Improved capillary rheometry for viscous Newtonian filaments

Abstract

The efficacy of the kinematic differential analysis of McCarroll et al. [“Differential analysis of capillary breakup rheometry for Newtonian liquids,” J. Fluid Mech. 804, 116 (2016)], expanding on McKinley and Tripathi [“How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer,” J. Rheol. 44, 653 (2000)], to evaluate the surface tension to viscosity ratio for Newtonian filaments is examined. The analysis is valid during and after stretch, while the latter is traditionally applied after cessation of stretch as the midfilament radius approaches zero. Through numerical simulations, the evaluation of viscosity is investigated for two common stretch histories: (a) the ramp function and (b) the modified step strain. The challenges with stretch are twofold: rapid stretch (large capillary number) results in a nearly cylindrical filament with a rapid change near the plate that challenges the one-dimensional (1D) approximation, while slow stretch results in a nearly static solution with limited viscous information. We examine the capillary number-aspect ratio parameter space and find the ramp function with small stretching speeds optimal. Hence, the most accurate measurements are taken while the filament is being stretched.