Anthony Wachs

Flows laden with rigid bodies are ubiquitous in both industrial and natural environments. A comprehensive knowledge of particle-laden flows facilitates the effective functioning of numerous industrial processes. However, in order to accurately resolve flows laden with ?(1000) particles in a computational model, ?(10⁹) spatial variables are required. Numerical computing of these variables on parallel platforms over ?(1000) cores is challenging. We begin this dissertation by proposing a scalable Direction-Splitting solver for flows containing non-spherical moving and fixed rigid bodies. We enhance the discretizations of advection and divergence terms in order to correctly capture the sharp changes in flow that occur in the vicinity of a fluid-solid interface. We rigorously verify the effectiveness of the numerical scheme through a comprehensive comparison of our outcomes with numerous benchmark simulations documented in the literature. We demonstrate the accuracy, speed, and scalability up to 6,400 cores. By expanding the functionality of our solver to incorporate intricate three-dimensional geometries defined by a collection of triangles in Standard Triangle Language (STL) files, we enhance the solver suitability for geometries that depict industrial processes. We also demonstrate that using an STL file does not affect the spatial accuracy of the computed flow field. Following this, we analyze the impact of a wall on the pairwise interaction of two spheres using our solver. Our calculations are verified against data from the literature in order to establish the accuracy of the simulations. We propose a Fourier Predictive Model to represent the modulations in the streamwise and spanwise components of force using the data produced by our fast and accurate solver. The model exhibits exceptional performance, as evidenced by the coefficient of determination of ~ 0.99. Next, we examine the effect of particle shape on the hydrodynamic forces and torques in a random array of Platonic polyhedrons. In order to illustrate the effect of particle sphericity, we depict the variation of forces and torques by comparing our outcomes to a random array of spheres. The effect of sphericity on a random array is illustrated through the use of sophisticated models, including a probability-driven model and physics-inspired neural networks.

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Biological fluids such as blood accomplish many vital tasks in the human body, including carrying oxygen and nutrients to tissues, regulating internal temperature and pH, or transporting white blood cells to infected areas. A better understanding of these fluids can provide insight into many pathologies such as the formation of aneurysms and the effect of sickle cell disease on the flow of red blood cells, as well as help design efficient diagnosis tools on microfluidic devices. Such fluids are composed of a continuous viscous phase and suspended bodies, including rigid particles and deformable membranes enclosing an inner fluid, referred to as capsules. In this thesis, we develop numerical tools aiming to simulate cell-resolved biological fluids such as blood. In a first part, we focus on the dispersed solid phase, a field known as granular mechanics. In this context, we implement a contact force able to accurately model static assemblies of granular media. After extensive validation, we use this contact model in a purely granular setting to study avalanches of entangled particles. Our numerical results are compared to experiments and show very good qualitative and quantitative agreement. Moreover, we present a variety of novel avalanching behaviors, as well as an intermittent regime in which reproducibility is lost. After analyzing the microstructure of granular assemblies in this regime, we conclude that it likely arises from mesoscale clusters of particles. In a second part, we concentrate on flowing biological capsules. We develop an adaptive front-tracking method which enables simulations of capsules in very large geometries for a wide range of Reynolds number. We validate our solver extensively and we show excellent qualitative and quantitative agreement with the literature. We then study the dynamics of capsules flowing through a sharp corner, a commonly encountered geometry in microfluidic devices. We analyze the trajectory, normalized velocity and area variations of the capsules and we show that in our case of strong confinement, the capsules interact weakly unless they are located very close to each other. Finally, we present and implement a fully Eulerian alternative method to simulate flowing capsules, and we highlight its advantages and limits.

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Polydisperse particle-laden flows are ubiquitous in both nature and industry across diverse disciplines. An in-depth understanding of the intricate interactions between the dispersed solid phase and carrier fluid phase is essential in terms of designing and optimizing the key components of various industrial processes. Due to the large separation of temporal and spatial scales across different phases in real-world problems, previous studies encountered difficulty establishing a proper two-way coupling with both satisfactory accuracy and efficiency: either the various interactions are coarse-grained and oversimplified by the average drag closures in large-scale models, or the computational costs may soar beyond affordability while fully resolving the boundary of smallest particles in industrial-level simulations. To address this challenge, we develop two deterministic models based on the particle-resolved simulation data to estimate the force and torque fluctuations within polydisperse sphere assembly, which provides a channel for bottom-up knowledge transfer to evaluate the macroscale interphase interactions via the microscale hydrodynamic behaviors. Accordingly, the primary contributions of this dissertation feature the following aspects: First, we develop a highly scalable Immersed Boundary-Lattice Boltzmann method (IB-LBM) that is implemented on the adaptive quadtree/octree grids to model the complex solid-fluid interactions in different contexts such as flows laden with fixed or moving particles. Second, we perform a series of particle-resolved simulations of flow past random arrays of moderately to strongly bidisperse and polydisperse spheres which seemed computationally impossible on uniform grids in the past. We explore the statistical distributions of hydrodynamic forces and torques exerted on individual spheres over a wide range of simulation parameters. Finally, we extend two data-driven methods to predict such force and torque distributions, namely a Microstructure-informed Probability-driven Point-particle (MPP) model and a Physics-Informed Neural Network (PINN). We demonstrate their applicability from different perspectives including prediction and generalization performance, model complexity (i.e., computational efficiency), and interpretability in the form of binary and trinary interactions. We highlight the potential of our PINN model, which appropriately balances accuracy and efficiency, to substitute the conventional average drag closures for solid-fluid coupling in Eulerian-Lagrangian simulations.

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Particle-laden flows where a dispersion of a solid phase is carried by a fluid phase are at the core of numerous industrial and natural processes, such as fluvial sediment transport and fluidized-bed reactors. The dynamics of each phase is intimately coupled with that of the other phase, leading to the emergence of complex, nontrivial interactions that can span wide ranges of spatial and temporal scales. The focus of this thesis is two-fold; namely, analysis of particle shape effects, and modeling hydrodynamic forces and torques in particle-laden flows. To this end, direct numerical simulations are performed for the generation of high-fidelity data, based on which all analyses of this thesis are carried out. In the first part, we scrutinize the dynamics of an isolated polyhedron, i.e. a cube, in highly inertial regimes and various density ratios. Robust helical motions and wake patterns are found for Reynolds numbers at which a sphere moves rectilinearly. An isolated cube exhibits remarkably larger rotational and lateral motions compared to a sphere, by which the effective drag on the particle is greatly affected. We then extend the analysis to inertial suspensions of cubes, where detailed comparisons are made with their counterpart sphere suspensions for various solid volume fractions. While strong clustering occurs in sphere suspensions, cube suspensions are found to be remarkably more homogeneous, as evident from their microstructure and momentum transfer properties. As demonstrated by their intensive transverse velocity fluctuations, cubes are more likely to break up and escape clusters, thus resisting local accumulation and making suspensions better mixed. In the second part, we develop a novel probability-driven point-particle model for the prediction of hydrodynamic forces and torques based on local microstructure in dense arrays of spheres. Following probabilistic arguments, necessary statistical information is extracted from particle-resolved simulations to construct force/torque-conditioned probability distribution maps, which are in turn used as basis functions for a regressive-type model. We subsequently show that our model is capable of predicting a substantial part of the observed force and torque variations, and is thus conceived to be highly promising for accurate interphase coupling in Euler-Lagrange simulations.

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A theoretical and numerical study of yield-stress fluid creeping flow about a particle is presented motivated by theoretical aspects and industrial applications. Yield stress fluids can hold rigid particles statically buoyant if the yield stress is large enough. In addressing sedimentation of rigid particles in viscoplastic fluids, we should know this critical `yield number' beyond which there is no motion. As we get close to this limit, the role of viscosity becomes negligible in comparison to the plastic contribution in the leading order, since we are approaching the zero-shear-rate limit. Admissible stress fields in this limit can be found by using the characteristics of the governing equations of perfect plasticity (i.e., the sliplines). This approach yields a lower bound of the critical plastic drag force or equivalently the critical yield number. Admissible velocity fields also can be postulated to calculate the upper bound. This analysis methodology is examined for different families of particle shapes. Numerical experiments of either resistance or mobility problems in a viscoplastic fluid validate the predictions of slipline theory and reveal interesting aspects of the flow in the yield limit. For instance, the critical limit is not unique and here we show that for the same critical limit we may have different shaped particles that are cloaked inside the same unyielded envelope. The critical limit (or critical plastic drag coefficient) is related to the unyielded envelope rather than the particle shape. We show how to calculate the unyielded envelope directly. Here we also address the case of having multiple particles, which introduces interesting new phenomena. Firstly, plug regions can appear between the particles and connect them together, depending on the proximity and yield number. This can change the yielding behaviour since the combination forms a larger (and heavier) "particle". Moreover, small particles (that cannot move alone) can be pulled/pushed by larger particles or assembly of particles. Increasing the number of particles leads to interesting chain dynamics, including breaking and reforming.

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