are linear functions of pressure to a very high accuracy. These two functional forms are mutually exclusive and may diverge by an order of magnitude over the pressure-temperature regime of mantle fluids. Here we show that over the extended range of densities and pressures available to the diamond-anvil cell supercritical fluids are, in fact, better fit by the Doolittle equation. We show also that the law of corresponding states may still be of reasonable accuracy even at large compressions where the differences among intermolecular potentials might be supposed to preclude such scaling.