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Abstract This paper concerns the existence of global weak solutionsá la Lerayfor compressible Navier–Stokes–Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given.
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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 geofluidηat 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 ofη. 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 overcorrectη. We also suggest the uncertainty inηis best captured by the correction rather than propagated errors from experimental parameters. We develop an overlying view of Stokes' Law viscometry at high pressures.
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- PAR ID:
- 10504380
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Solid Earth
- Volume:
- 129
- Issue:
- 5
- ISSN:
- 2169-9313
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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