Investigation of Scale Effects in Extensional Rheology Measurements of Polymer Solutions Using a Liquid Dripping Method

The influence of geometric scale on the extensional rheology of viscoelastic fluids was systematically investigated using a liquid dripping method. Polyethylene oxide aqueous solutions were tested with seven nozzles of different outer diameters ranging from 0.23 mm to 2.77 mm. The temporal evolution of the filament diameter was analyzed to obtain the extensional relaxation time, extensional viscosity, and maximum Weissenberg number. To quantitatively evaluate the scale effect, a surface-area-to-volume ratio was introduced as a geometric parameter. The results show that as the nozzle diameter increases, both the extensional relaxation time and the maximum Weissenberg number gradually approach asymptotic values. This indicates that when the influence of scale effects is negligible, the measured rheological properties more accurately represent the intrinsic viscoelastic response of the fluid. These findings demonstrate that the geometric scale significantly affects the observed extensional behavior in filament thinning experiments. Furthermore, this study establishes a practical experimental guideline that recommends the use of sufficiently large nozzle diameters to minimize scale effects. The use of large nozzles enables reliable evaluation of the extensional viscosity of complex fluids and contributes to improving the accuracy of rheological measurements in complex flow systems.