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Bidisperse supension balance model

The suspension balance model (SBM) for viscous Stokes flow has been well studied for the case of identical, monodisperse spherical particles in a channel, however, more work remains to be done to explore the bidisperse and polydisperse SBM. Here, we present a simple extension of the SBM that allows for modeling of suspensions of particles of bidisperse size. The comparison with avaiable experiments and direct simulations is found to be good. Additionally, we present a range of simulations to justify the assumptions made in the polydisperse suspension balance model for non-Brownian, neutrally buoyant particles that vary in size with a bidisperse distribution. The aim is to study the effects of moderate size variation on the rheology of the suspension and the distribution of the particles across the flow, especially in the near-wall regions. It is shown that, at the size ratios considered, bidispersity in the particle size does not significantly affect rheological parameters including the particle volume fraction and relative viscosity in the bulk of a Couette flow. The particle phase stresses are distributed between small and large particles in proportion to the relative volume fractions of each species. In bidisperse suspensions, the large particles in the wall layer develop a spatial structure and form chains in the streamwise direction.

97 MATHEMATICS AND COMPUTING↗

Machine learning methods for particle stress development in suspension Poiseuille flows

Numerical simulations are used to study the dynamics of a developing suspension Poiseuille flow with monodispersed and bidispersed neutrally buoyant particles in a planar channel, and machine learning is applied to learn the evolving stresses of the developing suspension. The particle stresses and pressure develop on a slower time scale than the volume fraction, indicating that once the particles reach a steady volume fraction profile, they rearrange to minimize the contact pressure on each particle. Here we consider how the stress development leads to particle migration, time scales for stress development, and present a new physics-informed Galerkin neural network that allows for learning the particle stresses when direct measurements are not possible. The particle fluxes are compared with the Suspension Balance Model with good agreement. We show that when stress measurements are possible, the MOR-physics operator learning method can also capture the particle stresses.

97 MATHEMATICS AND COMPUTING↗

Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systems

Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems are coarse-grained into low-dimensional models, the entropic loss of information leads to emergent physics which are dissipative, history-dependent, and stochastic. To machine learn coarse-grained dynamics from time-series observations of particle trajectories, we propose a framework using the metriplectic bracket formalism that preserves these properties by construction; most notably, the framework guarantees discrete notions of the first and second laws of thermodynamics, conservation of momentum, and a discrete fluctuation-dissipation balance crucial for capturing non-equilibrium statistics. We introduce the mathematical framework abstractly before specializing to a particle discretization. As labels are generally unavailable for entropic state variables, we introduce a novel self-supervised learning strategy to identify emergent structural variables. We validate the method on benchmark systems and demonstrate its utility on two challenging examples: (1) coarse-graining star polymers at challenging levels of coarse-graining while preserving non-equilibrium statistics, and (2) learning models from high-speed video of colloidal suspensions that capture coupling between local rearrangement events and emergent stochastic dynamics. We provide open-source implementations in both PyTorch and LAMMPS, enabling large-scale inference and extensibility to diverse particle-based systems.

Computational Engineering, Finance, and Science (c↗

Resolving Salt-Induced Agglomeration of Laponite Suspensions Using X-ray Photon Correlation Spectroscopy and Molecular Dynamics Simulations

Linking the physics of the relaxation behavior of viscoelastic fluids as they form arrested gel states to the underlying chemical changes is essential for developing predictive controls on the properties of the suspensions. In this study, 3 wt.% laponite suspensions are studied as model systems to probe the influence of salt-induced relaxation behavior arising from the assembly of laponite nanodisks. X-ray Photon Correlation Spectroscopy (XPCS) measurements show that laponite suspensions prepared in the presence of 5 mM concentrations of CaCl2, MgCl2 and CsCl salts accelerate the formation of arrested gel states, with CaCl2 having a significant impact followed by CsCl and MgCl2 salts. The competing effects of ion size and charge on relaxation behavior are noted. For example, the relaxation times of laponite suspensions in the presence of Mg2+ ions are slower compared to Cs+ ions despite the higher charge, suggesting that cation size dominates in this scenario. The faster relaxation behavior of laponite suspensions in the presence of Ca2+ ions compared to Cs+ ions shows that a higher charge dominates the size of the ion. The trends in relaxation behavior are consistent with the cluster formation behavior of laponite suspensions and the electrostatic interactions predicted from MD simulations. Charge balance is achieved by the intercalation of the cations at the negatively charged surfaces of laponite suspensions. These studies show that the arrested gel state of laponite suspensions is accelerated in the presence of salts, with ion sizes and charges having a competing effect on relaxation behavior.

36 MATERIALS SCIENCE↗