Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session R37: NonNewtonian Flows: Theory 
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Chair: Fabio Ramos, Federal University of Rio de Janeiro Room: 203AB 
Monday, November 20, 2023 1:50PM  2:03PM 
R37.00001: The shape of a maximal pile of yieldstress fluid supported by an obstruction Nitay Ben Shachar, Douglas R Brumley, Andrew J Hogg, Edward M Hinton Viscoplastic fluid flows that occur in nature, such as lava, mud or debris flows, frequently interact with natural or constructed barriers leaving static mounds of material. Using Charpit's method, we present an analytical solution to the shape of the static mound supported by a square barrier on an inclined plane in the lubrication approximation. Expressions for the physical characteristics of the mound, such as its maximal height and total weight, are found from the solution. The calculated shape represents the maximal static mound supported by the barrier, and thus is independent of the original upstream flux source. A single dimensionless parameter describes the shape of the mound, the ratio of the yield stress to the slopeinduced stress, and hence it is independent of the constitutive relation beyond the yield stress. A new rheometric technique is suggested based on our solution, where the yield stress is determined using a simple experimental setup. We demonstrate that the method generalises to other barrier shapes, such as circular and rhomboidal barriers. Comparison with preliminary experimental results are discussed. 
Monday, November 20, 2023 2:03PM  2:16PM Author not Attending 
R37.00002: Abstract Withdrawn

Monday, November 20, 2023 2:16PM  2:29PM 
R37.00003: Shallow viscoplastic flow around the inside of a rotating cylinder Neil J Balmforth, Thomasina V Ball Lubrication theory is presented for the flow of a viscoplastic fluid (described by the HerschelBulkley law) around the inside surface of a rotating cylinder. The analysis predicts the steady states typically reached after a small mumber of rotations, at speeds for which the fluid largely collects in a prominent pool in the lower part of the cylinder. The analysis also captures the drainage of the film around the inside of a stationary cylinder. Specific consideration is given to the plastic limit, arising for arbitrarily small rotation rates where the fluid behaves like a perfectly plastic material satisfying the von Mises yield condition. Theoretical predictions are compared with experiments using a Carbopol suspension. 
Monday, November 20, 2023 2:29PM  2:42PM 
R37.00004: Similarity relations for laminar pipe flows of Bingham fluids in friction coordinates Fabio A Ramos, Gabriel Sanfins We introduce novel similarity relations, along with their corresponding symmetry groups, for examining the velocity profile and friction factor of laminar Bingham fluid flows using friction coordinates. Specifically, we provide a valuable new expression for calculating the friction factor of Bingham plastic fluids when pressure gradient data is accessible. Our findings reveal that there are no clear similarity relations for the mean velocity profile (MVP) and friction factor formulas in bulk coordinates. Consequently, friction coordinates serve as the most suitable framework for describing this problem. 
Monday, November 20, 2023 2:42PM  2:55PM 
R37.00005: Quasisteady sedimentation of a sphere in an OldroydB fluid Tachin Ruangkriengsin, Evgeniy Boyko, Howard A Stone We investigate the quasisteady sedimentation of a sphere perpendicular 
Monday, November 20, 2023 2:55PM  3:08PM 
R37.00006: Theoretical Model for Velocity Profile and Pressure Drop in Perfect Coreannular Flow of Immiscible Herschelâ€“Bulkley Fluids in a Horizontal Pipe Mayank K Saini, Shreyaskar Gautam, Sumit Tripathi This study investigates an axisymmetric perfect coreannular flow (PCAF) scenario where two incompressible and immiscible Herschelâ€“Bulkley fluids flow in a horizontal pipe. A theoretical model is developed for steady and fully developed PCAF to predict the velocity profiles and pressure drops for different yield stress and power law characteristics of both the fluids. The model presented in this study clearly demonstrates that the velocity profiles and pressure drops in a PCAF arrangement depend on the power law characteristics of both the core and annular fluids, as well as on the respective yield stress values. As the consistency index of the core fluid increases, it behaves more like a solid, leading to a reduced dependency on its flow behaviour index. However, when there are smaller viscosity differences between the core and annular fluids, the flow behaviour index of the core fluid plays a significant role in determining velocity profiles. The yield stresses of the core and annular fluids are also found to significantly affect the velocity profiles and pressure drop in the PCAF arrangement, even at comparable values of actual shear stresses of the coflow system. Lastly, the validation of the theoretical model is presented through experimental data and numerical simulations available in the literature. 
Monday, November 20, 2023 3:08PM  3:21PM 
R37.00007: Global nonlinear stability of OldroydB fluids in plane Couette flow Andrew Wynn, Joshua Binns This talk will give a rigorous proof of global nonlinear stability for OldroydB fluids in plane Couette flow. Specifically, we derive conditions under which perturbations of arbitrary magnitude must decay asymptotically, which naturally extend classical results for Newtonian fluids to the nonNewtonian setting. The challenge of performing nonlinear stability analysis for viscoeasltic flows is in finding an appropriate quantification of both perturbations from a basestate. To this end, we introduce a new measure, the perturbation entropy, which generalises the notion of relative entropy and gives a probabilistic measure of the deviation of the polymer configuration tensor from its steady distribution. We will show that at any Reynolds number lower than the Newtonian energy stability limit, there exists a range of polymer densities and Weissenberg numbers for which the OldroydB viscoelastic model is also nonlinearly stable. 
Monday, November 20, 2023 3:21PM  3:34PM 
R37.00008: Viscoelastic contributions to the infinite length journal bearing Jonathon K Schuh Viscoelastic fluids in shear produce normal stresses. In rotating devices, these normal stresses produce a nonzero pressure field that would not exist in the same flow conditions with purely viscous fluids. This additional elastic pressure field has been used to increase the load carrying capacity of thrust bearings, and that same analysis can be extended to journal bearings. Here, the Cauchy momentum equations in polar coordinates are solved in the thin film limit using a perturbation expansion in the Deborah number (De). Viscoelasticity is included through an Upper Convected Maxwell model with a solvent viscosity (Upper Convected Jeffreys model). When De=0, the model resembles the Reynolds equation (a restatement of conservation of mass and momentum for a purely viscous fluid) for an infinite length journal bearing. The De=0 results match the predictions of the Reynolds equation over all eccentricity ratios, validating the model. As the De increases, the load carrying capacity and altitude angle for a given eccentricity ratio also increase. This suggests that viscoelasticity is beneficial in journal bearing applications and provides designers another mechanism for decreasing friction in lubricated journal bearings. 
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