Viscosity Measurements at High Pressures: A Critical Appraisal of Corrections to Stokes' Law

Abstract

Fluids and melts in planetary interiors significantly influence geodynamic processes from volcanism to global‐scale differentiation. The roles of these geofluids depend on their viscosities (η). Constraining geofluid η at relevant pressures and temperatures relies on laboratory‐based measurements and is most widely done using Stokes' Law viscometry with falling spheres. Yet small sample chambers required by high‐pressure experiments introduce significant drag on the spheres. Several correction schemes are available for Stokes' Law but there is no consensus on the best scheme(s) for high‐pressure experiments. We completed high‐pressure experiments to test the effects of (a) the relative size of the sphere diameter to the chamber diameter and (b) the top and bottom of the chamber, that is, the ends, on the sphere velocities. We examined the influence of current correction schemes on the estimated viscosity using Monte Carlo simulations. We also compared previous viscometry work on various geofluids in different experimental setups/geometries. We find the common schemes for Stokes' Law produce statistically distinct values of η. When inertia of the sphere is negligible, the most appropriate scheme may be the Faxén correction for the chamber walls. Correction for drag due to the chamber ends depends on the precision in the sinking distance and may be ineffective with decreasing sphere size. Combining the wall and end corrections may overcorrect η. We also suggest the uncertainty in η is best captured by the correction rather than propagated errors from experimental parameters. We develop an overlying view of Stokes' Law viscometry at high pressures.

Ultramafic Melt Viscosity: A Model

“…We elected not to calibrate our model using the high-pressure measurements of ultramafic melt viscosity reported by Liebske et al (2005) and Brown (2012). We made this decision because of the significantly larger scatter in their data (as previously observed by Xie et al, thus, less precision (see Ashley et al, 2024) and more potential scatter (Fig. 6B).…”

“…The maximum in viscosity and the negative P-dependence proposed by Liebske et al (2005) is mainly driven by data derived from Cell C which show more scatter (Fig. 6B) and may be less precise (see Ashley et al, 2024).…”