Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session G1: Non-Newtonian Flows: Rheology |
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Chair: Juan C. Del Alamo, University of California, San Diego Room: 3000 |
Monday, November 24, 2014 8:00AM - 8:13AM |
G1.00001: Quantitative Rheological Model Selection Jonathan Freund, Randy Ewoldt The more parameters in a rheological the better it will reproduce available data, though this does not mean that it is necessarily a better justified model. Good fits are only part of model selection. We employ a Bayesian inference approach that quantifies model suitability by balancing closeness to data against both the number of model parameters and their a priori uncertainty. The penalty depends upon prior-to-calibration expectation of the viable range of values that model parameters might take, which we discuss as an essential aspect of the selection criterion. Models that are physically grounded are usually accompanied by tighter physical constraints on their respective parameters. The analysis reflects a basic principle: models grounded in physics can be expected to enjoy greater generality and perform better away from where they are calibrated. In contrast, purely empirical models can provide comparable fits, but the model selection framework penalizes their a priori uncertainty. We demonstrate the approach by selecting the best-justified number of modes in a Multi-mode Maxwell description of PVA-Borax. We also quantify relative merits of the Maxwell model relative to powerlaw fits and purely empirical fits for PVA-Borax, a viscoelastic liquid, and gluten. [Preview Abstract] |
Monday, November 24, 2014 8:13AM - 8:26AM |
G1.00002: Improved johnson segalman model for couette flow Nariman Ashrafi An improved nonlinear viscoelastic model is proposed and examined for a flow between parallel plates. The model takes into account the interrelations of velocity gradients and stress components through introduction of appropriate coefficients. For a typical viscoelastic material, the coefficients are evaluated and incorporated within the model to simulate the flow of nonlinear Couette flow. In special cases, of the proposed model, typical upper convected Maxwell model and Johnson-Segalman fluid can be recovered from the proposed model further verifying the formulation. The proposed form of constitutive equation almost completely models the physical behavior of a wide range of nonlinear materials, yet it is computationally appropriate as well. The model also allows for the velocity and stress components to be represented by truncated series functions to be used for numerical purposes. [Preview Abstract] |
Monday, November 24, 2014 8:26AM - 8:39AM |
G1.00003: 2-Point Particle Tracking Microrheology of Directional Viscoelastic Gels Manuel Gomez-Gonzalez, Juan C. del Alamo By applying Particle Tracking Microrheology we can measure the stiffness of the cell cytoplasm, using a spherical microparticle as a probe. PTM relies on the assumption of isotropy, but this hypothesis breaks for highly oriented materials. In order to apply PTM to them, we have calculated the drag force of a particle embedded in a directional viscoelastic gel, modeled as a directional viscoelastic network frictionally coupled to a viscous isotropic fluid. The directional network is modeled with the Leslie-Ericksen equations and the fluid with the Stokes equation. The motion of particles embedded in such a directional gel is dependent on up to three viscoelasticity coefficients, but only two can be calculated from tracking a single probing particle. We have calculated the first order perturbation that the motion of one probe induces on a distant particle, as a function of the three viscoelasticity coefficients. By correlating the motion of two distant particles we can measure such a perturbation and obtain three independent equations that univocally determine the three viscoelasticity coefficients. We show the accuracy of the Directional 2-Point PTM by applying it to a control numerical experiment, and finally we apply it to an essential biological sample such as nematic F-actin. [Preview Abstract] |
Monday, November 24, 2014 8:39AM - 8:52AM |
G1.00004: Immersed Particle Dynamics in Fluctuating Fluids with Memory Christel Hohenegger, Scott McKinley Multibead passive microrheology characterizes bulk fluid properties of viscoelastic liquids by connecting statistically measurable quantities (e.g. mean-square displacement, auto-correlation to mechanical fluid properties (loss and storage modulus). Understanding how these material properties relate to biological quantities (e.g. exit time, first passage time through a layer) is of crucial importance for many pharmaceutical and industrial applications. To correctly model the correlations due to the fluid's memory, it is necessary to include a thermally fluctuating stress in the Stokes equations (Landau and Lifschitz 1958). We present such a model for an immersed particle passively advected by a fluctuating Maxwellian fluid. We describe the resulting stochastic partial differential equations for the underlying non-Markovian, stationary fluid velocity process and we present a covariance based numerical method for generating particle paths. Finally, we apply standard experimental one and two-point microrheology protocol to recover bulk loss and storage modulus and quantify the resulting errors. Our approach can be applied to a Stokes fluid with memory created by a large suspension of active swimmers or to the diffusion of a particle in a crowded environment. [Preview Abstract] |
Monday, November 24, 2014 8:52AM - 9:05AM |
G1.00005: Membrane Elastegrities: A New Model Viscoelastic Structure Eleftherios Pavlides, Jennifer Pearce We propose a new class of structures, membrane elastegrities, a network of rigid and elastic members maintaining shape through elastic forces, named by analogy to tensegrities that maintain shape through tension alone. Numerous researchers have proposed tensegrities as models to biological structure. Elastegrities expand tensegrity properties primarily by suggesting a mechanism for containing and pumping non-Newtonian fluids in living organisms. The chiral icosahedral elastegrity compared to the 6-strut tensegrity have identical symmetry, negative Poisson Ratio, and the reaction force to external forces is distributed throughout the elastic members causing reversible deformation. They also have important differences: a) elastic hinge connections enable containment and pumping of fluids versus nodal connections, b) simple assembly by folding a flat shape-memory material versus assembly requiring scaffolding, c) hinge connections limit freedom of movement resulting in isometric forces as members rotate cooperatively contracting versus large freedom of movement with unpredictable deformation. d) The chiral icosahedral elastegrity can contain liquid and requires increased force for equal displacement as it rotates towards a zero volume octahedron suggesting a mechanism for a non-Newtonian pump. [Preview Abstract] |
Monday, November 24, 2014 9:05AM - 9:18AM |
G1.00006: Rubber and gel origami: visco- and poro-elastic behavior of folded structures Arthur Evans, Nakul Bende, Junhee Na, Ryan Hayward, Christian Santangelo The Japanese art of origami is rapidly becoming a platform for material design, as researchers develop systematic methods to exploit the purely geometric rules that allow paper to folded without stretching. Since any thin sheet couples mechanics strongly to geometry, origami provides a natural template for generating length-scale independent structures from a variety of different materials. In this talk I discuss some of the implications of using polymeric sheets and shells over many length scales to create folded materials with tunable shapes and properties. These implications include visco-elastic snap-through transitions and poro-elastically driven micro origami. In each case, mechanical response, dynamics, and reversible folding is tuned through a combination of geometry and constitutive properties, demonstrating the efficacy of using origami principles for designing functional materials. [Preview Abstract] |
Monday, November 24, 2014 9:18AM - 9:31AM |
G1.00007: Particle migration in two-phase, viscoelastic flows Nick Jaensson, Martien Hulsen, Patrick Anderson Particles suspended in creeping, viscoelastic flows can migrate across stream lines due to gradients in normal stresses. This phenomenon has been investigated both numerically and experimentally. However, particle migration in the presence of fluid-fluid interfaces is hardly studied. We present results of simulations in 2D and 3D of rigid spherical particles in two-phase flows, where either one or both of the fluids are viscoelastic. The fluid-fluid interface is assumed to be diffuse and is described using Cahn-Hilliard theory. The particle boundary is assumed to be sharp and is described by a boundary-fitted, moving mesh. The governing equations are solved using the finite element method. We show that differences in normal stresses between the two fluids can induce a migration of the particle towards the interface in a shear flow. Depending on the magnitude of the surface tension and the properties of the fluids, particle migration can be halted due to the induced Laplace pressure, the particle can be adsorbed at the interface, or the particle can cross the interface into the other fluid. [Preview Abstract] |
Monday, November 24, 2014 9:31AM - 9:44AM |
G1.00008: Experimental study of the solid-liquid interface in a yield-stress fluid flow upstream of a step Li-Hua Luu, Philippe Pierre, Chambon Guillaume We present an experimental study where a yield-stress fluid is implemented to carefully examine the interface between a liquid-like unyielded region and a solid-like yielded region. The studied hydrodynamics consists of a rectangular pipe-flow disturbed by the presence of a step. Upstream of the step, a solid-liquid interface between a dead zone and a flow zone appears. This configuration can both model geophysical erosion phenomenon in debris flows or find applications for industrial extrusion processes. We aim to investigate the dominant physical mechanism underlying the formation of the static domain, by combining the rheological characterization of the yield-stress fluid with local measurements of the related hydrodynamic parameters. In this work, we use a model fluid, namely polymer micro-gel Carbopol, that exhibits a Hershel-Bulkley viscoplastic rheology. Exploiting the fluid transparency, the flow is monitored by Particle Image Velocimetry thanks to internal visualization technique. In particular, we demonstrate that the flow above the dead zone roughly behaves as a plug flow whose velocity profile can successfully be described by a Poiseuille equation including a Hershel-Bulkley rheology (PHB theory), with exception of a thin zone at the close vicinity of the static domain. The border inside the flow zone above which the so-called PHB flow starts, is found to be the same regardless of the flow rate and to move with a constant velocity that increases with the flow rate. We interpret this feature as a slip frontier. [Preview Abstract] |
Monday, November 24, 2014 9:44AM - 9:57AM |
G1.00009: The Propagation of the Gravity Current of Viscoplastic Fluid Ye Liu We are studying the spreading of the viscoplastic fluid of Bingham type over a horizontal plane, using both mathematical derivation and numerical experiments. We are interested in its final shape and whether theory and numerics correspond well. There are two theories for comparison: lubrication theory from asymptotics, and slipline theory from plasticity. The numerical method we are using is based on the volume-of-fluid method, with both regularization and Augmented Lagrangian for the constitutive law of Bingham type fluid. [Preview Abstract] |
Monday, November 24, 2014 9:57AM - 10:10AM |
G1.00010: Effects of confinement {\&} surface roughness in electrorheological flows Ahmed Helal, Maria J. Telleria, Julie Wang, Marc Strauss, Mike Murphy, Gareth McKinley, A.E. Hosoi Electrorheological (ER) fluids are dielectric suspensions that exhibit a fast, reversible change in rheological properties with the application of an external electric field. Upon the application of the electric field, the material develops a field-dependent yield stress that is typically modeled using a Bingham plastic model. ER fluids are promising for designing small, cheap and rapidly actuated hydraulic devices such as rapidly-switchable valves, where fluid flowing in a microchannel can be arrested by applying an external electric field. In the lubrication limit, for a Bingham plastic fluid, the maximum pressure the channel can hold, before yielding, is a function of the field-dependent yield stress, the length of the channel and the electrode gap. In practice, the finite width of the channel and the surface roughness of the electrodes could affect the maximum yield pressure but a quantitative understanding of these effects is currently lacking. In this study, we experimentally investigate the effects of the channel aspect ratio (width/height) and the effects of electrode roughness on the performance of ER valves. Based on this quantitative analysis, we formulate new performance metrics for ER valves as well as design rules for ER valves that will help guide and optimize future designs. [Preview Abstract] |
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