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Transport and particulate processes are ubiquitous in environmental, industrial and biological applications, often involving complex geometries and porous media. In this work we present a general population balance model for particle transport at the pore-scale, including aggregation, breakage and surface deposition. The various terms in the equations are analysed with a dimensional analysis, including a novel collision-induced breakage mechanism, and split into one- and two-particles processes. While the first are linear processes, they might both depend on local flow properties (e.g. shear). This means that the upscaling (via volume averaging and homogenisation) to a macroscopic (Darcy-scale) description requires closures assumptions. We discuss this problem and derive an effective macroscopic term for the shear-induced events, such as breakage caused by shear forces on the transported particles. We focus on breakage events as prototype for linear shear-induced events and derive upscaled breakage frequencies in periodic geometries, starting from nonlinear power-law dependence on the local fluid shear rate. Results are presented for a two-dimensional channel flow and a three dimensional regular arrangement of spheres, for arbitrarily fast (mixing-limited) events. Implications for linearised shear-induced collisions are also discussed. This work lays the foundations of a new general framework for multiscale modelling of particulate flows.

Single-use bioreactors (SUBs) are revolutionizing biotechnology and biopharmaceutical manufacturing by offering cost-efficient, flexible, and scalable alternatives to traditional reusable systems. These bioreactors, made from disposable and pre-sterilized materials, streamline cell cultivation for biological production while minimizing the need for complex cleaning and sterilization. A critical aspect of SUB performance lies in optimizing hydrodynamic parameters flow field, power consumption, mixing time, and energy efficiency, which directly influence process outcomes. This study investigates the hydrodynamic performance of an SUB system through stereo Particle Image Velocimetry (PIV) to analyze flow fields, Planar Laser-Induced Fluorescence (PLIF) for mixing time, and Electro Resistance Tomography (ERT) for further insights into mixing dynamics. The results, evaluated at varying impeller speeds and fill heights, provide a comprehensive understanding of flow behavior, mixing efficiency, and power requirements. This work highlights the importance of hydrodynamic characterization in optimizing SUB design and operation, contributing to more sustainable and efficient biopharmaceutical production.

The geometry optimization of a water molecule with a novel type of energy function called FFLUX is presented, which bypasses the traditional bonded potentials. Instead, topologically-partitioned atomic energies are trained by the machine learning method kriging to predict their IQA atomic energies for a previously unseen molecular geometry. Proof-of-concept that FFLUX’s architecture is suitable for geometry optimization is rigorously demonstrated. It is found that accurate kriging models can optimize 2000 distorted geometries to within 0.28 kJ mol −1 of the corresponding ab initio energy, and 50% of those to within 0.05 kJ mol −1 . Kriging models are robust enough to optimize the molecular geometry to sub-noise accuracy, when two thirds of the geometric inputs are outside the training range of that model. Finally, the individual components of the potential energy are analyzed, and chemical intuition is reflected in the independent behavior of the three energy terms E intra A (intra-atomic), V cl AA ' (electrostatic) and V x AA ' (exchange), in contrast to standard force fields.

The systematic development of coarse-grained (CG) models via the Mori–Zwanzig projector operator formalism requires the explicit description of a deterministic drift term, a dissipative memory term and a random fluctuation term. The memory and fluctuating terms are related by the fluctuation–dissipation relation and are more challenging to sample and describe than the drift term due to complex dependence on space and time. This work proposes a rational basis for a Markovian data-driven approach to approximating the memory and fluctuating terms. We assumed a functional form for the memory kernel and under broad regularity hypothesis, we derived bounds for the error committed in replacing the original term with an approximation obtained by its asymptotic expansions. These error bounds depend on the characteristic time scale of the atomistic model, representing the decay of the autocorrelation function of the fluctuating force; and the characteristic time scale of the CG model, representing the decay of the autocorrelation function of the momenta of the beads. Using appropriate parameters to describe these time scales, we provide a quantitative meaning to the observation that the Markovian approximation improves as they separate. We then proceed to show how the leading-order term of such expansion can be identified with the Markovian approximation usually considered in the CG theory. We also show that, while the error of the approximation involving time can be controlled, the Markovian term usually considered in CG simulations may exhibit significant spatial variation. It follows that assuming a spatially constant memory term is an uncontrolled approximation which should be carefully checked. We complement our analysis with an application to the estimation of the memory in the CG model of a one-dimensional Lennard–Jones chain with different masses and interactions, showing that even for such a simple case, a non-negligible spatial dependence for the memory term exists.

We present the coupling of two frameworks -- the pseudo-open boundary simulation method known as constant potential Molecular Dynamics simulations (C\\(\\mu\\)MD), combined with QMMD calculations -- to describe the properties of graphene electrodes in contact with electrolytes. The resulting C\\(\\mu\\)QMMD model was then applied to three ionic solutions (LiCl, NaCl and KCl in water) at bulk solution concentrations ranging from 0.5 M up to 6 M in contact with a charged graphene electrode. The new approach we are describing here provides a simulation protocol to control the concentration of the electrolyte solutions while including the effects of a fully polarizable electrode surface. Thanks to this coupling, we are able to accurately model both the electrode and solution side of the double layer and provide a thorough analysis of the properties of electrolytes at charged interfaces, such as the screening ability of the electrolyte and the electrostatic potential profile. We also report the calculation of the integral electrochemical double layer capacitance in the whole range of concentrations analysed for each ionic species, while the QM simulations provide access to the differential and integral quantum capacitance. We highlight how subtle features, such as the adsorption of potassium at the interface or the tendency of the ions to form clusters, emerge from our simulations, contribute to explaining the ability of graphene to store charge and suggest implications for desalination.

We implement the Multi-Rate Mass Transfer (MRMT) model for mobile-immobile transport in porous media within the open-source finite volume library \\textsc{OpenFOAM}\\reg \\citep{Foundation2014}. Unlike other codes available in the literature [Geiger, S., Dentz, M., Neuweiler, I., SPE Reservoir Characterisation and Simulation Conference and Exhibition (2011); Silva, O., Carrera, J., Dentz, M., Kumar, S., Alcolea, A., Willmann, M., Hydrology and Earth System Sciences 13, (2009)], we propose an implementation that can be applied to complex three-dimensional geometries and highly heterogeneous fields, where the parameters of the MRMT can arbitrarily vary in space. Furthermore, being built over the widely diffused OpenFOAM\\reg library, it can be easily extended and included in other models, and run in parallel. We briefly describe the structure of the < multiContinuumModels > library that includes the formulation of the MRMT based on the works of [Haggerty, R., Gorelick, S.M., Water Resources Research 31, (1995)] and [F. Municchi and M. Icardi Phys. Rev. Research 2, 013041, (2020)]. The implementation is verified against benchmark solutions and tested on two- and three-dimensional random permeability fields. The role of various physical and numerical parameters, including the transfer rates, the heterogeneities, and the number of terms in the MRMT expansions is investigated. Finally, we illustrate the significant role played by heterogeneity in the mass transfer when permeability and porosity are represented using Gaussian random fields.

Significant efforts have been devoted in the last decade towards improving the predictivity of coarse-grained models in molecular dynamics simulations and providing a rigorous justification of their use, through a combination of theoretical studies and data-driven approaches. One of the most promising research effort is the (re-)discovery of the Mori-Zwanzig projection as a generic, yet systematic, theoretical tool for deriving coarse-grained models. Despite its clean mathematical formulation and generality, there are still many open questions about its applicability and assumptions. In this work, we propose a detailed derivation of a hybrid multi-scale system, generalising and further investigating the approach developed in [Espa\\~{n}ol, P., EPL, 88, 40008 (2009)]. Issues such as the general co-existence of atoms (fully-resolved degrees of freedom) and beads (larger coarse-grained units), the role of the fine-to-coarse mapping chosen, and the approximation of effective potentials are discussed. The concept of an approximate projection is introduced along with a discussion of its use as measure of the error committed with the approximation of the true interactions among the beads. The theoretical discussion is supported by numerical simulations of a monodimensional non-linear periodic benchmark system with an open-source parallel Julia code, easily extensible to arbitrary potential models and fine-to-coarse mapping functions. The results presented highlight the importance of introducing, in the macroscopic model, a non-constant dissipative term, given by the Mori-Zwanzig approach, to correctly reproduce the reference fine-grained results without requiring \\emph{ad-hoc} calibration of interaction potentials and thermostats.

Even though the study of interfacial phenomena dates back to Laplace and was formalised by Gibbs, it appears that some concepts and relations among them are still causing some confusion and debates in the literature, particularly for interfaces involving solids. Moreover, ever since the Molecular Dynamics (MD) simulations have started to be widely used in the study of surface properties, these debates only intensified. In this work, we present a systematic description of the interfacial properties from the thermodynamic and statistical mechanics points of view. In particular, we link our derivations to MD simulations, describing precisely what different quantities represent and how they can be calculated. We do not follow the usual way that consists of describing the thermodynamics of the surfaces in general and then considering specific cases (e.g. liquid-liquid interface, liquid-solid interface). Instead, we present our analysis of various properties of surfaces in a hierarchical way, starting with the simplest case that we have identified: a single component liquid-vacuum interface, and then adding more and more complications when we progress to more complex interfaces involving solids. We propose that the term \"surface tension\" should not be used in the description of surfaces and interfaces involving solids, since its meaning is ambiguous. Only \"Surface Free Energy\" and \"Surface Stress\" are well defined and represent distinct, but related, properties of the interfaces. We demonstrate that these quantities, as defined in thermodynamics and measured in MD simulations, satisfy the Shuttleworth equation.

The reverse osmosis membrane module is an integral element of a desalination system as it determines the overall performance of the desalination plant. The fraction of clean water that can be recovered via this process is often limited by salt precipitation which plays a critical role in its sustainability. In this work, we present a model to study the complex interplay between flow, transport and precipitation processes in reverse osmosis membranes, which together influence recovery and in turn process sustainability. A reactive porous interface model describes the membrane with a dynamic evolving porosity and permeability to capture the scaling and clogging of the membrane. An open-source finite-volume numerical solver is implemented within the OpenFOAM library and numerical tests are presented here showing the effect of the various parameters of the model and the robustness of the model to describe a wide range of operating conditions.

We present a general procedure to introduce electronic polarization into classical Molecular Dynamics (MD) force-fields using a Neural Network (NN) model. We apply this framework to the simulation of a solid-liquid interface where the polarization of the surface is essential to correctly capture the main features of the system. By introducing a multi-input, multi-output NN and treating the surface polarization as a discrete classification problem, for which NNs are known to excel, we are able to obtain very good accuracy in terms of quality of predictions. Through the definition of a custom loss function we are able to impose a physically motivated constraint within the NN itself making this model extremely versatile, especially in the modelling of different surface charge states. The NN is validated considering the redistribution of electronic charge density within a graphene based electrode in contact with aqueous electrolyte solution, a system highly relevant to the development of next generation low-cost supercapacitors. We compare the performances of our NN/MD model against Quantum Mechanics/Molecular dynamics simulations where we obtain a most satisfactorily agreement.