## Arratia, Paulo E

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Publication Regular and Irregular Splashing of Drops on Geometric Targets(2012-09-17) Juarez, Gabriel; Gastopoulos, Thomai; Zhang, Yibin; Siegel, Michael L; Arratia, Paulo EThe effect of target cross-sectional geometry on drop splashing is investigated using surfaces with length scales comparable to the drop diameter. The target cross-sectional geometries are regular polygon shapes that vary from a triangle (n = 3) to a decagon (n = 10), where n is the number vertices. The impacting cross-sectional surface area of all targets is constrained to equal the cross-sectional area of the impacting drop which is 6.38 mm2.Publication The effects of polymer molecular weight on filament thinning and drop breakup in microchannels(2009-11-04) Arratia, Paulo E.; Gollub, Jerry P.; Durian, Douglas J.; Cramer, L-AWe investigate the effects of fluid elasticity on the dynamics of filament thinning and drop breakup processes in a cross-slot microchannel. Elasticity effects are examined using dilute aqueous polymeric solutions of molecular weight (MW) ranging from 1.5Ã—103 to 1.8Ã—107. Results for polymeric fluids are compared to those for a viscous Newtonian fluid. The shearing or continuous phase that induces breakup is mineral oil. All fluids possess similar shear-viscosity (~0.2 Pa s) so that the viscosity ratio between the oil and aqueous phases is close to unity. Measurements of filament thickness as a function of time show different thinning behavior for the different aqueous fluids. For Newtonian fluids, the thinning process shows a single exponential decay of the filament thickness. For low MW fluids (103, 104 and 105), the thinning process also shows a single exponential decay, but with a decay rate that is slower than for the Newtonian fluid. The decay time increases with polymer MW. For high MW (106 and 107) fluids, the initial exponential decay crosses over to a second exponential decay in which elastic stresses are important. We show that the decay rate of the filament thickness in this exponential decay regime can be used to measure the steady extensional viscosity of the fluids. At late times, all fluids cross over to an algebraic decay which is driven mainly by surface tension.Publication Flagellar dynamics in viscous fluids(2009-09-11) Sakar, Mahmut-Selman; Arratia, Paulo E.; Lee, C.Publication Multi-Environment Model Estimation for Motility Analysis of Caenorhabditis elegans(2010-07-22) Sznitman, Raphael; Gupta, Manaswi; Hager, Gregory D.; Arratia, Paulo E.; Sznitman, JosuÃ©The nematode Caenorhabditis elegans is a well-known model organism used to investigate fundamental questions in biology. Motility assays of this small roundworm are designed to study the relationships between genes and behavior. Commonly, motility analysis is used to classify nematode movements and characterize them quantitatively. Over the past years, C. elegansâ€™ motility has been studied across a wide range of environments, including crawling on substrates, swimming in fluids, and locomoting through microfluidic substrates. However, each environment often requires customized image processing tools relying on heuristic parameter tuning. In the present study, we propose a novel Multi Environment Model Estimation (MEME) framework for automated image segmentation that is versatile across various environments. The MEME platform is constructed around the concept of Mixture of Gaussian (MOG) models, where statistical models for both the background environment and the nematode appearance are explicitly learned and used to accurately segment a target nematode. Our method is designed to simplify the burden often imposed on users; here, only a single image which includes a nematode in its environment must be provided for model learning. In addition, our platform enables the extraction of nematode â€˜skeletonsâ€™ for straightforward motility quantification. We test our algorithm on various locomotive environments and compare performances with an intensity-based thresholding method. Overall, MEME outperforms the threshold-based approach for the overwhelming majority of cases examined. Ultimately, MEME provides researchers with an attractive platform for C. elegansâ€™ segmentation and â€˜skeletonizingâ€™ across a wide range of motility assays.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 Propulsive Force Measurements and Flow Behavior of Undulatory Swimmers at Low Reynolds Number(2010-12-22) Shen, Xiaoning; Sznitman, JosuÃ©; Arratia, Paulo E; Sznitman, RaphaelThe swimming behavior of the nematode Caenorhabditis elegans is investigated in aqueous solutions of increasing viscosity. Detailed flow dynamics associated with the nematodeâ€™s swimming motion as well as propulsive force and power are obtained using particle tracking and velocimetry methods. We find that C. elegans delivers propulsive thrusts on the order of a few nanonewtons. Such findings are supported by values obtained using resistive force theory; the ratio of normal to tangential drag coefficients is estimated to be approximately 1.4. Over the range of solutions investigated here, the flow properties remain largely independent of viscosity. Velocity magnitudes of the flow away from the nematode body decay rapidly within less than a body length and collapse onto a single master curve. Overall, our findings support that C. elegans is an attractive living model to study the coupling between small-scale propulsion and low Reynolds number hydrodynamics.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.Publication Microfluidic Rheology of Soft Colloids above and below Jamming(2010-10-21) Nordstrom, Kerstin N.; Arratia, Paulo E; Basu, Anindita; Gollub, Jerry P.; Verneuil, E.; Durian, Douglas J.; Zhang, Zheng; Yodh, Arjun G.The rheology near jamming of a suspension of soft colloidal spheres is studied using a custom microfluidic rheometer that provides the stress versus strain rate over many decades. We find non-Newtonian behavior below the jamming concentration and yield-stress behavior above it. The data may be collapsed onto two branches with critical scaling exponents that agree with expectations based on Hertzian contacts and viscous drag. These results support the conclusion that jamming is similar to a critical phase transition, but with interaction-dependent exponents.Publication Polymeric filament thinning and breakup in microchannels(2008-03-18) Arratia, Paulo E; Gollub, Jerry P; Durian, Douglas JThe effects of elasticity on filament thinning and breakup are investigated in microchannel cross flow. When a viscous solution is stretched by an external immiscible fluid, a low 100 ppm polymer concentration strongly affects the breakup process, compared to the Newtonian case. Qualitatively, polymeric filaments show much slower evolution, and their morphology features multiple connected drops. Measurements of filament thickness show two main temporal regimes: flow- and capillary-driven. At early times both polymeric and Newtonian fluids are flow-driven, and filament thinning is exponential. At later times, Newtonian filament thinning crosses over to a capillary-driven regime, in which the decay is algebraic. By contrast, the polymeric fluid first crosses over to a second type of flow-driven behavior, in which viscoelastic stresses inside the filament become important and the decay is again exponential. Finally, the polymeric filament becomes capillary-driven at late times with algebraic decay. We show that the exponential flow thinning behavior allows a measurement of the extensional viscosities of both Newtonian and polymeric fluids.