Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session L36: Suspensions: Theory and Modelling 
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Chair: Pavlos Vlachos, Purdue University Room: Georgia World Congress Center B408 
Monday, November 19, 2018 4:05PM  4:18PM 
L36.00001: 1D ShearThinning Flow: A Numerical Challenge for Physical Reliability Canberk Ozan, Gérard Labrosse, Abdullah Uguz A 1D shearthinning model is considered as a first approximation of the synovial fluid flow which occurs in an infinitely long channel bounded by moving solid boundaries. The viscosity is assumed to obey a power law expression, namely Modified Cross Model. The concentration of the hyaluronic acid influences the shearthinning behavior. Consequently, the viscosity depends on both the concentration and the strain rate. The problem contains two length scales whose ratio can reach extremely large values, 10^{200}. The failure is guaranteed to doubleprecision solvers. Their results can open the way to fake behaviors and erroneous interpretations. A physically reliable solution can be obtained provided the machine accuracy is fixed up to 200 accurate digits. Using the Mathematica software is a way to manage this control. 
Monday, November 19, 2018 4:18PM  4:31PM 
L36.00002: Combined quadrupolar–swapping trajectory model for microstructural evolution of drops in a strongly confined shear flow. Sagnik Singha, Abhilash Reddy Malipeddi, Mauricio ZuritaGotor, Kausik Sarkar, Jerzy Blawzdziewicz In strongly confined geometries deformable multidrop systems in shear flow rearrange to form highly ordered arrays aligned in the flow direction. Using a simplified numerical model, validated with direct simulations of collective drop dynamics, we show that microstructure evolution is controlled by two mechanisms: i) the hydrodynamic farfield quadrupolar interactions, which cause drop attraction and alignment, and ii) the nearfield swappingtrajectory mechanism, which produces drop repulsion. The interplay between the quadrupolar attraction and swappingtrajectory repulsion results in a characteristic drop separation d, corresponding to the stationary separation of a pair of drops. In a lowdensity regime a multidrop system forms fragmented chains with a constant drop spacing d. In contrast, at high densities, drops form percolating chains. While the interdrop distance within each chain remains constant, the spacing in different chains shows a variable distribution ranging from the nearcontact separation to drop separation under dilution.

Monday, November 19, 2018 4:31PM  4:44PM 
L36.00003: A twofluids model for numerical simulation of shear dominated suspension flows Federico Municchi, Pranay P. Nagrani, Ivan C. Christov Suspension flows are ubiquitous in nature and industry. However, these flows are notoriously difficult to model due to the variety of fluidparticle and particleparticle interactions involved. We focus on nonBrownian sheardominated suspensions, where irreversible phenomena like particle diffusion and migration develop, requiring anisotropic stress models to describe the suspension rheology. On a continuum level, reducedorder models like the suspension balance model (SBM) or the diffusive flux model are commonly used to predict particle migration phenomena. We propose a new method based on the twofluid model (TFM), where both the phases are considered as interpenetrating continua. Specifically, we show that when an anisotropic stress analogous to that used in the SBM is added to the equilibrium equations for the particle phase, the TFM is able to predict particle migration. Unlike the SBM, the TFM does not require the assumptions of a steady suspension velocity and Stokesian fluid. Thus, the TFM can be easily extended to include buoyancy and even kinetic collisional models. 
Monday, November 19, 2018 4:44PM  4:57PM 
L36.00004: Apparent and effective viscosity of 2D suspensions Harishankar Manikantan, Todd Squires Many lipid and surfactant monolayers exhibit coexistence of discrete condensed domains in a continuous 2D liquid. These domains are typically more resistant to deformation than the surrounding liquid, and therefore alter the effective rheology of the monolayer. Such a system is well approximated by a 2D liquid containing rigid inclusions, with the added caveat that the inclusions grow at the expense of the continuous phase upon compression. We look at the dilatational rheology of such a monolayer. When the 2D liquid is surface inviscid, we use a simple linear model for the exchange flux between the condensed and liquid phases to show that the monolayer behaves like a Maxwell fluid. Notably, our model suggests a ratedependent elastic modulus during phase coexistence and an apparent surface dilatational viscosity, both in agreement with recent experiments. On the other hand, when the continuous phase is inherently surface viscous, the presence of rigid domains introduces an additional source of viscous dissipation. We calculate the hydrodynamic stress and effective surface viscosity in this case, and illustrate its implications in experimental systems. 
Monday, November 19, 2018 4:57PM  5:10PM 
L36.00005: Spheres settling in an OldroydB fluid TsorngWhay Pan, Roland Glowinski In this talk we present a numerical study of two balls settling in a vertical channel with a square crosssection filled with an OldroydB fluid. Two initial configurations have been studied: two balls released side by side and one atop the other. For the side by side initial configuration, two balls may stay apart and interact periodically or form a vertical chain. For the initial configuration with one ball atop the other, we have obtained that either the trailing ball catches up the leading one to form a vertical chain or two balls separate with a stable final distance as observed experimentally in Boger fluid. 
Monday, November 19, 2018 5:10PM  5:23PM 
L36.00006: Exact Solutions, Asymptotics and Applications for Unequal Spheres in in Viscous Fluid Benjamin Goddard, Rory Mills, Jin Sun Hydrodynamic interactions between bodies immersed in viscous fluid have been shown to be important in modelling many complex fluid phenomena. Of particular interest for applications are suspensions of solid particles, e.g., high solid volume fraction cornstarch suspensions and fluidised beds, which exhibit highly nonNewtonian characteristics, such as shear thickening and normal stress differences, posing great challenges in predicting the flow. We study the problem of two spheres approaching each other along their line of centres suspended in viscous fluid, fundamental to understand the dense suspension behaviour. We give, for the first time, the complete formula of the hydrodynamic interaction force between the spheres. We also rigorously derive the behaviour of the forces as the nondimensional separation goes to zero and infinity, reproducing known heuristic results. The formulae are then implemented in the recently developed dynamical density functional theory (DDFT) to obtain novel solutions to problems concerning short range hydrodynamic interactions. Such interactions will be seen to be crucial in capturing phenomena associated with the dynamics of differentlysized and shaped species of particles, the effects of confinement and systems with enforced background flow. 
Monday, November 19, 2018 5:23PM  5:36PM 
L36.00007: Kinematics of αemitting dilute colloidal dispersions Graham Wilson, Amir Bahadori, Hitesh Bindra Colloidal dispersions and their rheology are wellunderstood and have been used for many scientific applications. Kinematics of dilute or dense colloidal dispersions, which play a critical role in their application deployment potential, are modeled using Stokesian dynamics and the Langevin equation. These models are applied for predicting rheological behavior under an external field or for selfpropelled colloids. Explored here is a new class of colloidal dispersions with αemitting radioactive isotopes as constituents of colloidal particles. Emission of a heavy charged nucleus (^{4}He^{2+}) can impart substantial momentum to the nano or microscale colloidal particle that is the source of the radioactive emission. For a certain size and composition of αemitting colloidal particles, kinematics are largely governed by the impulse generated from radioactive discharge. Other forces, such as Brownian forces or those due to an external field, such as gravity, have reduced importance. In light of this, a new force term with random and fixed components accounting for radioactive emission impulse has been derived analytically and verified via numerical simulations. 
Monday, November 19, 2018 5:36PM  5:49PM 
L36.00008: Contact Friction and Normal Stresses in Particle Suspensions Jurriaan Gillissen Starting with the Smoluchowski equation for the twoparticle configuration space, where particles interact via lubrication and Coulomb friction forces, we derive a continuum model for the particle suspension microstructure and stress. The model predicts, that contact friction induces an interparticle pull in the flow direction and an interparticle push in the gradient direction, i.e., a positive first normal stress difference. These results rationalise experimental observations in shear thickening suspensions, reported in the literature. 
Monday, November 19, 2018 5:49PM  6:02PM 
L36.00009: The effect of hydrodynamic interactions on the Brownian diffusion of spheroidal particles in a suspension Navaneeth Kizhakke marath, John S. Wettlaufer Batchelor (1976) determined the effect of hydrodynamic interactions on the diffusivity of rigid spheres in a suspension. In general, the particles in a colloidal suspension are anisotropic, interact with each other hydrodynamically and exhibit both translational and rotational diffusivities, which underlie the estimates of the particle size and shape from dynamic light scattering experiments. Unlike spheres, the translation of a spheroid is coupled to its rotation. We calculate the effect of hydrodynamic interactions on the shorttime selfdiffusivities of rigid spheroids in a suspension in terms of a correction to the diffusivities of rigid spheroidal particles in a suspension to O(nL^{3}), where n is the number density of the spheroids and L is their characteristic length. G. K. Batchelor, Brownian diffusion of particles with hydrodynamic interaction, J. Fluid Mech., 74, 129 (1976) 
Monday, November 19, 2018 6:02PM  6:15PM 
L36.00010: A scalable O(N) computational framework for spheres in Stokes and Laplace fields Wen Yan, Dhairya Malhotra, Eduardo Corona, Shravan Veerapaneni, Michael Shelley The balance of flexibility, accuracy, and efficiency is one longstanding topic in the design and implementation of computational tool. Based on recent advances in Boundary Integral Equation (BIE) theories, we developed a software framework which fits modern computers and inherits the flexibility of BIE. Further, this framework is spectrally accurate because spherical harmonics are used and special formulas are derived for close pairs. Due to such accuracy, lubrication effects can be directly resolved. This framework is also coupled to a new collision resolving algorithm formulated as a solution to a linear complementarity problem, to guarantee the stability of time stepping at large timestep sizes. We demonstrate the capability of this framework in sedimentation and other problems. 
Monday, November 19, 2018 6:15PM  6:28PM 
L36.00011: Power Series for Shear Stress of Polymeric Liquid in Largeamplitude Oscillatory Shear Flow Pongthep Poungthong, Chaimongkol Saengow, A. Jeffrey Giacomin, Chanyut Kolitawong Exact solutions for shear stress in a polymeric liquid subjected to largeamplitude oscillatory shear flow (LAOS) contain many Bessel functions. Approximate analytical solutions for shear stress in LAOS often take the form of the first few terms of a power series in the shear rate amplitude, and without any Bessel functions. There is thus interest in extending the Goddard integral expansion (GIE), to an arbitrary number of terms. In continuum theory, these truncated series are arrived laboriously using GIE. However, each term in the GIE requires much more work than its predecessor. In this paper, we begin with the exact solution for shear stress responses in corotational Maxwell fluids, and then perform an expansion by symbolic computation to confirm up to the sixth power, and to then continue the GIE. In this paper for example, we continue the GIE to the 40th power of the shear rate amplitude. We use Ewoldt grids to show our main result to be highly accurate. We also show the radius of convergence of the GIE to be an infinite. 
Monday, November 19, 2018 6:28PM  6:41PM 
L36.00012: Multiparticle Collision Dynamics Modelling of Nematic Liquid Crystal with Variable Order Parameter Shubhadeep Mandal, Marco G Mazza In this study we have generalized the particlebased multiparticle collision dynamics (MPC) method to model the hydrodynamics of nematic liquid crystals. We follow the tensorial formulation of nematodynamics given by the QianSheng theory [Phys. Rev. E 58, 7475 (1998)]. A tensor assigned to each MPC particle represents the orientation of the nematic director, and whose average corresponds to the macroscopic tensor order parameter. The applicability of this new method is verified by performing several physical and numerical tests. We have tested: (a) the isotropicnematic phase transition, (b) the annihilation dynamics of a pair of point defects, (c) the flow alignment of the nematic director in shear and Poiseuille flows, and (d) the velocity profile in shear and Poiseuille flows. We have found excellent agreement with existing literature. Additionally, we study the threedimensional solutions of the Stokes equation. We describe the decay of stokeslets stresslet and rotlet flow fields in nematic liquid crystals. The present method can have farreaching implications not only in modeling of nematic flows, but also to study the motion of colloids and microswimmers immersed in an anisotropic medium. 
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