Scientific Frontline: Extended "At a Glance" Summary: Viscosity Upper Limit
The Core Concept: Researchers have identified a practical upper bound for material viscosity, estimated at \(10^{30 \pm 2}\) Pa s, beyond which substances function as essentially rigid bodies over finite timescales.
Key Distinction/Mechanism: Unlike classical assumptions of infinite viscosity for solid materials, this study establishes a finite quantitative threshold determined by the convergence of geodetic, experimental, and numerical simulation data.
Major Frameworks/Components:
- Geodetic observations of tectonic plate stability.
- Laboratory-derived flow laws for major rock-forming minerals, including olivine, clinopyroxene, diopside, anorthite, and quartz.
- Numerical simulations of mantle convection and visco-elasto-brittle deformation.
Branch of Science: Geophysics, Mineral Physics, Fluid Dynamics, Materials Science.
Future Application: Improving numerical simulations of Earth's internal dynamics, modeling high-viscosity non-Newtonian fluids, and advancing the fundamental understanding of glassy materials and soft matter systems.
Why It Matters: This framework provides a standardized physical criterion to distinguish between deformable fluid-like behavior and rigid behavior in long-term natural systems, significantly refining the accuracy of models regarding planetary evolution and tectonic motion.
Viscosity is a fundamental physical property used to describe how materials flow. It governs the movement of liquids, molten rock, and slowly deforming regions deep inside Earth. While scientists have long studied materials with low or moderate viscosities, a simple but important question has remained largely unexplored: Is there a physically meaningful upper limit to viscosity? Extremely high-viscosity materials usually consist of rock-forming minerals, which are rarely discussed within the traditional framework of fluid dynamics, leaving this question largely unanswered.
To address this question, a study by Professor Masaki Yoshida of the Department of Physical Sciences in the College of Science and Engineering at Ritsumeikan University in Japan investigated whether Earth's interior could provide a natural constraint on the highest physically meaningful viscosity over finite timescales. Rather than relying on a single dataset, the study integrated evidence from geodetic observations spanning years to decades, laboratory rock-deformation experiments conducted over hours to years, and geological processes, such as lithospheric bending and plate subduction, that evolve over millions of years.
The study focused on the physical definition of viscosity as resistance to material flow over finite timescales. Geodetic observations indicate that the stable parts of tectonic plates have effective viscosities of approximately \(10^{24}\) Pa·s or greater. Laboratory-derived flow laws for major rock-forming minerals, including olivine, clinopyroxene, diopside, anorthite, and quartz, were then used to estimate viscosity under realistic temperature and pressure conditions. Numerical simulations of mantle convection and visco-elasto-brittle deformation further examined how highly viscous lithospheres behave during plate motion and subduction.
Three independent approaches—geodetic observations, mineral-physics-based flow laws, and geodynamic simulations—converged on a similar viscosity range. By combining these independent lines of evidence, the researchers found that the maximum viscosity inferred from stable lithospheric regions is broadly consistent with the highest viscosities predicted for major rock-forming minerals. The analysis suggests that the upper bound of viscosity is \(10^{30 \pm 2}\) Pa·s.
For comparison, water has a viscosity of approximately \(10^{-3}\) Pa·s and honey about \(10^1\) Pa·s, making the proposed upper bound roughly \(10^{33}\) times greater than the viscosity of water.
At such values, the accumulated viscous strain over geological timescales becomes extremely small, and the associated Maxwell relaxation time can approach or greatly exceed the age of Earth. In practical terms, materials with such effective viscosities behave as essentially rigid bodies over Earth-history timescales.
Professor Yoshida explains, "This study suggests that the upper bound of viscosity is \(10^{30 \pm 2}\) Pa·s, based on the physical definition of viscosity as resistance to flow over finite timescales, from human-observable to Earth-history timescales."
Rather than supporting the concept of infinite viscosity, the study discusses how materials become effectively rigid at a finite viscosity range long before reaching any hypothetical infinite value. The findings also demonstrate that the meaning of viscosity depends not only on its numerical value but also on stress, strain rate, and deformation time. Instead of treating infinite viscosity as a physical reality, the study argues that there is a finite range beyond which a material effectively loses its ability to flow within relevant observational timescales.
Professor Yoshida adds, "The proposed upper viscosity range represents a timescale-dependent criterion above which a material behaves as an effectively rigid body rather than as a deformable viscous continuum."
The implications extend beyond geophysics. The proposed upper limit may provide a broader rheological perspective for understanding high-viscosity non-Newtonian fluids, glassy materials, soft matter, and related systems. The research also supports ongoing efforts to reconstruct Earth's past interior dynamics and improve predictions of future geological evolution through numerical simulations.
Overall, the study bridges geodetic observations, laboratory mineral physics, and geodynamic modeling to establish a physically meaningful upper bound for viscosity. By defining when an extremely viscous material should be regarded as effectively rigid, the work offers a new framework for interpreting the behavior of slowly deforming natural systems across a vast range of timescales.
Published in journal: Physics of Fluids
Title: Upper bound of viscosity from a geophysical perspective
Authors: Masaki Yoshida
Source/Credit: Ritsumeikan University
Edited by: Scientific Frontline
Reference Number: phy070626_01
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