CHAOTIC ADVECTION IN CREEPING FLOW OF VISCOELASTIC FLUIDS BETWEEN SLOWLY MODULATED ECCENTRIC CYLINDERS

Recent experiments show that very low levels of elasticity can either enhance or diminish the area over which chaotic advection occurs in cr eeping flows [T. C. Niederkom and J. M. Ottino, J. Fluid Mech. 256, 24 3 (1993)]. No mechanistic explanation of this phenomenon is currently available. This has motivated us to consider the problem of two-dimens ional flow between counter-rotating eccentric cylinders where the angu lar velocities are subject to slow, continuous modulation. Regular per turbation theory for low levels of elasticity is used to semi-analytic ally determine the viscoelastic correction to the Newtonian flow field based on the Oldroyd-B constitutive model. The geometric theory of Ka per and Wiggins [J. Fluid Mech. 253, 211 (1993)] is then applied to ma ke 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 mech anisms: (1) area changes of the maximum area over which chaotic advect ion can occur, the potential mixing zone (PMZ); (2) area changes of th e region in the PMZ where fluid particles execute non-chaotic trajecto ries below a critical modulation frequency; (3) area changes of the re gion 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, whic h in turn appears to be hue to first normal stress differences caused by shearing. Numerical calculations of fluid particle trajectories con firm 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, th e critical modulation frequency is decreased. Second, the rate of chao tic mixing, as measured by the largest Liapunov exponent, is increased for modulation frequencies greater than the critical Newtonian value. (C) 1996 American Institute of Physics.