## Arratia, Paulo E

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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.Publication Material Properties of Caenorhabditis Elegans Swimming at Low Reynolds Number(2010-02-01) Purohit, Prashant Kishore; Krajacic, Predrag; Lamitina, Samuel Todd; Sznitman, Josué; Arratia, Paulo EUndulatory locomotion, as seen in the nematode Caenorhabditis elegans, is a common swimming gait of organisms in the low Reynolds number regime, where viscous forces are dominant. Although the nematode’s motility is expected to be a strong function of its material properties, measurements remain scarce. Here, the swimming behavior of C. elegans is investigated in experiments and in a simple model. Experiments reveal that nematodes swim in a periodic fashion and generate traveling waves that decay from head to tail. The model is able to capture the experiments’ main features and is used to estimate the nematode’s Young’s modulus E and tissue viscosity η. For wild-type C. elegans, we find E ≈ 3.77 kPa and η ≈ –860 Pa•s; values of η for live C. elegans are negative because the tissue is generating rather than dissipating energy. Results show that material properties are sensitive to changes in muscle functional properties, and are useful quantitative tools with which to more accurately describe new and existing muscle mutants.Publication Polymer drop breakup in microchannels(2007-12-27) Arratia, Paulo E; Durian, Douglas J; Gollub, Jerry PPublication 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, Jerry P; Ecke, R. EAlthough 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 Fluid Elasticity Can Enable Propulsion at Low Reynolds Number(2012-08-17) Keim, Nathan C; Garcia, Mike; Arratia, Paulo EConventionally, a microscopic particle that performs a reciprocal stroke cannot move through its environment. This is because at small scales, the response of simple Newtonian fluids is purely viscous and flows are time-reversible. We show that by contrast, fluid elasticity enables propulsion by reciprocal forcing that is otherwise impossible. We present experiments on rigid objects actuated reciprocally in viscous fluids, demonstrating for the first time a purely elastic propulsion set by the object’s shape and boundary conditions. We describe two different artificial “swimmers” that experimentally realize this principle.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 1.5×103 to 1.8×107. 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, JosuéThe 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. elegans’ 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 ‘skeletons’ 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. elegans’ segmentation and ‘skeletonizing’ across a wide range of motility assays.