Arratia, Paulo E
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Publication Stretching and mixing of non-Newtonian fluids in time-periodic flows(2005-05-05) Arratia, Paulo E.; Voth, Greg A.; Gollub, J. P.The stretching of fluid elements and the dynamics of mixing are studied for a variety of polymer solutions in nearly two-dimensional magnetically driven flows, in order to distinguish between the effects of viscoelasticity and shear thinning. Viscoelasticity alone is found to suppress stretching and mixing mildly, in agreement with some previous experiments on time-periodic flows. On the other hand, the presence of shear thinning viscosity (especially when coupled with elasticity) produces a dramatic enhancement in stretching and mixing compared to a Newtonian solution at the same Reynolds number. In order to understand this observation, we study the velocity field separately in the sheared and elongational regions of the flow for various polymer solutions. We demonstrate that the enhancement is accompanied by a breaking of time-reversal symmetry of the particle trajectories, on the average. Finally, we discuss possible causes for the time lags leading to this temporal symmetry breaking, and the resulting enhanced mixing.Publication Stretching fields and mixing near the transition to nonperiodic two-dimensional flow(2008-05-30) Twardos, M. J.; Arratia, Paulo E.; Rivera, M. K.; Voth, G. A.; Gollub, J. P.; Ecke, R. E.Although time-periodic fluid flows sometimes produce mixing via Lagrangian chaos, the additional contribution to mixing caused by nonperiodicity has not been quantified experimentally. Here, we do so for a quasi-two-dimensional flow generated by electromagnetic forcing. Several distinct measures of mixing are found to vary continuously with the Reynolds number, with no evident change in magnitude or slope at the onset of nonperiodicity. Furthermore, the scaled probability distributions of the mean Lyapunov exponent have the same form in the periodic and nonperiodic flow states.Publication Elastic Instabilities of Polymer Solutions in Cross-Channel Flow(2006-04-14) Arratia, Paulo E.; Thomas, C. C.; Diorio, J.; Gollub, J. P.When polymer molecules pass near the hyperbolic point of a microchannel cross flow, they are strongly stretched. As the strain rate is varied at low Reynolds number ( < 10-2), tracer and particle-tracking experiments show that molecular stretching produces two flow instabilities: one in which the velocity field becomes strongly asymmetric, and a second in which it fluctuates nonperiodically in time. The flow is strongly perturbed even far from the region of instability, and this phenomenon can be used to produce mixing.