Session L26: Suspensions: Theory, Modeling, and Simulations

Fast Simulation of Particulate Suspensions Enabled by Graph Neural Network Part I: Theory and Framework

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 long-range HI and short-range lubrication effects. In this talk, we introduce the HIGNN framework and demonstrate its accuracy, efficiency, and transferability in a variety of particulate suspension systems.   

Fast Simulation of Particulate Suspensions Enabled by Graph Neural Network Part II: Computational Efficiency and Scalability

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(N²) because the two-body hydrodynamic interaction (HI) not only dominates the short-range 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.   

Author not Attending

We present a scalable and accurate algorithm for evaluating singular and nearly-singular boundary integral operators on smooth, genus-zero, three-dimensional 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 radial-manifold shapes and demonstrate that our algorithm can achieve spectral accuracy and superalgebraic convergence while maintaining low computational complexity.   

Author not Attending

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 force-dipole 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 non-trivial dynamics.   

Orientation dynamics of spheroids in linear flows

We study the orientation dynamics of a neutrally buoyant spheroid suspended in the one-parameter 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 small-Re, St framework. An examination of the governing two-dimensional 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.

    

Author not Attending

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 monomer-monomer interactions.

In this work, fractals are created by various mechanisms such as the Diffusion Limited Aggregation (DLA), Cluster-Cluster Aggregation (CCA), Tunable Monte Carlo (TMC) with fractal dimensions ranging from 1.76 to 3 with varying interparticle potentials will be considered. The resistance faced by the cluster is expected to directly relate to the penetration of fluid into the cluster. Hydrodynamic properties of clusters with similar geometrical parameters but governed by different interparticle interactions will be characterized compared with a previous study on rigid fractals (Amalaruban et al., 2022). 

 

 

This proposed methodology allows for a quick assessment of the hydrodynamic properties of a wide variety of aggregates.    

Reciprocal theorem and Faxen's laws for particles in linear two-phase materials

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 two-fluid 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 two-phase 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.   

Controlling Extrudate Volume Fraction through Poroelastic Extrusion of Entangled Fibers

When a suspension of spherical or near-spherical 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 model-derived 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, three-dimensional printing, or material repair.   

Physics-informed machine learning for particle stresses in dense suspensions

In experiments with dense suspensions it is relatively easy to measure particle positions and velocities. However, it is difficult or impossible to measure quantities such as the particle stresses. We use physics-informed Galerkin neural networks to learn the particle stresses by enforcing that the particle stresses, volume fractions, and fluxes satisfy the monodisperse or bidisperse suspension balance model. Results are validated with Force Coupling Method simulations of monodisperse and bidisperse suspensions, where the particle stress is available, to show that the learned stresses agree well with the simulation stresses. This work allows for uncovering unknown quantities that are unable to be measured from experimental results.   

Simulation of band sedimentation of a log-normally distributed particulate suspension

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 particle-rich 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 Rayleigh-Taylor 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.