Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session L26: Suspensions: Theory, Modeling, and Simulations 
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Chair: Wenxiao Pan, University of WisconsinMadison Room: 234 
Monday, November 21, 2022 8:00AM  8:13AM 
L26.00001: Fast Simulation of Particulate Suspensions Enabled by Graph Neural Network Part I: Theory and Framework Zhan Ma, Zisheng Ye, Wenxiao Pan Predicting the dynamic behaviors of particles in suspension subject to hydrodynamic interaction (HI) and external drive can be critical for many applications. By harvesting advanced deep learning techniques, we present a new framework, hydrodynamic interaction graph neural network (HIGNN), for inferring and predicting the particles' dynamics in Stokes suspensions. It overcomes the limitations of traditional approaches in computational efficiency, accuracy, and/or transferability. In particular, by uniting the data structure represented by a graph and the neural networks with learnable parameters, the HIGNN constructs surrogate modeling for the mobility tensor of particles which is the key to predicting the dynamics of particles subject to HI and external forces. It can accurately capture both the longrange HI and shortrange lubrication effects. In this talk, we introduce the HIGNN framework and demonstrate its accuracy, efficiency, and transferability in a variety of particulate suspension systems. 
Monday, November 21, 2022 8:13AM  8:26AM 
L26.00002: Fast Simulation of Particulate Suspensions Enabled by Graph Neural Network Part II: Computational Efficiency and Scalability Zhan Ma, Zisheng Ye, Wenxiao Pan We have introduced a new framework, the hydrodynamic interaction graph neural network (HIGNN), for fast simulation of particulate suspensions. The HIGNN, once constructed, permits fast predictions of the particles' velocities and is transferable across suspensions of different numbers/concentrations of particles subject to any external forcing. The prediction cost by the HIGNN scales at O(N^{2}) because the twobody hydrodynamic interaction (HI) not only dominates the shortrange lubrication effect but also decays very slowly (O(r^{1})) in long range. As a result, we cannot presume a cutoff distance but must include all the particles when computing their velocities. The edge connections are hence built between any two vertices in the graph as an input of GNN. In this talk, we focus on how to reduce the scaling of cost down to quasi linear, i.e., O(N logN), to further accelerate the HIGNN’s computational efficiency, by leveraging the hierarchical matrix techniques. 
Monday, November 21, 2022 8:26AM  8:39AM Author not Attending 
L26.00003: A spectral integral equation method for smooth genuszero surfaces using spherical grid rotations Bryce Palmer, Metin Aktulga, Tong Gao, Balasubramaniam Shanker We present a scalable and accurate algorithm for evaluating singular and nearlysingular boundary integral operators on smooth, genuszero, threedimensional surfaces. Boundary integrals of this type often arise when solving, for example, the hydrodynamic interaction between particles suspended in a Stokes flow. Our algorithm relies on decomposing surface quantities in terms of spherical or vector spherical harmonics. We then apply a smooth quadrature rule in combination with spherical grid rotations to rewrite the desired operator in terms of known analytical integrals on the sphere. We validate our method against several benchmark tests for single and multiple particles with spherical, ellipsoidal, and radialmanifold shapes and demonstrate that our algorithm can achieve spectral accuracy and superalgebraic convergence while maintaining low computational complexity. 
Monday, November 21, 2022 8:39AM  8:52AM Author not Attending 
L26.00004: Effect of point viscosity variations in a fluid on the dynamics of a particle Debasish Das We derive the flow field disturbance produced by point viscosity variations in a heterogeneous fluid when subject to a background flow while neglecting fluid inertia. The disturbance flow field is found to be identical to that generated by a forcedipole called stresslet. Using a combination of theory and numerical simulations based on boundary element method, we show how the hydrodynamics of an active rigid particle is altered due to the presence of point viscosity variations. In particular, we model areas of the fluid with viscosity lower than the mean viscosity as sinks and those higher as sources. Modelling a fluid with viscosity gradient in this manner, we reproduce the phenomena published by Oppenheimer et al. Phys. Rev. Fluids 1, 014001 (2016) where it was shown that the translation and rotation of a spherical particle can get coupled giving rise to nontrivial dynamics. 
Monday, November 21, 2022 8:52AM  9:05AM 
L26.00005: Orientation dynamics of spheroids in linear flows Pulkit Kumar Dubey, Sangamesh Gudda, Ganesh Subramanian We study the orientation dynamics of a neutrally buoyant spheroid suspended in the oneparameter family of planar linear flows, in the presence of weak fluid and particle inertia, as characterized by the Reynolds (Re) and Stokes numbers (St). Recent numerical studies have shown a rich dynamical behavior for finite Re and St. In particular, an intricate sequence of bifurcations mediates the transition from a closed to an open trajectory topology, on the unit sphere of orientations, with increasing inertia; although, these studies are for restricted values of the spheroid aspect ratio and for simple shear flow. We demonstrate that the sequence of bifurcations can be reproduced within the smallRe, St framework. An examination of the governing twodimensional system of equations, obtained from earlier efforts, allows us to organize the possible bifurcation scenarios in a parameter space consisting of the spheroid aspect ratio (κ) , the planar linear flow parameter (λ) and the ratio St/Re. 
Monday, November 21, 2022 9:05AM  9:18AM Author not Attending 
L26.00006: Exploration of Flexible Aggregate Mobility  Size Dependence and Fluid Penetration Depth Over a wide range of fractal dimensions using Stokesian Dynamics Narayani V Kelkar, Jyoti R Seth, Ashwin Amalaruban, Y.S Mayya, Jayant Krishnan, S Anand The hydrodynamic behavior of flexible fractal aggregates has important applications in the chemical industry and biotechnology. The dependence of the mobility radius with respect to different fractal dimensions and fluid penetration depth for different interparticle interactions can be characterized by the method of Stokesian dynamics (SD), which is a powerful tool that accounts for all orders of monomermonomer interactions. 
Monday, November 21, 2022 9:18AM  9:31AM 
L26.00007: Reciprocal theorem and Faxen's laws for particles in linear twophase materials Moslem Moradi, Wenzheng Shi, Ehssan Nazockdast Many soft and biological materials, including the cell cytoskeleton and polymer gels, are composed of a filamentous network that is permeated by a fluid, and they often contain particles of various shape, sizes and mechanical properties. In many applications we are interested in computing the net force/toque and velocity of these particles in response to external and active forces. The net force and velocity of inclusions in continuum scale are conventionally computed by solving the governing equations and integrating over the particle's surface. Here we present a reciprocal theorem for linear twofluid models, which formulates the governing equations of the elastic network and the viscous fluid in terms of integrals of their traction and displacement fields over the particle's surfaces. This formulation allows for direct calculations of the net variables without the need to solve the governing equations. To demonstrate its utility, we use the reciprocal theorem to develop Faxen's laws for calculating the force on a rigid sphere in a general twophase background deformation field. Faxen's laws can be used to develop fast particle simulation methods such as Stokesian Dynamics. Finally, we use the reciprocal theorem to develop a boundary integral formulation of the governing equations. 
Monday, November 21, 2022 9:31AM  9:44AM 
L26.00008: Controlling Extrudate Volume Fraction through Poroelastic Extrusion of Entangled Fibers Zehao Pan, Janine K Nunes, Camille Duprat, Ho Cheung Shum, Howard A Stone When a suspension of spherical or nearspherical particles passes through a constriction the volume fraction typically either remains the same or decreases. In this talk, in contrast to these particle suspensions, we observe that an entangled fiber suspension increases its volume fraction by 2 to 14 fold after passing through a constriction. We attribute this feature to the entanglements among the fibers that yield an elastic response when stretched, which allows the fiber network to move faster than the surrounding liquid in a converging channel. By changing the geometry of the fibers, we find that the entanglements may originate from interlocking shapes or high flexibility. Through direct imaging inside an extrusion channel, we quantify the velocity variations of the fibers during extrusion. A quantitative poroelastic model is used to explain the increase in velocity and extrudate volume fractions. The modelderived product of the permeability and Young's modulus of the fiber suspension demonstrates a universal relationship with the fiber volume fraction. These results provide opportunities to control suspension concentration, and so porosity, during its delivery through a needle or a catheter, as occurs in healthcare, threedimensional printing, or material repair. 
Monday, November 21, 2022 9:44AM  9:57AM 
L26.00009: Physicsinformed machine learning for particle stresses in dense suspensions Amanda Howard, Justin Dong, Stany GALLIER, Panagiotis Stinis

Monday, November 21, 2022 9:57AM  10:10AM 
L26.00010: Simulation of band sedimentation of a lognormally distributed particulate suspension Heng Li, Lorenzo Botto We present Stokesian Dynamics simulation results for sedimentation of a suspension of spherical particles in the Stokes flow regime. Unlike in previous studies, the suspension is located in a band overlaying clear fluid and the suspension is polydispersed. The motivation for the work is to develop an efficient method to fractionate particles by size. The simulations show that for moderate particle concentrations the particlerich region behaves macroscopically as an effective dense fluid with a clearly recognizable suspension/clear fluid interface; this interface develops vertical fingers that grow in time by a RayleighTaylor instability. On the other hand, for very small particle volume fractions the particles sediment as individual objects with a velocity close to their Stokes velocity. The question is what sets the transition between these "effective fluid" and "particulate" regimes, as only in the latter regime fractionation is possible. In the talk, we will present visualizations of the particle dynamics as a function of the volume fraction, and statistics of the particle concentration calculated from the simulations, comparing against the case of monodispersed suspensions. We anticipate that an important feature is the convection of smaller particles by the larger ones. 
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