Concept of an Evaluation Technique for Planar Elongational Stress and Relaxation Time Using Hoop Stress in Swirling Flow

Abstract

The paper reports a novel idea of an experimental approach to estimate the apparent planar elongational viscosity and the relaxation time of low viscosity fluids. A two-dimensional swirling contraction channel is designed to maintain a constant elongation rate to the flow direction. The hydrodynamic focusing creates a stable planar elongation flow field. The flow is injected into the center of the channel and a sheath flow is injected through both sides. The sample fluid is stretched in the flow field, and then forms the ribbon-shaped filament. In the swirling contraction part, a static force balance between the hoop force caused by the planar elongational stress and the centrifugal force determines the radial position of the filament. The distribution of the planar elongational stress can be estimated by observing this position, and then the apparent planar elongational viscosity was calculated using developed simplified expressions. On the other hand, when a channel with a constant width swirling part is used, the elongational stress generated in the straight contraction part gradually decreases passing through the constant width part. The sample filament position is then shifted based on the stress relaxation. The relaxation time can be evaluated by observing this variation.