Chaotic advection in creeping flow of viscoelastic fluids between slowly modulated eccentric cylinders

Journal Article · Mon Jul 01 04:00:00 EDT 1996 · Physics of Fluids (1994)

DOI:https://doi.org/10.1063/1.868960· OSTI ID:284679

Kumar, S; Homsy, G M ^[1]

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1. Department of Chemical Engineering, Stanford University, Stanford, California 94305 (United States)

Recent experiments show that very low levels of elasticity can either enhance or diminish the area over which chaotic advection occurs in creeping flows [T. C. Niederkorn and J. M. Ottino, J. Fluid Mech. {bold 256}, 243 (1993)]. No mechanistic explanation of this phenomenon is currently available. This has motivated us to consider the problem of two-dimensional flow between counter-rotating eccentric cylinders where the angular velocities are subject to slow, continuous modulation. Regular perturbation theory for low levels of elasticity is used to semi-analytically determine the viscoelastic correction to the Newtonian flow field based on the Oldroyd-B constitutive model. The geometric theory of Kaper and Wiggins [J. Fluid Mech. {bold 253}, 211 (1993)] is then applied to make predictions about how elasticity affects chaotic advection in quasi-steady flows. It is found that elasticity can act to either increase or decrease the area over which chaotic advection occurs, depending on the boundary motion. This is accomplished through three distinct mechanisms: (1) area changes of the maximum area over which chaotic advection can occur, the potential mixing zone (PMZ); (2) area changes of the region in the PMZ where fluid particles execute non-chaotic trajectories below a critical modulation frequency; (3) area changes of the region between the extrema of the Newtonian stagnation streamlines which does not belong to the PMZ. The mechanism responsible for these area changes is a modified pressure gradient in the angular direction, which in turn appears to be due to first normal stress differences caused by shearing. Numerical calculations of fluid particle trajectories confirm the predictions of the geometric theory. For the boundary motions considered here, the calculations yield two additional results about the effect of low levels of elasticity on chaotic advection. First, the critical modulation frequency is decreased. (Abstract Truncated)

• OSTI ID: 284679
• Journal Information: Physics of Fluids (1994), Journal Name: Physics of Fluids (1994) Journal Issue: 7 Vol. 8; ISSN PHFLE6; ISSN 1070-6631
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ADVECTION
CHAOTIC SYSTEMS
CREEP
DYNAMICAL SYSTEMS
ELASTICITY
NON-NEWTONIAN FLOW
PERTURBATION THEORY
ROTATION
VISCOELASTICITY