Study suggests an upper viscosity limit beyond which materials effectively become rigid

Viscosity is a fundamental property that determines how easily a material flows, affecting systems from industrial materials to the Earth's deep interior. Yet, scientists have rarely considered whether viscosity has an upper limit because high-viscosity materials are usually rock-forming minerals outside fluid dynamics studies. Now, a Japanese researcher has combined Earth observations, laboratory experiments, and numerical simulations to estimate a physically meaningful upper viscosity bound of 10^30±2 Pa s, with implications for geophysics and materials.

Viscosity is one of the most fundamental physical properties used to describe how materials flow. It governs the movement of liquids, molten rocks, and even slowly deforming regions deep inside the 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 are usually composed of rock-forming minerals, which are rarely discussed within the traditional framework of fluid dynamics, leaving this question largely unanswered.

To address this question, the study by Professor Masaki Yoshida from the Department of Physical Sciences, College of Science and Engineering, Ritsumeikan University, Japan, investigated whether the 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. Their findings were published on June 29, 2026, in the journal Physics of Fluids.

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 10²⁴ 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±2 Pa s.

For comparison, water has a viscosity of approximately 10^-3 Pa s and honey about 10¹ Pa s, making the proposed upper bound roughly 10³³ 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 the Earth. In practical terms, materials with such effective viscosities behave as essentially rigid bodies over Earth-history timescales.

Prof. Yoshida explains, "This study suggests that the upper bound of viscosity is 10^30±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.

Prof. 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.

Title of original paper: Upper bound of viscosity from a geophysical perspective
Journal: Physics of Fluids
DOI: 10.1063/5.0335802

About Professor Masaki Yoshida from Ritsumeikan University, Japan

Dr. Masaki Yoshida is a professor at Department of Physical Sciences, College of Science and Engineering, Ritsumeikan University, Japan. He earned his Ph.D. in Science from the Department of Earth and Planetary Science, University of Tokyo in 2003. His research focuses on geophysics, Earth's evolution, plate tectonics, and computational fluid dynamics, advancing understanding of the planet's internal processes. He served as Guest Editor for the Nature Publishing Group Scientific Reports collection "Plate Tectonics" and "Plate Tectonics Modelling." He currently serves as an Associate Editor for Geoscience Frontiers, a leading Earth science journal with an impact factor of 12.7 in 2025.