Polydisperse Model Research Articles

Revealing the Structural Intricacies of Biomembrane-Interfaced Emulsions with Small- and Ultra-Small-Angle Neutron Scattering.

Utilizing cell membranes from diverse cell types for biointerfacing has demonstrated significant advantages in enhancing colloidal stability and incorporating biological properties, tailored specifically for various biomedical applications. However, the structures of these materials, particularly emulsions interfaced with red blood cell (RBC) or platelet (PLT) membranes, remain an underexplored area. This study systematically employs small- and ultra-small-angle neutron scattering (SANS and USANS) with contrast variation to investigate the structure of emulsions containing perfluorohexane within RBC (RBC/PFH) and PLT membranes (PLT/PFH). The findings reveal that the scattering length density of RBC and PLT membranes is 1.5 × 10-6Å-2, similar to 30% (w/w) deuterium oxide. Using this solvent as a cell membrane-matching medium, estimated droplet diameters are 770nm (RBC/PFH) and 1.5µm (PLT/PFH), based on polydispersed sphere model fitting. Intriguingly, calculated patterns and invariant analysis reveal native droplet architectures featuring entirely liquid PFH cores, differing significantly from the observed bubble-droplet core system in electron microscopy. This highlights the advantage of SANS and USANS in differentiating genuine colloidal structures in complex dispersions. In summary, this work underscores the pivotal role of SANS and USANS in characterizing biointerfaced colloids and in uncovering novel colloidal structures with significant potential for biomedical applications and clinical translation.

Size polydisperse model ionic liquid under confinement: A molecular dynamics study

The performance of an electric double-layer capacitor is strongly influenced by the choice of electrolyte, and the use of ionic liquid (IL) mixtures as an electrolyte has shown great promise. In this study, a model IL made of a mixture of anions and size-polydisperse cations in equal numbers and confined between two electrodes is investigated by means of molecular dynamics simulations. In particular, using the extent of size-polydispersity (characterized by polydispersity index, δ) as a control parameter, we systematically explore its effect on the local structure, charge profile, ion size distribution in the vicinity of electrode surfaces, and differential capacitance. It is observed that the charge density profiles near cathode, i.e., region comprising both Stern and diffused layers, are significantly affected under the variation of δ in addition to the electrode charge density. Ion population, ordering of different-size cations, and its effective size in the vicinity of electrodes under neutral and applied potential conditions are also quantified. An interesting observation is that the effective cation size in the Stern layer decreases with increasing value of δ in the case of moderate to strong electrode surface charge density. This behaviour can be qualitatively understood from the interplay of enthalpic and entropic forces in the system. Finally, a non-monotomic dependence of capacitance on δ is observed with maximum value of capacitance at a rather small value of δ(≈3%) for the model system.

Study of anisotropy in polydispersed 2D micro and nano-composites by Elbow and K-Means clustering methods

A new two-dimensional polydisperse model for testing multiphase composites is developed. The verification of the model is carried out based on the microstructure of two composites obtained in the ex-situ and in-situ techniques produced in the Friction Stir Processing (Al–Si–Cu/SiCp) and the Self-propagating High temperature Synthesis (Al/nano-TiCp). The examined microstructure is considered on macro-, meso- and micro- levels. Besides the reinforcement phase distribution concentration, an anisotropy coefficient κ is calculated for every meso-cell. It is the cumulative vector parameter that characterizes the spatial two-point correlation of inclusions. In particular, κ determines the principal axes of the effective conductivity tensor over a meso-cell. The anisotropy spatial distribution ϰ(x) is introduced as the discrete function of values κ calculated over meso-cells centered at the point x. This new distribution ϰ(x) accumulates the geometrical information of the considered microstructure. A computational experiment is designed and carried out in order to study the influence of the reinforcement phase redistribution on the anisotropy. Therefore, it adequately describes the anisotropy of fields in composites modeling thermal and electric conductivity, diffusion, and elastic antiplane deformation. The results of the computational experiments are analyzed using the Elbow and K-Means clustering machine learning algorithm. The detailed analysis is carried out to divide the data set into up to 5 clusters. A research hypothesis concerning the criterion of isotropy of the distribution of reinforcing phase particles in the composite structure is formulated

Local vs. cooperative: Unraveling glass transition mechanisms with SEER

Which phenomenon slows down the dynamics in supercooled liquids and turns them into glasses is a long-standing question of condensed matter. Most popular theories posit that as the temperature decreases, many events must occur in a coordinated fashion on a growing length scale for relaxation to occur. Instead, other approaches consider that local barriers associated with the elementary rearrangement of a few particles or "excitations" govern the dynamics. To resolve this conundrum, our central result is to introduce an algorithm, Systematic Excitation ExtRaction, which can systematically extract hundreds of excitations and their energy from any given configuration. We also provide a measurement of the activation energy, characterizing the liquid dynamics, based on fast quenching and reheating. We use these two methods in a popular liquid model of polydisperse particles. Such polydisperse models are known to capture the hallmarks of the glass transition and can be equilibrated efficiently up to millisecond time scales. The analysis reveals that cooperative effects do not control the fragility of such liquids: the change of energy of local barriers determines the change of activation energy. More generally, these methods can now be used to measure the degree of cooperativity of any liquid model.

Grain polydispersity and non-sphericity effects on gas flow through granular beds using measurements and modelling

ABSTRACT The quality of cometary surface activity simulations and erosion models of icy moons depends on a good knowledge of the surface layer permeability to gas flow. Therefore, we study various models of the Knudsen diffusion coefficient and the viscous permeability, which are used to describe the flow of rarefied gases through porous materials. Usually, these models are expressed for monodisperse packed beds. In this work, we describe a generalization to polydisperse packed beds and compare them with experimental results. In addition, we analyse non-spherical packings to test how well the recently developed models are applicable. For this purpose, the gas flow parameters of these samples are measured in a dedicated measurement set-up. Special attention had to be paid to biases in measuring the porosity and the pressure drop in the sample, which are discussed in detail. Our measurements confirm that the Knudsen diffusion coefficient is inversely proportional to the specific surface area of the grains and that the viscous permeability is inversely proportional to the specific surface area squared. Further, we were able to identify a relation between the gas flow parameters, represented by a parameter β, which seems to be an indicator of the mean orientation of the grains. The findings give further evidence of the importance of the grain size distribution and the grain shape for rarefied gas flow. In particular, the results show that the standard polydisperse model is not sufficient when a considerable part of the pore space consists of traps or other rarely percolated parts.

Polydisperse sea spray effect on the vertical momentum transport in hurricanes

Abstract This study focuses on the influence of the sea spray polydispersity on the vertical transport of momentum in a turbulent marine atmospheric boundary layer in high-wind conditions of a hurricane. The Eulerian multifluid model treating air and spray droplets of different sizes as interacting inter-penetrating continua is developed and its numerical solutions are analyzed. Several droplet size distribution spectra and correlation laws relating wind speed and spray production intensity are considered. Polydisperse model solutions have confirmed the difference between the roles small and large spray droplets play in modifying the turbulent momentum transport that have been previously identified by monodisperse spray models. The obtained results have also provided a physical explanation for the previously unreported phenomenon of the formation of thin low-eddy-viscosity “sliding” layers in strongly turbulent boundary layer flows laden with predominantly fine spray.

CFD modelling of flashing flows for nuclear safety analysis: possibilities and challenges

Abstract Because of its relevance for the safety analysis of pressurized water reactors (PWR), many research activities on flashing flows in pipes and nozzles arose from the mid of last century. Most of them have been focused on the critical mass flow rate and transient pressure or temperature fluctuations by means of experiments and system codes. Since the beginning of this century, owing to the increase in computer speed and capacity, computational fluid dynamics (CFD) is being used more and more in the investigation of flashing flows, which has the advantage of providing three-dimensional insights in the internal flow structure as well as its evolution. This work presents an overview of relevant flashing scenarios in the nuclear safety analysis, and focuses on the discussion about possibilities and challenges of using CFD modelling. It is shown that a two-fluid model with the thermal phase-change model is superior to a mixture model with pressure phase-change, relaxation and equilibrium models, respectively, in terms of interfacial mass transfer, however, efforts are still required to improve the interphase heat-transfer model. Furthermore, since flashing is accompanied with high void fraction and broad bubble size ranges, a poly-disperse two-fluid model is recommended, but the effect of phase change on bubble coalescence and breakup needs further research. In addition, during flashing the flow pattern may change from single phase to bubbly flow, churn flow, annular flow, and even mist flow. The rapid change of interfacial topology as well as its influence on the applicability of closure models remains a challenge.

Large-eddy simulation of elliptic hydrofoil tip vortex cavitation under incipient conditions

Large-eddy simulation (LES) is used to simulate flow over a three-dimensional elliptical hydrofoil at 12 degrees angle of attack and Reynolds numbers (Re) of 9×105 and 1.4×106 based on root chord length and freestream velocity. The simulations are performed at the cavitation number (σ) of 2.1 and are based on the experiments of Boulon et al. (1999), who studied the tip vortex cavitation behavior under the confinement of side and bottom walls. The present simulations correspond to their case where the confinement due to the bottom wall is negligible. The computational model of Brandao and Mahesh (2022) that treats vapor as a passive scalar in an incompressible liquid is extended to account for multiple groups of bubbles of different sizes, effectively making it a polydisperse model. This allows us to investigate the effects of water quality on inception. The simulations include two different freestream nuclei distributions that are taken from the water tunnel data of Khoo et al. (2020c). It was found that inception is strongly dependent on the amounts of nuclei in the freestream. When the flow is depleted of nuclei, inception is an intermittent event confined to a location very close to the hydrofoil tip. However, when the flow is rich in nuclei, a larger portion of the tip vortex cavitates, as well as part of the suction side very close to the leading edge of the hydrofoil. Probability density functions revealed that cavitation occurs in any region experiencing a pressure field lower than vapor pressure when the flow is rich in nuclei, while extremely low values of pressure (usually kPa of tension) are required to make a flow depleted of nuclei cavitate. The topology of a flow poor in nuclei was investigated and inception was found to occur in regions dominated by irrotational straining with high stretching rates. Lagrangian statistics showed that as Re is increased, nuclei have higher likelihood of experiencing very low pressure fields. However, the amount of time they are subject to very low pressures is also shorter with increasing Re.

Phase Behavior of Polydisperse Y-Shaped Polymer Brushes under Good Solvent Conditions.

Y-shaped polymer brushes represent a special class of binary mixed polymer brushes, in which a combination of different homopolymers leads to unique phase behavior. While most theoretical and simulation studies use monodisperse models, experimental systems are always polydisperse. This discrepancy hampers linking theoretical and experimental results. In this theoretical study, we employed dissipative particle dynamics to study the influence of polydispersity on the phase behavior of Y-shaped brushes grafted to flat surfaces under good solvent conditions. Polydispersity was kept within experimentally achievable values and was modeled via Schulz-Zimm distribution. In total, 10 systems were considered, thus covering the phase behavior of monodisperse, partially polydisperse and fully polydisperse systems. Using such generic representation of real polymers, we observed a rippled structure and aggregates in monodisperse systems. In addition, polydisperse brushes formed a stable perforated layer not observed previously in monodisperse studies, and influenced the stability of the remaining phases. Although the perforated layer was experimentally observed under good solvent conditions and in the melt state, further confirmation of its presence in systems under good solvent conditions required mapping real polymers onto mesoscale models that reflected, for example, different polymer rigidity, and excluded volume effects or direct influence of the surface, just to mention a few parameters. Finally, in this work, we show that mesoscale modeling successfully describes polydisperse models, which opens the way for rapid exploring of complex systems such as polydisperse Y-shaped brushes in selective or bad solvents or under non-equilibrium conditions.

A kinetic-based model for polydisperse, high-speed, fluid–particle flows

Hyperbolic conservation equations for polydisperse, high-speed, compressible, fluid–particle flows with added mass and fluid-phase pseudoturbulence are derived. First, the kinetic-based model for monodisperse particles that accounts for collisional and frictional pressure, as well as added mass and internal energy, is reviewed. Then, a kinetic-based model for polydisperse particles is formulated in terms of the moments of the particle size distribution, and velocity moments conditioned on the particle mass or size. Transport equations for velocity moments up to second order (or total kinetic energy) are closed using the hyperbolic quadrature method of moments. In the numerical implementation for the spatial fluxes and source terms, the particle mass distribution is treated using the generalized quadrature method of moments and the size-conditioned moments are found with the conditional quadrature method of moments. Example results for spatially 1-D test cases demonstrate the ability of the polydisperse model to capture a wide range of particle-size-dependent multiphase flow physics.

Understanding the swap Monte Carlo algorithm in a size-polydisperse model glassformer.

The dynamics of a polydisperse model glassformer are investigated by augmenting molecular dynamics (MD) simulation with swap Monte Carlo (SMC). Three variants of the SMC algorithm are analyzed with regard to convergence and performance. We elucidate the microscopic mechanism responsible for the drastic speed-up of structural relaxation at low temperature. It manifests in a stepwise increase of the mean-squared displacement when the timescale between the application of swap sweeps is significantly larger than a characteristic microscopic timescale. Compared to Newtonian dynamics, with the hybrid MD-SMC dynamics the glass transition shifts to a lower temperature and a different temperature dependence of the localization length is found.

A polydisperse model for thixotropic elasto‐viscoplastic suspensions of aggregating particles using population balances

AbstractAn improved population balance‐based rheological constitutive framework for polydisperse aggregating suspensions is derived by incorporating detailed models for orthokinetic and perikinetic aggregation and shear breakage processes. The framework accounts for critical properties such as dynamic arrest, viscoelasticity, kinematic hardening, thixotropy, and yield stress to generate a full range of thixotropic elasto‐viscoplastic (TEVP) response. Additionally, the model is thermodynamically consistent because the dynamics and timescales are completely determined by internal structural and kinetic variables. The model connects the rheological response to the structural descriptors such as the size distribution of agglomerates, mean sizes, fractal dimension, and agglomerate volume fraction. Predictions are compared against a wide range of shear rheology measurements data for model thixotropic suspensions of fumed silica and carbon black, including large amplitude oscillatory shear (LAOS), as well as ultra‐small angle neutron scattering under steady shear (Rheo‐uSANS).

Continuum and discrete element modelling for describing coupled hydro-mechanical effects of earthworm burrow coatings on soil shrinkage

Structured soils with earthworm burrows are locally heterogeneous due to coatings along these biopore walls that are superimposed on the inter- and intra-aggregate pore network of the soil matrix. The partially compacted finer-textured and organic matter-rich coatings can limit the flow exchange between the macropores and the soil matrix during preferential flow. Still unknown are dynamic hydro-mechanical interrelations in coating and matrix domains that affect stress–strain behaviour at the macroscopic scale. Such hydro-mechanic interactions may be described with the discrete element method (DEM) coupled with a two-phase pore finite volume (2PFV) approach if relevant pore structures are represented in the model. The objective was to develop a coupled DEM-2PFV model together with a parameterization procedure. Major task was to create a parameterization procedure to calibrate micro parameters of the model by macro properties quantified from drainage experiments of soil samples with earthworm burrow wall coatings.The solid phase was modelled by particle aggregation creating inter and intra-aggregate pore network for the soil matrix in a cube of about 5 cm edge length and one side with the coating structure. This DEM model was coupled with a 2PFV model to simulate hydro-mechanic effects during drainage. Sand box drainage experiments were carried out on soil matrix and biopore samples with laser surface elevation measurements to obtain the mechanical stress–strain macro parameters necessary for model calibration. The poly-dispersed DEM-2PFV model was able to describe effects of two-phase air–water flow on stress–strain macro parameters. The micro parameters (i.e., particle stiffness and bond strength) of the pore scale model were obtained from macro parameters of the primary and secondary stress–strain stages by training a random forest meta-estimator. The model was able to reproduce the pore network of coating material and the inter- and intra-aggregate pore network of the matrix that are dynamically changing with the effective stress. The machine learning model revealed that the bond strength among particles within aggregates governed the shrinkage of soil matrix, while the particle stiffness of the coating material reduced the susceptibility of aggregate breakage producing a more stable inter-aggregated pore network during the drainage process. This study confirmed that coating material present in biopore surface increases the horizontal soil hydro structural stability. The microscale hydro-mechanic modelling can be useful for finding flow exchange parameters inputs for upscaled models and correlating pore-scale parameters to experimentally determined stress–strain macro parameters.

Choice of diameters in a polydisperse model glassformer: Deterministic or stochastic?

In particle-based computer simulations of polydisperse glassforming systems, the particle diameters σ=σ_{1},⋯,σ_{N} of a system with N particles are chosen with the intention to approximate a desired distribution density f with the corresponding histogram. One method to accomplish this is to draw each diameter randomly and independently from the density f. We refer to this stochastic scheme as model S. Alternatively, one can apply a deterministic method, assigning an appropriate set of N values to the diameters. We refer to this method as model D. We show that, for sample-to-sample fluctuations, especially for the glassy dynamics at low temperatures, it matters whether one chooses model S or model D. Using molecular dynamics computer simulations, we investigate a three-dimensional polydisperse nonadditive soft-sphere system with f(s)∼s^{-3}. The swap Monte Carlo method is employed to obtain equilibrated samples at very low temperatures. We show that for model S the sample-to-sample fluctuations due to the quenched disorder imposed by the diameters σ can be explained by an effective packing fraction. Dynamic susceptibilities in model S can be split into two terms: one that is of thermal nature and can be identified with the susceptibility of model D, and another one originating from the disorder in σ. At low temperatures the latter contribution is the dominating term in the dynamic susceptibility. Our study clarifies the pros and cons of the use of models S and D in practice.

CFD-DEM study of segregation and mixing characteristics under a bi-disperse solid-liquid fluidised bed

In this work, a recent smoothed CFD-DEM model is employed to study the segregation and mixing behaviours in a bi-disperse solid–liquid fluidised bed (SLFB) with different superficial liquid velocities and wide size ratios. Here, the poly-disperse drag model is applied, and its validity and advantage are confirmed. Besides, the qualitative and quantitative characteristics are systematically studied using a variety of indices, while the intermixing behaviour in the transition zone is investigated. The results show that segregation degree is well quantified by the mixing index, and the circulation motion of particles and liquid is confirmed in the transition zone. The more drastic motions can be observed in the transition zone under lower superficial velocities or size ratios. Furthermore, the force analysis in terms of the drag force and collision force indicates that the combined contribution of hydrodynamics and collision is the main underlying mechanism of segregation behaviour in the bi-disperse SLFB.

A theory of localized excitations in supercooled liquids.

A new connection between the structure and dynamics in glass-forming liquids is presented. We show how the origin of spatially localized excitations, as defined by the dynamical facilitation (DF) theory, can be understood from a structure-based framework. This framework is constructed by associating excitation events in the DF theory to hopping events between energy minima in the potential energy landscape (PEL). By reducing the PEL to an equal energy well picture and applying a harmonic approximation, we develop a field theory to describe elastic fluctuations about inherent states, which are energy minimizing configurations of the PEL. We model an excitation as a shear transformation zone (STZ) inducing a localized pure shear deformation onto an inherent state. We connect STZs to T1 transition events that break the elastic bonds holding the local structure of an inherent state. A formula for the excitation energy barrier, denoted as Jσ, is obtained as a function of inherent-state elastic moduli and the radial distribution function. The energy barrier from the current theory is compared to the one predicted by the DF theory where good agreement is found in various two-dimensional continuous poly-disperse atomistic models of glass formers. These results strengthen the role of structure and elasticity in driving glassy dynamics through the creation and relaxation of localized excitations.

Modeling of gas jet flow into a liquid bath using the inhomogeneous poly-dispersed method

Precise modeling of gas injection into a liquid bath is essential for both determining the enormous interaction mechanisms between phases and promoting its better utilization in nuclear industry. For this purpose, an investigation on three CFD methods was performed and compared with the experimental results from air injected vertically into a water pool through a circular nozzle with diameter of 1.58 mm in this work. An inhomogeneous poly-dispersed method based on a bubble-size-dependent lift force model was integrated into the traditional gas-liquid two-fluid model for the simulation of gas-liquid jet flow with air injected vertically in a water bath. Results show that the computer resources consumption can be kept at a low level using the method. Compared with the mono-dispersed and homogeneous poly-dispersed models, the predicted results of the void fraction distribution obtained by using the inhomogeneous poly-dispersed model considering the adjustable coefficients for the break up and coalescence models show good agreements with those of the experiment, with a maximum deviation less than 20%. Hence, the model should be more reliable to predict two-phase flow parameters. Bubble distributions analyses of varying scales were also demonstrated, indicating that the adoption of both inhomogeneous gas flow field and lift force model able to change sign of its coefficient play an important role for predicting the gas injection into liquid bath correctly.

Kinetic theory models for granular mixtures with unequal granular temperature. Derivation of analytical constitutive equations

We consider kinetic theory of granular mixtures in which each solid phase is described by its own granular temperature. The particle velocities are assumed to follow a Mawellian distribution with zero-order approximation of the Boltzmann equation. The literature proposes a number of approximate solutions to the constitutive equations resulting from particle collisions. Here, we derive and show that analytical solutions exist, and reveal that some of the proposed approximate solutions are inaccurate whereas others might give good approximations.We also review the balance laws and constitutive relations resulting from the mono- and poly-disperse kinetic granular flow model frameworks. Such a review has been done here because the model framework on kinetic theory of mono-disperse granular flow systems has sometimes been adopted in models for granular mixtures. The consequence of such a simplification is that the kinetic energy loss in a collision between two particles of different species is equally shared among them.

Numerical Study of Spray-Induced Turbulence Using Industrial Fire-Mitigation Nozzles

A numerical investigation of the spray-induced turbulence generated from industrial spray nozzles is carried out to better understand the roles of the nozzle spray on the fires or explosions in different accidental scenarios. Numerical simulations are first validated against experimental data in the single nozzle case using the monodisperse and polydisperse assumption for droplet diameters. The polydispersion of the nozzle spray is proven to be necessary to correctly predict the gas and droplet velocities. The turbulent kinetic energy has dominant values inside the spray cone, decreases rapidly with the vertical distance from the spray nozzle, and is strongly affected by the spray droplet diameter. On the contrary, the integral length scale is found to have high values outside the spray cone. Two interacting sprays injected from different nozzles are then investigated numerically using the validated polydisperse model. The water sprays generated from such industrial nozzles can generate turbulence of high intensity in the near-nozzle region, and this intensity decreases with the distance from the nozzles. A better understanding of the turbulence generated by the spray system can be beneficial for the evaluation of several important phenomena such as explosion enhancement. The guideline values obtained from this investigation of single and double nozzles can be useful for large-scale numerical simulations.

Numerical assessment of performance characteristics and two-phase flow dynamics of a centrifugal rotor operating under gas entrainment condition

This work presents a numerical study of performance characteristics and flow dynamics of a centrifugal rotor operating with gas-liquid flow. An Euler-Euler polydispersed model is adopted, which was validated in a previous publication and is used in this work to assess quantities not addressed in the earlier study. An analysis of the rotor performance under two-phase is performed, for which suitable expressions are presented. In particular, an analysis of the rotor head components is carried out including the dynamic head evaluation through the rotor, which is often neglected in most studies. The numerical model is explored further to analyze flow patterns and relevant gas-liquid flow quantities. This includes analysis of the three-dimensional distribution of the gas phase inside the rotor, evaluation of gas-liquid interphase forces, and the effect of the intake gas flow rate on the bubble diameter, gas-liquid relative velocities, and the overall turbulence levels through the rotor. Such analyses, which are usually hard to obtain through experimental methods, are also rarely found in related numerical studies. Thus, this work could bring useful information to help in the understanding of the gas-liquid flow behavior in centrifugal rotors, while also contributing to the progress of numerical solution of this problem.