Gravity-Driven Microfluidic Viscosity Measurement with a Small Capillary Radius and Strong Pinning Effect

In this study, we introduce a novel method for microscale viscosity measurement that eliminates the need for direct contact angle determination. By utilizing a capillary with a sufficiently small radius (R < 0.2 mm), the sharp outlet edge pins the three-phase contact line, stabilizing the apparent contact angle near 90° and nullifying the capillary pressure term. The rheological parameters (K and n) of power-law fluids are then calculated directly by analyzing image sequences of a growing pendant droplet to obtain its volume flow rate Q. Experiments verify through inversion calculation that the apparent contact angle indeed converges to 90° at a small capillary radius. The proposed method is employed to measure 20 wt% and 40 wt% glycerol aqueous solutions (Newtonian fluids) as well as 0.01 wt% and 0.02 wt% xanthan gum aqueous solutions (non-Newtonian fluids). The obtained rheological parameters agree well with reference values within this range, confirming the method's reliability for these low-viscosity and moderately non-Newtonian fluids. However, measurements on higher concentration fluids (e.g., 0.1 wt% and 0.2 wt% xanthan gum solutions) reveal increased errors, indicating a current limitation in accurately characterizing fluids with high viscosity or pronounced non-Newtonian behavior under gravity-driven flow. This simple technique provides a reliable and low-cost approach for measuring the viscosity of microliter-volume fluids within its characterized operational range.