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Transitional pathway to elastic turbulence in torsional, parallel-plate flow of a polymer solution

Published online by Cambridge University Press:  24 April 2006

BRUCE A. SCHIAMBERG
Affiliation:
Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
LAURA T. SHEREDA
Affiliation:
Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
HUA HU
Affiliation:
Proctor & Gamble, West Chester, OH 45069, USA
RONALD G. LARSON
Affiliation:
Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA

Abstract

Multiple scenarios have been discovered by which laminar flow undergoes a transition to turbulence in Newtonian fluids. Here we show in non-Newtonian fluids a transition sequence to ‘elastic turbulence’ due to elasticity from polymers, with negligible inertia. Multiple dynamic states are found linking the base flow to ‘elastic turbulence’ in the flow between a rotating and stationary disk, including circular and spiral rolls. Also, a surprising progression from apparently ‘chaotic’ flow to periodic flow and then to ‘elastic turbulence’ is found. These transitions are found in experiments where either shear stress or shear rate is incrementally increased and then held at fixed values; the modes found following stable base flow are ‘stationary ring’, ‘competing spirals’, ‘multi-spiral chaotic’ and ‘spiral bursting’ modes, followed then by ‘elastic turbulence’. Each mode has a distinct rheological signature, and accompanying imaging of the secondary-flow field (simultaneous with rheological measurement) reveals kinematic structures including stationary and time-dependent rolls. The time-dependent changes in the secondary-flow structure can be related to the time-dependent viscosity in the case of several of the modes. Finally, the effect of polymer concentration on the transitional pathway modes is studied systematically.

Type
Papers
Copyright
© 2006 Cambridge University Press

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Schiamberg et al. supplementary movie

Movie 1. The movie shows formation of an axisymmetric recirculation during 'stationary ring' mode at a shear stress of 0.96 Pa for the 492 p.p.m. polyacrylamide solution (Mw= 18 x 106 g mol-1), corresponding to figure 4(b). The movie begins 2 minutes after the start of shearing at a shear stress of 0.96 Pa and spans a 3 minute 30 second period, with video rate set at 20 times real time.

Video 318 KB

Schiamberg et al. supplementary movie

Movie 1. The movie shows formation of an axisymmetric recirculation during 'stationary ring' mode at a shear stress of 0.96 Pa for the 492 p.p.m. polyacrylamide solution (Mw= 18 x 106 g mol-1), corresponding to figure 4(b). The movie begins 2 minutes after the start of shearing at a shear stress of 0.96 Pa and spans a 3 minute 30 second period, with video rate set at 20 times real time.

Video 684 KB

Schiamberg et al. supplementary movie

Movie 2. The movie shows a single 'multi-spiral chaotic' cycle at a shear stress of 2.6 Pa for the 492 p.p.m. polyacrylamide solution (Mw=18 x 106 g mol-1), corresponding to figure 5(a). The movie begins at the start of shearing at a shear stress of 2.6 Pa and spans a 12 minute period in real time, with video rate set at 50 times real time.

Video 482 KB

Schiamberg et al. supplementary movie

Movie 2. The movie shows a single 'multi-spiral chaotic' cycle at a shear stress of 2.6 Pa for the 492 p.p.m. polyacrylamide solution (Mw=18 x 106 g mol-1), corresponding to figure 5(a). The movie begins at the start of shearing at a shear stress of 2.6 Pa and spans a 12 minute period in real time, with video rate set at 50 times real time.

Video 1 MB

Schiamberg et al. supplementary movie

Movie 3. The movie shows three successive 'spiral bursting' cycles at a shear stress of 7.4 Pa for the 492 p.p.m. polyacrylamide solution (Mw= 18 x 106 g mol-1), corresponding to figure 5(b). The movie begins 11 minutes 30 seconds after the start of shearing at a shear stress of 7.4 Pa and spans an 8 minute 30 second period in real time, with video rate set at 50 times real time.

Video 438 KB

Schiamberg et al. supplementary movie

Movie 3. The movie shows three successive 'spiral bursting' cycles at a shear stress of 7.4 Pa for the 492 p.p.m. polyacrylamide solution (Mw= 18 x 106 g mol-1), corresponding to figure 5(b). The movie begins 11 minutes 30 seconds after the start of shearing at a shear stress of 7.4 Pa and spans an 8 minute 30 second period in real time, with video rate set at 50 times real time.

Video 923 KB

Schiamberg et al. supplementary movie

Movie 4. The movie shows 'elastic turbulence' at a shear stress of 54.9 Pa for the 492 p.p.m. polyacrylamide solution (Mw= 18 x 106 g mol-1), corresponding to figure 5(c). The movie begins 8 minutes after the start of shearing at a shear stress of 54.9 Pa and spans a 2 minute period in real time, with video rate set at 10 times real time.

Video 581 KB

Schiamberg et al. supplementary movie

Movie 4. The movie shows 'elastic turbulence' at a shear stress of 54.9 Pa for the 492 p.p.m. polyacrylamide solution (Mw= 18 x 106 g mol-1), corresponding to figure 5(c). The movie begins 8 minutes after the start of shearing at a shear stress of 54.9 Pa and spans a 2 minute period in real time, with video rate set at 10 times real time.

Video 1 MB

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