Particle Length Scale Research Articles

Effect of size and homogeneity of rigid inclusions on the sintering of composites

The effect of volume fraction, size and homogeneity of rigid non-sintering inclusions on the densification behavior of the matrix is investigated using discrete element simulations at the particle length scale. It is found that the densification rate of the matrix decreases with increasing volume fraction of inclusions and with decreasing size of inclusions. For a given volume fraction and size of inclusions, improving dispersion of the inclusions results in a stronger retardation of densification.

Application of the complex network method in solid-state sintering

The microstructure evolution and force distribution during solid-state sintering are studied at the particle length scale for a planar layer system of copper particles. The complex network as well as discrete element methods (DEM) is adopted, in which the contact network and the force network are mainly considered. Comparing the contact network to the microstructure evolution, we find that pores always form in a large contact polygon. In the force network, the normal contact forces distribute extremely non-uniform. An interesting phenomenon is that a ring-like structure of force chain emerges spontaneously in the sintering force networks, whose life expectance is much longer than other linear force chains. Furthermore, a high contact force is more likely to form at a new contact site. To our knowledge, it is the first time to study force distributions and microstructure evolutions in sintering from the complex network point of view, which should be a promising method for further investigating the complex sintering process in the future.

Simulation of the toughness of partially sintered ceramics with realistic microstructures

Increasing the pore volume fraction of porous ceramics enhances their functionality for a wide range of applications. However, the increased functionality comes at the expense of their toughness. Discrete element method (DEM) three-dimensional simulations, which operate at the length scale of individual particles, are used to investigate the toughness of microstructures typical of partially sintered ceramics. The method is first validated by comparing DEM simulations to the linear elastic fracture mechanics elastic solution at the crack tip of a pre-cracked numerical sample. The toughness of realistic random microstructures is then obtained using DEM simulations and compared to experimental data. Green density is shown to have a significant effect on toughness. Discrete simulations also suggest that the linear relationship between toughness and Young’s modulus is primarily linked to the size of the solid necks formed during sintering of particles.

Interface-Induced Anisotropy and the Nematic Glass/Gel State in Jammed Aqueous Laponite Suspensions

Aqueous suspensions of Laponite, a system composed of disklike nanoparticles, are found to develop optical birefringence over several days, well after the suspensions solidified because of jamming. The optical anisotropy is particularly enhanced near the air-Laponite suspension interface over length scales of several millimeters, which is beyond 5 orders of magnitude larger than the particle length scale, suggestive of large-scale ordering influenced by the interface. The orientational order increases with time and is always greater for higher concentration of salt, higher concentration of Laponite, and higher temperatures of the suspension. Although weakly birefringent, Laponite suspensions covered by paraffin oil do not show any enhancement in optical anisotropy near the interface compared to that in the bulk. We suggest that the expedited structure formation near the air interface propagating progressively inside the sample is responsible for the observed behavior. We discuss the observed nematic ordering in the context of glass-like and gel-like microstructure associated with aqueous Laponite suspensions.

Polymeradsorption onto a micro-sphere from optical tweezers electrophoresis

We explore the design and operation of an optical-tweezers electrophoresis apparatus to resolve polymer adsorption dynamics onto a single micro-sphere in a micro-fluidic environment. Our model system represents a broader class of micro-fluidic electrophoresis experiments for biosensing and fundamental colloid and surface science diagnostics. We track the adsorption of 100 kDa poly(ethylene oxide) homopolymer onto a colloidal silica sphere that is optically trapped in a crossed parallel-plate micro-channel. The adsorption dynamics are probed on the ∼1 μm particle length scale with ∼1 s temporal resolution. Because the particle electrophoretic mobility and channel electro-osmotic flow are exquisitely sensitive to the polymer layer hydrodynamic thickness, particle dynamics can be complicated by polymer adsorption onto the micro-channel walls. Nevertheless, using experiments and a theoretical model of electro-osmotic flow in channels with non-uniform wall ζ-potentials, we show that such influences can be mitigated by adopting a symmetrical flow configuration. The equilibrium hydrodynamic layer thickness of 100 kDa poly(ethylene oxide) on colloidal silica is ∼10 nm at polymer concentrations ≳10 ppm (weight percent), with the dynamics reflecting polymer solution concentration, flow rate, and polydispersity.

Regulating Volume Transitions of Highly Responsive Hydrogel Scaffolds by Adjusting the Network Properties of Microgel Building Block Colloids

We present a simple method to control the volume change of thermally responsive hydrogel scaffolds, providing a remarkably fast swelling and deswelling response to temperature changes. These scaffolds have 3-dimensional colloidal-network structures which are made from microgel particles while they are above their deswelling transition temperatures. By tuning the cross-link density of the microgel particles, we achieve controllable changes of the volume of the scaffolds in response to temperature. Their fast response rate is determined by the length scale of the unit microgel particles and is not influenced by the properties of the network. The release profile of a model drug (Rhapontin) loaded within the scaffolds can also be regulated by the cross-linking density of the microgel particles. These results offer a new way of fabricating hydrogel scaffolds with tunable matrix geometry and function by adjusting the properties of the unit microgel colloids, without loss of their fast response to temperature change.

Analysing the sintering of heterogeneous powder structures by in situ microtomography

This work analyses the microstructure changes of various copper-based powder systems during sintering from 3D images provided by in situ synchrotron microtomography. The investigated systems include a copper powder with a wide particle size distribution of 0–63 µm poured into a quartz capillary, a pre-sintered copper compact with artificially created large pores and a mixture of copper and alumina particles. The experiments were carried out at the European Synchrotron in Grenoble, France. Powders were sintered up to 1060°C under reducing atmosphere in a furnace located between the X-ray source and the detector. During each experiment, 3D images were taken at various times of the thermal cycle. We have obtained images with a resolution of 1.5 µm and the time of acquisition of every image was ∼1 min. Quantitative analysis of these images allowed the changes of various important parameters to be followed. Such parameters characterise the sintering process at the particle length scale: interparticle coordination, pore size distribution and particle centre-to-centre distance. Moreover, by tracking the displacement of each particle centre and comparing it to the displacement predicted by classical mean field assumption, we have been able to assess the magnitude of particle rearrangement occurring during sintering. From these data, the sintering behaviour of heterogeneous powder systems is discussed with particular emphasis of collective particle phenomena.

Blood cell transport and aggregation using discrete ellipsoidal particles

A computational model is presented for efficient mesoscale simulation of the transport, collision and aggregation of blood cells, which can be applied to examine red blood cells (RBCs), leukocytes, or platelets in various types of blood flows in which the fluid length scale is substantially larger than the particle length scale. This method is intended to be intermediate between microscale models, which examine deformation and flow around a small number of individual blood cells, and more phenomenological continuum models. The computational model utilizes a particle approximation for the blood cells and introduces other physically-justifiable approximations in order to accommodate computations with large numbers of cells. For instance, the non-spherical RBC and platelet shape is incorporated into the model by use of ellipsoidal particles. A novel method based on particle level-surfaces is presented for rapid identification of particle collision. It is shown that receptor–ligand binding between the cells can be modeled under certain conditions using a formulation that is mathematically similar to van der Waals adhesion of particles, but in which the surface energy density is variable in time. The method is demonstrated to provide computations of the interaction and adhesion of over 13,000 red-blood-cell particles on an ordinary workstation. These computations exhibit formation of chain-like rouleaux aggregates, modification of rouleaux structure due to shear flow, and capture and/or breakup of colliding rouleaux. The model predictions are examined for rouleaux size distribution in channel flow in comparison to experimental data, as well as for the effect of RBC aggregation on margination of white blood cells and platelets in channel flows.

Particle Trajectory in a Bidirectional Vortex Flow

In this research particle trajectory in a bidirectional vortex flow has been numerically predicted and the results experimentally validated. Scale analyses of forces show their order of magnitudes and give a criterion to recognize the order of magnitude of exerting forces on the particle. The particle has been assumed to be a rigid sphere. Initial velocity, diameter, density, and position of entering particle are assumed to be known. If the particle length scale is considered not to be comparable with the chamber length and if particle number density is low, then influence of particle on the flow field is negligible and a one-way solution is applicable. The governing equation is converted to a set of nonlinear, coupled, second-order ODE and solved by a numerical scheme. Results show that higher density, larger diameter, and higher initial axial velocity tend to move the particles further in the axial direction. Also, the maximum axial movement of the particle occurs when the initial radial velocity is zero and there is an optimum entrance position that provides a maximum traveling trajectory for particles. Increasing initial z-direction velocity component and density will result in increasing traveling trajectory.

Micrometric Granular Ripple Patterns in a Capillary Tube

The oscillatory motion of a fluid carrying micron-sized particles inside a capillary tube is investigated experimentally. It is found that initially uniformly distributed particles can segregate and accumulate to form regularly spaced micron-sized particle clusters. The wavelength of the microclusters is compared to data for macroscale sand-ripple patterns and found to obey the same universal scaling as these. A dimensional analysis is performed that confirms the universality of the experimentally observed scaling. The experimental data for the microripple clusters further suggest the existence of a minimum particle length scale for which patterns can form and below which the Brownian motion associated with the molecules of the matrix fluid inhibits pattern formation.

Equivalent particle diameter and length scale for pressure drop in porous metals

The internal architecture of metal foam is significantly different from that of traditional porous media. This provides a set of challenges for understanding the fluid flow in this relatively new class of materials. This paper proposes that despite the geometrical differences between metal foam and traditional porous media, the Ergun correlation is a good fit for the linear pressure drop as a function of the Darcian velocity, provided that an appropriate equivalent particle diameter is used. The paper investigates an appropriate particle diameter considering the physics of energy dissipation, i.e. the viscous shear and the form drag. The above approach is supported by wind tunnel steady-state unidirectional pressure drop measurements for airflow through several isotropic open-cell aluminum foam samples having different porosities and pore densities. For each foam sample, the equivalent particle diameter correlated well with the surface area per unit volume of the foam. This was also very well valid for previous porous metal pressure drop data in the open literature.

Continuous inertial focusing, ordering, and separation of particles in microchannels

Under laminar flow conditions, when no external forces are applied, particles are generally thought to follow fluid streamlines. Contrary to this perspective, we observe that flowing particles migrate across streamlines in a continuous, predictable, and accurate manner in microchannels experiencing laminar flows. The migration is attributed to lift forces on particles that are observed when inertial aspects of the flow become significant. We identified symmetric and asymmetric channel geometries that provide additional inertial forces that bias particular equilibrium positions to create continuous streams of ordered particles precisely positioned in three spatial dimensions. We were able to order particles laterally, within the transverse plane of the channel, with >80-nm accuracy, and longitudinally, in regular chains along the direction of flow. A fourth dimension of rotational alignment was observed for discoidal red blood cells. Unexpectedly, ordering appears to be independent of particle buoyant direction, suggesting only minor centrifugal contributions. Theoretical analysis indicates the physical principles are operational over a range of channel and particle length scales. The ability to differentially order particles of different sizes, continuously, at high rates, and without external forces in microchannels is expected to have a broad range of applications in continuous bioparticle separation, high-throughput cytometry, and large-scale filtration systems.

Bridging length scales in colloidal liquids and interfaces from near-critical divergence to single particles

Boiling and condensation are among the best recognized phase transitions of condensed matter. Approaching the critical point, a liquid becomes indistinguishable from its vapour, the interfacial thickness diverges and the system is dominated by long-wavelength density fluctuations1. Long wavelength usually means hundreds of particle diameters, but here we consider the limits of this assumption, using a mesoscopic analogue of simple liquids, a colloid–polymer mixture2,3. We simultaneously visualize both the colloidal particles and near-critical density fluctuations, and reveal particle-level images of the critical clusters and liquid–gas interface. Surprisingly, we find that critical scaling does not break down until the correlation length approaches the size of the constituent particles, where there is a smooth transition to non-critical classical behaviour. Our results could provide a framework for unifying the disparate particle and correlation length scales, and bring new insight into the nature of the liquid–gas interface and the limit of the critical regime.

Effect of length scale of alumina particles of different sizes on the damping characteristics of an Al–Mg alloy

Pure Al was reinforced with alumina particles with size ranging from micro to nano-size dimension. Magnesium was added to the Al matrix to enhance the wettability of alumina particles. Synthesis of materials was accomplished using the solidification route viz., disintegrated melt deposition technique. Energy dissipation in the form of damping capacity was determined using free–free type suspended beam arrangement coupled with circle-fit approach. Three samples with Al–4 wt.% Mg matrix were prepared that were reinforced by alumina particles whose size ranged from μm to nm length scale (viz., 10, 0.3 μm and 50 nm and with a volume percentage of 10.13, 1.47 and 0.94, respectively). Damping per unit volume percentage of alumina particles in the Al–Mg matrix increased by 58%, 30% and 3% for the alumina particles size of 50 nm, 0.3 and 10 μm, respectively, with respect to the monolithic Al–Mg specimen. Such increase in damping can be rationalized in terms of microstructural changes that arise due to the presence of the alumina particles in the composite samples compared to that of unreinforced sample.

Thermal transport in sheared electro- and magnetorheological fluids

Thermal energy transport in sheared electrorheological and magnetorheological (ER and MR) fluids is analyzed. Although energy production by viscous dissipation can be significant, energy transport on the particle length scale can be analyzed by ignoring viscous dissipation. For typical situations, energy transport normal to the flow direction is dominated by conduction. Particle-level simulations were employed to determine the suspension structure as a function of Mason number and volume fraction. A self-consistent mean-field dipole model is used to estimate the effective thermal conductivities for these simulated structures. The field-induced chain-like aggregates that form at small Mason number result in a larger effective thermal conductivity at small Mason number than at large Mason number. Effects of higher-order multipoles are estimated by analyzing effective thermal conductivities of model structures. For highly conducting particles, the effective thermal conductivity of a sheared ER or MR suspension is predicted to roughly double as the Mason number is decreased from the large to the small Mason number limits.

Pore network model of deactivation of immobilized glucose isomerase in packed-bed reactors. Part III: Multiscale modelling

A widely used method for converting glucose to fructose is by enzymatic isomerization. This process, which uses immobilized glucose isomerase, takes place in a packed-bed reactor that consists of microporous particles with a range of pore sizes, characterized by a pore size distribution. The micropores are also interconnected, giving rise to a three-dimensional (3D) network of pores with distributed sizes and connectivities. The particles themselves generate a 3D pore network at the reactor level with distributed pore sizes, but with a fixed connectivity. In this paper, Part III of a series, we develop a multiscale modelling approach to this problem, beginning with the relevant phenomena at the scale of the micropores, and integrating them into the particle and reactor length scales. As the efficiency of the process is significantly affected by deactivation of the microporous particles, we take this phenomenon into account at all the relevant length scales. We use a real random packing of particles, originally constructed by Finney (Proc. R. Soc. Lond. A, 319 (1970) 479), and map its pore space onto an equivalent 3D Voronoi network in which the pores are represented by the edges of the Voronoi polyhedra. The flow field in the Voronoi network is determined, and the convection–diffusion–reaction equation is then solved in the Voronoi network, taking into account the gradual deactivation of the microporous particles. Several plausible mechanisms of deactivation of the microporous particles are considered, and their effect on the performance of the reactor is investigated. Good agreement is found between the results of the computer simulations and the relevant experimental data.

Turbulence Modification in Vertical Jets Laden with Slow Large Particles.

The turbulence structure of the liquid-solid vertical jet flows impinging on a flat plate has been experimentally investigated. The diameter of the particles is nearly ten times as large as the Kolmogorov length scale and the volumetric concentration of the dispersed phase was set at 0.13%. The particle speed is about 45% of the liquid velocity at the nozzle outlet. As a result of the measurements with LDA and PIV systems, it was shown that the turbulent intensity in the carrier fluid has been enhanced due to the effect of the large-scale particles. The increase of power spectra and dissipation spectra has been clearly found in the high wavenumber range, which corresponds to the particle length scale. Since the energy variation evaluated by the model, in which turbulence modification is caused by particle wake eddies, is equivalent to the measured values, it can be concluded that the turbulence enhancement is mainly caused by the wakes behind the particles.

TURBULENCE STRUCTURE IN VERTICAL IMPINGING JETS LADEN WITH SOLID PARTICLES

A turbulence structure has been experimentally investigated in the particle-laden vertical jet flows impinging on a horizontal flat plate. The diameter of the particles is nearly ten times as large as the Kolmogorov length scale. In experiments, the volumetric concentration c of the dispersed phase was set at 0.08% and 0.13%. In addition, the distance H between the nozzle outlet and the impinging wall was widely varied, thereby varying H/D from 10 to 30, where D is the nozzle diameter. The characteristic flow patterns and turbulent quantities were measured with a Laser Doppler Anemometer (LDA). As a result, it has been confirmed that the turbulent intensity in the carrier fluid has been enhanced due to the existence of the large-scale particles. In the wavenumber space, the power spectra have been clearly enhanced mainly in the high wavenumber range, which corresponds to the particle length scale.

INERTIAL EFFECTS IN SUSPENSION AND POROUS-MEDIA FLOWS

▪ Abstract The current understanding of the average flow properties of packed beds and particle suspensions, in which inertia plays a significant role on the particle length scale, is examined. The features of inertial suspensions posing challenges to theoriticians include the nonlinear and unsteady nature of the governing equations, the inability to superimpose solutions, the prevalence of hydrodynamic instabilities, and the existence of particle-particle collisions. We discuss two special cases of inertial suspensions, for which detailed kinetic theories have been developed: (a) particles in a gas, and (b) spherical, high-Reynolds number bubbles in liquid. Subsequently, we review recent applications of computational fluid dynamics to simulate the motion in particle suspensions with both inertia and vorticity in the continueous phase. The synthesis of these analytical and numerical techniques is a promising approach to address the many challenges of modelling inertial suspensions.

Fokker-Planck Equation, Molecular Friction, and Molecular Dynamics for Brownian Particle Transport near External Solid Surfaces

The Fokker–Planck (FP) equation describing the dynamics of a single Brownian particle near a fixed external surface is derived using the multiple-time-scales perturbation method, previously used by Cukier and Deutch and Nienhuis in the absence of any external surfaces, and Piasecki et al. for two Brownian spheres in a hard fluid. The FP equation includes an explicit expression for the (time-independent) particle friction tensor in terms of the force autocorrelation function and equilibrium average force on the particle by the surrounding fluid and in the presence of a fixed external surface, such as an adsorbate. The scaling and perturbation analysis given here also shows that the force autocorrelation function must decay rapidly on the zeroth-order time scale τ0, which physically requires NKn≪1, where NKn is the Knudsen number (ratio of the length scale for fluid intermolecular interactions to the Brownian particle length scale). This restricts the theory given here to liquid systems where NKn≪1. For a specified particle configuration with respect to the external surface, equilibrium canonical molecular dynamics (MD) calculations are conducted, as shown here, in order to obtain numerical values of the friction tensor from the force autocorrelation expression. Molecular dynamics computations of the friction tensor for a single spherical particle in the absence of a fixed external surface are shown to recover Stokes' law for various types of fluid molecule–particle interaction potentials. Analytical studies of the static force correlation function also demonstrate the remarkable principle of force-time parity whereby the particle friction coefficient is nearly independent of the fluid molecule–particle interaction potential. Molecular dynamics computations of the friction tensor for a single spherical particle near a fixed external spherical surface (adsorbate) demonstrate a breakdown in continuum hydrodynamic results at close particle–surface separation distances on the order of several molecular diameters.