Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session E12: Non-Newtonian Flows: Viscoplasticity |
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Chair: Neil Balmforth, University of British Columbia Room: 200 |
Sunday, November 22, 2015 4:50PM - 5:03PM |
E12.00001: Viscoplastic flow in a Hele-Shaw cell Neil Balmforth, Duncan Hewitt A theoretical study is presented of the flow of viscoplastic fluid through a Hele-Shaw cell that contains various kinds of obstructions. Circular and elliptical blockages of the cell are considered together with step-wise contractions or expansions in slot width, all within the simplifying approximation of a narrow gap. Specific attention is paid to the flow patterns that develop around the obstacles, particularly any stagnant plugged regions, and the asymptotic limits of relatively small or large yield stress. Periodic arrays of circular contractions or expansions are studied to explore the interference between obstructions. Finally, viscoplastic flow through a cell with randomly roughened walls is examined, and it is shown that constructive interferences of local contractions and expansions leads to a pronounced channelization of the flow. An optimization algorithm based on minimisation of the pressure drop is derived to construct the path of the channels in the limit of relatively large yield stress or, equivalently, relatively slow flow. [Preview Abstract] |
Sunday, November 22, 2015 5:03PM - 5:16PM |
E12.00002: Channelization of viscoplastic flow in a rough Hele-Shaw cell Duncan Hewitt, Neil Balmforth The flow of viscoplastic fluid down slender conduits or through porous media has application in a range of industrial and geophysical settings, from the plumbing of mud volcanoes to the transport of proppant slurries in hydraulic fracturing. The yield stress can cause the fluid locally to clog up, which can significantly affect the flow patterns. Flow of a viscoplastic fluid in a Hele-Shaw cell that has randomly ``roughened'' walls is investigated, both numerically and using analogue laboratory experiments. Fluid injected into the centre of the rough cell, which is initially full of the same fluid, show pronounced channelization: above a critical pressure drop (below which there is no flow and all the fluid is unyielded and stagnant), one or more thin conduits of yielded, flowing fluid develop. At larger pressure drops, more channels of yielded fluid develop. The quantity and width of the channels, and the value of the critical pressure drop, depend on the amplitude of the roughness of the walls of the cell. If this roughness is known, the locations of the first channels to flow and the corresponding pressure drop can be predicted by an optimization algorithm. [Preview Abstract] |
Sunday, November 22, 2015 5:16PM - 5:29PM |
E12.00003: Yield stress fluid flow in model porous media Johan Paiola, Hugues Bodiguel, Harold Auradou Yield stress fluids display interesting flow behavior due to their non-linear flow curve and some applications involve this flow in porous medial. Predicting the flow behavior is thus of great interest but is further complicated by the complexity of the geometry and the interplay between the heterogeneities of the medium and the existence of a yield stress. Models developed in order to describe Darcy's law assume a rheological law applied. Alternatively, micromechanical models predicts that the flow concentrates at low flow rates in preferential paths, which strongly depends on the details of the porous geometry. At this stage, rather few experiments are available at the scale of a few pores, and we propose in this work to study the flow of yield stress fluids in micromodels of porous media to address experimentally the existence and characteristic of these preferential paths. We use Carbopol as a model yield stress fluid. This fluid is injected into various model porous media. The main objective of our experiments is to map the fluid velocity field as a function of the global pressure drop applied. We develop a new experimental method where we can obtain simultaneously to measure local velocities at the scale of one channel (200 um) but on the entire porous geometry (5cm x 5cm). [Preview Abstract] |
Sunday, November 22, 2015 5:29PM - 5:42PM |
E12.00004: The transverse mobility of yield-stress fluids in fibrous media Setareh Shahsavari, Gareth H. McKinley The pressure-drop/flow-rate relationship for fluids that exhibit a yield stress and a shear dependent viscosity flowing through fibrous media is studied numerically. The Cauchy momentum equation along with the Bingham or Herschel-Bulkley constitutive equations are solved for flow transverse to a periodic array of fibers and systematic parametric studies are used to understand the individual roles of geometrical characteristics and fluid rheological properties. We develop a scaling model to predict the fluid mobility as a function of the medium porosity and the Bingham number. In addition, using this scaling model we estimate the width of the unyielded region between two adjacent fibers. Numerical computations are combined with the scaling model to obtain a criterion for the critical pressure gradient required to drive flow. Variations in the size of the yielded zones, the velocity profiles and the resulting stress fields are investigated for the limiting cases of (i) densely packed fiber arrays and (ii) very sparsely distributed fibers, and the hydrodynamic transition between these configurations is investigated. While this work focuses on the flow of inelastic fluids, the methodology can be extended to consider more complex rheology such as flow of elasto-visco-plastic fluids. [Preview Abstract] |
Sunday, November 22, 2015 5:42PM - 5:55PM |
E12.00005: Does Carbopol Elasticity affect its Yielding Dynamics? A study based on the Settling of a Particle in ''Plastic'' materials Dimitris Fraggedakis, Yiannis Dimakopoulos, John Tsamopoulos For several decades, Carbopol is assumed to be the ideal plastic material, exhibiting only yield phenomena without viscoelastic effects in yielded regions. Recently, it has been shown that when stresses do not overcome the yield criterion, it behaves as an ideal Hookean solid, Piau (2007). Also, experiments (Putz et al. (2006); Holenberg et al. (2012)) reveal phenomena which can be attributed only to elastic properties of the fluidized region, such as the appearance of the so-called ``negative wake,'' Harlen (2002), downstream the sphere and the loss of fore-aft symmetry of the yield surface around a sedimenting particle. Our study is based on the sedimentation of a confined particle in materials which exhibit elastoviscoplastic behavior and proves that Carbopol cannot be considered as the ideal plastic material anymore. Moreover, when elasticity comes into play, the derived stoppage criterion for a sedimenting sphere by Beris et al. (1985) and experimentally confirmed by Tabuteau et al. (2007) is not satisfied, as a complex stress field is developed around the particle and fluidization near the rigid surface is favored. The existence of the yield surface near the sphere enhances the formation of shear layers, which are responsible for the formation of the negative wake, irrespectively of the position of the confinement in relation to the sphere. [Preview Abstract] |
Sunday, November 22, 2015 5:55PM - 6:08PM |
E12.00006: Insights on the local dynamics during transient flows of waxy crude oils Michela Geri, Brice Saint-Michel, Thibaut Divoux, Sebastien Manneville, Gareth H. McKinley Waxy crude oils are mixtures of hydrocarbons and paraffin wax that behave as a Newtonian liquid at high temperatures and display solid-like properties below the solidification temperature of wax. In the latter case, waxy crude oils exhibit a yield stress and show a pronounced time-dependent behavior. By means of rheometry coupled to time-resolved ultrasonic velocimetry we investigate the local scenario associated with a series of decreasing and increasing ramps of shear rate composed of successive steps during which the stress is left to equilibrate for a fixed time. While being fully fluidized or 'shear-melted' at large shear rates, we observe that the sample experiences wall slip despite using rough boundary conditions and an arrested band grows inwards towards the rotor as the shear rate is decreased. This shear banding scenario arises from an underlying non-monotonic time-dependent response in the shear stress. As the shear rate is ramped back up to its initial value, the sample experiences a delayed yielding transition involving shear banding and wall slip over a range of shear rates that differs from the range observed on the decreasing branch. We finally discuss these results in the framework of a thixotropic elasto-visco-plastic model. [Preview Abstract] |
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