Operational limits of gravity-driven funnel protorheology tests with Newtonian fluids

We systematically analyze the physics of inferring viscosity from gravity-driven funnel flows and derive operational limit equations for Newtonian fluids based on non-idealities arising from measurement resolution (fill height and discharge time), fluid inertia, non-laminar flow, entrance losses, and surface tension. The framework applies generally to the Marsh Funnel, other standard geometries, and variations beyond current practice. Theoretical predictions are validated experimentally using Newtonian fluids spanning a wide viscosity range. The resulting operational windows, expressed in various representations (e.g., viscosity vs shear stress and viscosity vs shear rate), can be anticipated a priori, reveal physical insights into distinct flow regimes, and can be used to rationalize the use of these flows for estimating the zero-shear viscosity of non-Newtonian fluids. These results apply the concept of rheometric operating limits to a complex yet practical protorheology flow, enabling quantitative and credible viscosity estimation from simple tests.