Viscoelastic flow transitions in abrupt planar contractions

TL;DR

This study experimentally investigates viscoelastic flow transitions in planar contractions with various ratios, revealing critical Weissenberg numbers for flow pattern changes, including steady, diverging, and three-dimensional flows, influenced by boundary geometry.

Contribution

It provides new experimental insights into flow transition sequences and critical conditions in planar contractions, highlighting the influence of contraction ratio and boundary effects.

Findings

Flow transitions from steady to diverging streamline patterns at critical Weissenberg numbers.

Further increase leads to three-dimensional, time-dependent flow regimes.

Boundary shape significantly affects the sequence and nature of flow transitions.

Abstract

We present experimental evidence of global viscoelastic flow transitions in 2:1, 8:1 and 32:1 planar contractions under inertia-less conditions. Light sheet visualization and laser Doppler velocimetry techniques are used to probe spatial structure and time scales associated with the onset of these instabilities. The results are reported in terms of critical Weissenberg numbers characterizing the fluid flow rates. For a given contraction ratio and polymer fluid, a two-dimensional, steady flow with converging streamlines transitions to a two-dimensional pattern with diverging streamlines beyond a critical Weissenberg number. At even higher Weissenberg numbers, spatial transition to three-dimensional flow is observed. A relationship between the upstream Weissenberg number for the onset of this spatial instability and the contraction ratio is derived. For contraction ratios substantially greater than unity, we observe that further increase in the flow rate results in a second temporal transition to a three-dimensional, time-dependent flow. This complex flow arises due to a combination of the effects of stress-curvature interaction and three dimensional perturbations induced by the walls bounding the neutral direction. Comparison with studies on other geometries indicates that boundary shapes deeply influence the sequence and nature of flow transitions.