Upper bound of viscosity from a geophysical perspective

Viscosity is a fundamental physical property of fluids and plays a crucial role in both materials science and the natural sciences. However, discussions of viscosity rarely address its upper bound, because extremely high-viscosity materials are typically rock-forming minerals, which are not usually treated within the framework of fluid dynamics. Here, I focus on the upper bound of viscosity for solid-Earth materials. This study estimates this upper bound under temperature and pressure conditions relevant to natural systems by integrating constraints from different timescales of the solid Earth: geodetic observations over years to decades, laboratory rock-deformation experiments over hours to years, and geological processes such as lithospheric bending and subduction driven ultimately by mantle convection over millions of years. The results show that the maximum viscosity of stable lithospheric regions, inferred from geodetic observations, is approximately consistent with the maximum viscosities of major rock-forming minerals estimated from flow-law parameters obtained in laboratory deformation experiments. This study suggests that the upper bound of viscosity is 1030±2 Pa s, based on the physical definition of viscosity as resistance to flow over finite timescales ranging from human-observable to Earth-history timescales. These results may provide a broader rheological perspective on high-viscosity non-Newtonian fluids, glassy materials, soft matter, and related systems, rather than being confined to geophysical contexts.