Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session X34: NonNewtonian Flows: General 
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Chair: Antony Beris, University of Delaware Room: 201 
Tuesday, November 21, 2023 8:00AM  8:13AM 
X34.00001: Exploring the Influence of Wall Slip on Viscoplastic Saffman–Taylor Fingers Thomasina V Ball, Neil J Balmforth Viscoplastic SaffmanTaylor fingering in a HeleShaw cell is present when a Newtonian fluid displaces a viscoplastic fluid. Experimentally, the viscoplastic fluids typically used, such as Carbopol, suffer effective slip along the plate walls. This can dramatically alter the instability observed but is often ignored. 
Tuesday, November 21, 2023 8:13AM  8:26AM 
X34.00002: Modeling and Simulation of Inhomogeneous TimeDependent Poiseuille Pipe Flow of Aggregating Concentrated Suspensions Antony N Beris, Soham Jariwala, Norman J Wagner The development of appropriate models and an efficient methodology for the effective numerical simulation of transient pipe flows of aggregating suspensions fluids, exhibiting thixotropic and viscoelastic effects, is discussed. A pseudospectral method based on Chebyshev orthogonal polynomial spatial approximations is used. This numerical method has been validated against the analytical solution of Newtonian and upperconvected Maxwell fluids in oscillatory Poiseuille flows. 
Tuesday, November 21, 2023 8:26AM  8:39AM 
X34.00003: Microstructural origins of shear thickening in dense suspensions William C Buchholtz, Vinutha H. A., Jeffrey S Urbach, Daniel L Blair, Emanuela Del Gado We investigate the possible microstructural underpinnings of shear thickening in dense suspensions through the behavior of both local and extended particle structures. As a model, we consider a simulated 2D suspension of soft disks at densities slightly below shear jamming in which the particles experience only frictional contact forces and Stokes drag. In this model the thickening flow exhibits several instances of distinct microstructure when compared with the thinning. In particular, the peaks of the pair correlation function reveal the emergence of straight, connected triplets of disks during the thickening which then buckle during the thinning. Equilateral triangles and symmetric quadrilaterals also show significant compression during the thinning when compared with the thickening. The emergence and ultimate deformation of these local structures suggests that during the thickening there is the growth of stress bearing particle networks. We confirm this by tracking the size and percolation of overconstrained strong force networks. This analysis shows that a percolation transition of these networks occurs during the thickening regime and disappears with the onset of the thinning. 
Tuesday, November 21, 2023 8:39AM  8:52AM 
X34.00004: Lorentz force induced shear waves in a layer of a Maxwell fluid Sergio Cuevas, José OlveraOrozco, Aldo Figueroa We numerically analyze the generation of shear waves in a twodimensional region where an electrically conducting viscoelastic fluid is confined. By imposing a Lorentz force caused by the interaction of a unidirectional alternating electric current with a steady magnetic field produced by one or several magnetic dipoles, superimposed shear waves are created in an oscillating vortex pattern. The viscoelastic behavior of the fluid layer is modeled using the linearized Maxwell model, while it is assumed that the fluid has a low electrical conductivity, so that the induced electromagnetic effects are negligible. A vorticity – stream function formulation is used to solve the governing equations, assuming a low Reynolds number flow. The Womersley and Deborah numbers, along with the Lorentz force parameter, characterize the dynamics of the flow. According to the magnetic field configurations and the value of the dimensionless parameters, different vorticity maps are obtained which resemble electromagnetic radiation patterns. It is found that shear waves can cross the whole system and cause interference leading to constructive resonances that substantially increase the amplitude of the velocity profiles. The use of this system for mixing enhancement purposes is explored. 
Tuesday, November 21, 2023 8:52AM  9:05AM 
X34.00005: Measurement of viscoelastic properties of a liquid using a rotating body of a general shape subjected to oscillatory shear Wook Ryol Hwang, Hye Jin Ahn We propose a systematic approach for measuring linear and nonlinear viscoelastic properties of a liquid by the oscillatory motion of an immersed rotating body in a vessel. The shape of a rotating object is general and we tested four different types of impellers in the present work: a disk, an anchor, and two different flat bladed turbines. The effective shear stress was properly scaled with a torque through the expression of complex viscosity and the strain magnitude was scaled by the deflection angle with an effective shear rate coefficient (the MetznerOtto constant). Three different concentrations of aqueous polyethylene oxide (PEO) solutions were tested and linear viscoelastic responses of storage and loss moduli were measured as a function of the oscillation frequency. In spite of the presence of nonrheometric and highly nonuniform flow field, comparison with the data from the conventional coneandplate and parallelplate fixtures of a rheometer shows remarkably accurate measurement with at most 7% deviation within the frequency range from 0.01 [rad/s] to 100 [rad/s] for all the impeller geometries, except for the pitched bladed turbine. In addition, we show that this method can be applied to large amplitude oscillatory shear experiments for nonlinear viscoelastic properties. The proposed method provides a versatile measurement for viscoelasticity, eliminating complicated issues in the conventional rheometry such as the wall slip, free surface evaporation/solidification and the edge fracture without a significant loss of accuracy. Furthermore, the method may facilitate the insitu measurement of viscoelastic properties of a fluid within an industrial reactor/agitator as a tool for insitu/online monitoring of microstructures. 
Tuesday, November 21, 2023 9:05AM  9:18AM 
X34.00006: Capillary imbibition of shearthinning fluids: from LucasWashburn to oscillatory regimes Pietro Poesio, Camille Steinik, Davide Picchi, Gianluca Lavalle The study of capillary imbibition has ramifications in many fields, such as energy, biology, process industry, and subsurface flows. Although the capillary rise of Newtonian liquids has been the subject of several studies since the seminal works of Lucas (1918) and Washburn (1921), its generalization to the case of nonNewtonian fluids is still an open question. To fill this gap, starting from first principles, we derive a transient onedimensional model describing the rising dynamics of shearthinning fluid, whose viscosity is described by the Ellis viscosity model. Our model identifies the scaling for the different imbibition regimes accounting for the interplay of inertial, gravity, and viscous nonNewtonian effects (i.e., the zeroshearrate and the shearthinning behaviour). Specifically, the rising dynamics is described by the interplay of three dimensionless parameters: the Richardson number, the Ellis number, and the shearthinning index. At early times the system follows a universal inertial regime, followed by two possible limiting regimes, i.e., the classical LucasWashburn and the oscillatory regimes. The competition between the governing dimensionless numbers dictates the transition between the two. We show that when the viscous effect dominates over inertia, the identification of a (timedependent) scaling law for the effective viscosity leads to a generalization of the LucasWashburn theory and the rescaled trajectories toward equilibrium collapse over the classical 1/2 scaling law. On the contrary, when inertia dominates the later stage of the imbibition, the filling length oscillates around the equilibrium. By means of linear control theory, we discuss the physical mechanisms that lead to such oscillating behaviour and map the different regimes in terms of the governing dimensionless parameters. 
Tuesday, November 21, 2023 9:18AM  9:31AM 
X34.00007: Suppression of vortexinduced vibrations of a cylinder in inertialviscoelastic flow Pieter R Boersma, Jonathan P Rothstein, Yahya ModarresSadeghi The study of vortex induced vibrations (VIV) has been primarily focused on Newtonian fluids. Recently, there has been an interest in the VIV response of a cylinder in nonNewtonian flows. Previous work has examined the VIV response of a cylinder in an inelastic, shear thinning fluid. Now we experimentally examine the response of a flexibly mounted rigid cylinder in a viscoelastic flow where fluid inertia and elasticity are important. The vortices in the wake of the cylinder become elongated and the amplitude response is suppressed. The traditional belldome amplitude response is altered to a triangular response and the lockin range is reduced. The subcritical response is suppressed and the critical Reynolds number at which vortices shed in the fixed and flexibly mounted case become similar. The existence of a critical elastic number is discussed that captures the transition from a stable cylinder to an oscillating cylinder. 
Tuesday, November 21, 2023 9:31AM  9:44AM 
X34.00008: Network modelling of yieldstress fluid flow in disordered porous media Elliott Sutton, Kohei Ohei, Maziyar Jalaal, Yuji Tasaka, Claudio P Fonte, Anne Juel Yieldstress fluid flow occurs in many industrial applications, including in porous systems during enhanced oil recovery and membrane emulsification. However, the high computational cost of computational fluid dynamics (CFD) simulations for yieldstress fluids hinders the study of these largescale systems. In this work, we develop a fullypredictive network model for flow through 2D disordered porous media that obtains a solution in minutes on a single CPU core, considerably faster than the days or weeks required by CFD with multiple CPU cores. Our model generates network nodes using a Voronoi tessellation, extracts geometric parameters accounting for the topology of the domain, and numerically solves mass and momentum conservation equations with a NewtonRaphson solver. We accurately predict the pressure drop and velocity field of flows with and without wall slip, validating our results against CFD simulations produced inhouse and from the literature. Wall slip is ubiquitous in realworld flows of these materials, dramatically decreasing friction at solidfluid interfaces and changing the overall resistance in porous networks. Thus, it was imperative that we accounted for this phenomenon in our model. 
Tuesday, November 21, 2023 9:44AM  9:57AM 
X34.00009: Computational modelling of the rheological response of wormlike micellar solutions in simple and complex deformations: flow past a sphere and contractionexpansion flow J. Esteban LopezAguilar, Hamid R TamaddonJahromi, Octavio Manero In this work, novel numerical solutions are provided on the flow of wormlike micellar solutions in both banding and nonbanding regimes, in complex benchmark flows, such as flow past a sphere and a modified Couette contractionexpansion flow. The model used here is the latest modelvariant of the BautistaManeroPuig family of constitutive equations, i.e. the BMP+_τ_{p} model [13]. The properties of this micellar rheological equationofstate are exposed in simple ideal deformations, such as steady simple shear and uniaxial extension. Solutions in complex flow, in benchmark flow pastasphere and a modified contractionexpansion geometries, are obtained with our hybrid finite volume/element algorithm and expose the influence of the thixotropic and viscoelastic features of these models in flowstructure and yieldfront representations. In flow past a sphere [2], in the mode of particle settling in wormlike micelles, location of a negativewake instability is predicted, whilst for extremely concentrated wormlike micellar solutions, foreaft asymmetries are observed, much resembling experimental finding for the settling of particles in viscoelastic Carbopol gels. In the modified Couette contractionexpansion flow cell [1], the influence of a complexflow deformation in a shearbanded flow is studied, for which simple shearbanding features, i.e. flow segregation, are lost in the mixed inhomogeneous sheartoextensional deformation found in the constriction zone, and are recovered in the fullydeveloped flow region downstream from the constriction. 
Tuesday, November 21, 2023 9:57AM  10:10AM 
X34.00010: Anomalous crystalline ordering of particles in a viscoelastic fluid under high shear Sijie Sun, Nan Xue, Stefano Aime, Hyoungsoo Kim, Jizhou Tang, Gareth H McKinley, Howard A Stone, David A Weitz

Tuesday, November 21, 2023 10:10AM  10:23AM 
X34.00011: Elastic particle model for coilstretch transition of dilute polymers in elongational flows Tong Gao The phenomenon of the "coilstretch'" transition, wherein a longchain polymer initially in a coiled state undergoes a sudden configuration change to become fully stretched under steady elongational flows, has been widely recognized. This transition can display intricate hysteresis behaviors under specific critical conditions, giving rise to unique rheological characteristics in dilute polymer solutions. Historically, microscopic stochastic models and Brownian dynamics simulations have shed light on the underlying mechanisms of the transition by uncovering bistable configurations of polymer chains. Following the initial work by Cerf(1952), we introduce a continuum model in this study to investigate the coilstretch transition in a constant uniaxial elongational flow. Our approach involves approximating the unfolding process of the polymer chain as an axisymmetric deformation of an elastic particle. We make the assumption that the particle possesses uniform material properties, which can be represented by a nonlinear, strainhardening constitutive equation to replicate the finite extensibility of the polymer chain. Subsequently, we analytically solve for the steadystate deformation using a polarization method. By employing this reduced model, we effectively capture the coilstretch transition and establish its specific correlations with material and geometric properties. The hysteresis phenomena can be comprehended through a forcebalance analysis, which involves comparing the externally applied viscous forces with the intrinsic elastic responsive forces. While simple, we demonstrate that our model provides a comprehensive understanding of the elastohydrodynamic nature of the coilstretch transition, which is independent of any stochastic properties of polymers considered in microscopic models. 
Tuesday, November 21, 2023 10:23AM  10:36AM 
X34.00012: Modeling polymeric lubricants with nonlinear stress constitutive relations Luca Biancofiore, Humayun Ahmed Polymers are added to enhance the tribological performance of lubricating oils so that they can withstand the applied load and resist degradation due to thermal effects and high shear stress. However, their addition can lead to the onset of nonNewtonian effects, in particular viscoelasticity, measured via the Weissenberg number (Wi), i.e. the ratio between the polymer relaxation time and the shear time scale. In this work, we examine the effect of nonlinear polymer traits, specifically (i) shear thinning and (ii) the finite polymer extensibility, on the load carrying capacity of the thin lubricating film via the viscoelastic Reynolds approach [Ahmed & Biancofiore, Journal of nonNewtonian Fluid Mechanics, 292, 104524] using constitutive relationships non linear in the stress, such as FENECR and FENEP. We validate our approach by comparisons with direct numerical simulations of viscoelastic films in a parabolic slider bearing. Thereafter, we focus on a journal bearing whose geometry depends on its eccentricity ratio. Our results show that viscoelasticity has a strong impact on the load. Load is (i) enhanced initially for small values of Wi but decreases later at large Wi due to shear thinning), (ii) exhibits a nonlinear dependence on the finite extensibility of the polymers, and finally (iii) is strenghtened (weakened) at low (high) eccentricity ratio. 
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