Polymer depletion interaction between a particle and a wall

The attractive depletion interaction between a spherical particle and a planar wall in a dilute solution of long flexible nonadsorbing free polymer chains is found to depend crucially on the particle to polymer size ratio . While the polymer-induced force between particle and wall decreases monotonically with increasing distance for large , for small it has a maximum at a distance of the order of the polymer size. For ideal chains we study the crossover from large to small behavior in full quantitative detail. Besides the free energy of interaction and the force, we also discuss the spatial variations of the densities of chain-ends and chain-monomers near the wall and particle. Two independent procedures, (1) solving directly the diffusion equation for the density of ends in terms of planar and spherical waves and (2) minimizing the Ginzburg-Landau functional of the “magnetic analog” of the polymer problem, are used to obtain results numerically for a broad range of ratios of the three lengths particle size, polymer size and distance of particle from the wall. Besides previously known cases, we find two more interesting limiting regions of the length ratios for which analytical results can be obtained. [2mm] Received 11 December 1998     

The effect of soot particle optical inhomogenity and agglomeration on the analysis of light scattering measurements in flames

Computations have been performed for homogeneous and radially inhomogeneous spheres plus agglomerated structures composed of spherical primary units. The ranges of refractive index and particle size considered are typical of soot in flames. The effects of uncertainty in the refractive index and neglect of its radial distribution on inferring spherical particle sizes and concentrations from in situ light-scattering measurements are delineated. A framework is established for computing various scattering characteristics of agglomerated particles in terms of the scattering functions for spherical particles. The results achieved for agglomerates indicate that mean values of the particle concentration, number of units in an agglomerate and overall agglomerate size may be inferred from light-scattering data.     

Numerical investigation of pulverized coal particle group combustion using tabulated chemistry

The ignition and combustion of coal particle groups are investigated numerically in a laminar flow reactor. The Flamelet Generated Manifold method is extended to account for the complex mixture of gases being released during devolatilization, which is calculated with a competing two-step model. A second mixture fraction is introduced to include the mixing with the second methane fuel stream. The interactions of the gas phase with particles are modeled within a fully coupled Euler-Lagrange framework. To investigate the influence of particle groups on ignition and combustion, successively increasing densities of particle streams have been analyzed. The ignition delay time is increased significantly by higher particle densities. This delay is validated successfully with the available measurements. Moreover, the shape of the volatile flame was found to be strongly influenced by the particle number density inside the flame. A transition from spherical flames around single particles to a conical flame around the particle cloud could be found in numerical results as well as in experiments. As the primary mechanism for the substantial ignition delay and the formation of the flame, the increased heat transfer from the gas-phase to the particle group, resulting in lower gas-phase temperatures, was identified.     

Scattering of spatially inhomogeneous sound waves by a spherical particle

The problem of monopole, dipole, and rotational scattering of a spatially inhomogeneous time-harmonic sound field by an arbitrary spherical particle is solved for the cases of the medium being a viscous compressible liquid or an isotropic elastic medium. Equations for the spherical mean fields at the particle are obtained. These equations are used to derive the formulas for the scattered fields. Different limiting cases of particle behavior are considered. In particular, it is shown that the dipole scattering is determined by two components of particle oscillations, one of which corresponds to translational oscillatory motion and the other to oscillations of two antiphase monopoles. For these types of particle oscillations, a scattering matrix, which determines the scattering of an arbitrary field by a particle, is constructed. The matrix allows the formalization of the processes of multiple sound scattering by particles and is valid for any distances between the particles down to their contact.     

Light scattering by coated Gaussian and aggregate particles

Light scattering by nonspherical and inhomogeneous small particles is studied by varying particle shapes, sizes, and compositions. We introduce an efficient tool for deforming particle shape and composition by adding a coating on an initial particle. This concave-hull transformation is applied to wavelength-scale Gaussian and aggregate particles, and the differences in the optical properties of the coated particles are compared to those of the uncoated geometries. The light-scattering computations are performed using the discrete-dipole approximation method which allows for internal inhomogeneity and irregular particle shapes. The results are analyzed concentrating on the intensity of the scattered light, the degree of linear polarization for unpolarized incident light, and the depolarization ratio. Polarization results yield the most significant differences and, moreover, coated aggregates are observed to produce net positive polarization, whereas it is negative for the Gaussian particles, also resembling the polarization of a spherical particle. As for the depolarization ratio, an intriguing double-lobe feature is observed near the backscattering direction for both particle geometries regardless of size, shape, and composition. The double-lobe maxima and minima generally coincide with those of the intensity and polarization.     

Bidisperse granular avalanches on inclined planes: A rich variety of behaviors

Experiments were performed to provide insight into the flow behavior and structure of bimodal mixtures of grains in gravity-driven, free-surface flows. Unsteady unconfined flows were produced by releasing instantaneously a dry granular mass, composed of two particle sizes, over a rough inclined plane. As a result of size segregation, the small particles are found at the bottom of the flow and final deposit, the large particles are found at the free surface, but also on the lateral borders and at the front of the flow. The lateral and vertical inhomogeneous repartitions of particles lead to two main effects that are completely absent in monodispersed flows. The outline effect results from the accumulation of large beads on the periphery of the flow depending on the value of the relative friction of each particle species on the plane. This effect in turn causes a narrowing of the flow and/or an increase of length of the final deposit. The interface effect results of the interaction between layers of different size particles and causes the modification of the thickness of the deposit. These effects occur simultaneously and their combination leads to a great variety of behaviors. In this investigation, evidence of the diversity of behaviors is presented as the size ratio, relative friction and concentration of each particle species are varied.     

计算平均力势的理论方法

提出了一个用于计算平均力势的普适性的理论框架,方法克服了以前的方法的缺陷,仅仅需要溶剂粒子在单个溶质粒子附近的密度分布作为输入.计算了两个大尺寸溶质粒子浸在小尺寸硬球溶剂浴中的平均力势,理论预言与可能的模拟数据符合.调查了溶剂-溶质相互作用势、溶剂密度、溶质粒子尺寸对过量平均力势的影响.结论是:溶剂粒子在单个溶质粒子附近的减少导致吸引的过量平均力势,而溶剂粒子在单个溶质粒子附近的聚集导致排斥的过量平均力势,高溶剂密度与大溶质粒子尺寸能强化这种趋势.讨论了这种空耗吸引-聚集排斥与生物学中的疏水吸引-水化排斥的联系.     

A simulation study of an asymmetric exclusion model with open and periodic boundaries for parallel dynamics

The effect of jumping rate probability on the phase diagram of an asymmetric exclusion model is studied by numerical simulations. Density, current and velocity of particles are calculated for parallel dynamics. In the open boundaries case for one species of particles (particles 1), a passage from first to second order transition occurs by decreasing the jumping rate. In the periodic boundaries case, by introducing another species of particle (particle 2) which plays the role of obstacle for particles 1, the average velocity of particles 1 increases with increasing the jumping rate for small density. While the average velocity of particle 2 decreases for small and intermediate densities. Received: 21 October 1997     

Simulation of random mixed packing of different density particles

This paper presents the effects of density difference on the three-dimensional (3D) distribution of random mixed packing. The random mixed packing dynamics of particles of two different densities are simulated. The initial state is homogeneous, but the final packing state is inhomogeneous. The segregation phenomenon (inhomogeneous distribution) is also observed. In the final state, the top layers are composed of mostly light particles. The several layers beneath the top contain more heavy particles than light particles. At the bottom, they also contain more heavy particles than light particles. Furthermore, at both the top and the bottom, particle clustering is observed. The current study also analyses the cause of this inhomogeneity in detail. The main cause of this phenomenon is the velocity difference after collision of these two types of particles induced by the density difference. The present study reveals that even if particles were perfectly mixed, the packing process would lead to the final inhomogeneous mixture. It suggests that special treatment may be required to get the true homogeneous packing.     

New micromagnetic states of magnetically soft nanoparticles with a nearly cubic shape

The ground state of nonellipsoidal particles can be inhomogeneous due to the effect of a demagnetizing field. The approach proposed here for studying such particles is based on the combination of symmetry analysis and perturbation theory. The general formulation of this approach, which makes it possible to analyze weakly inhomogeneous states for particles with a complex shape, is considered. The ground state of cubic particles of magnetically soft materials is calculated analytically, and the effect of small strains of cubic particles on the magnetization distribution in the particles is investigated. It is shown for the example of magnetically soft cubic particles that even a small deviation of the particle shape from symmetrical may result in the realization of a special magnetic state in such particles, in which the symmetry in the magnetization distribution is lower than the particle symmetry. A change in the parameters of a particle can substantially modify its magnetic properties and may even induce a phase transition to a state with a different symmetry.     

Dynamics of a charged particle bunch in a penning trap

The Lagrangean equations for gas dynamics of a spherical bunch of charged particles in a Penning trap are solved. The solution describes the pulsation of an inhomogeneous particle bunch whose center behaves as a spatial oscillator in a coordinate system rotating with the Larmor frequency.     

Local fields close to the surface of nanoparticles and aggregates of nanoparticles

A refined discussion of the near-field scattering of spherical nanoparticles and the electromagnetic fields close to the particle surface is given. New results for the dependence on the distance from the surface and the angular distribution of the scattered light in the near-field are given. It will be shown that the radial component of the electric field leads to striking differences in the phase functions in the near-field and the far-field. Exemplary computations are presented for Ag and Au particles with different size. In a second part the discussion is extended to assemblies of spherical Ag and Au nanoparticles. It will be shown that large near-fields at wavelengths commonly used in SERS experiments are obtained for aggregates. In the near-field scattering intensity “hot spots” mark regions between particles in the aggregate where the near-field is particularly high. Received: 4 May 2001 / Revised version: 20 July 2001 / Published online: 19 September 2001     

Fractal Analysis of Surface Roughness of Particles in Porous Media

A fractal dimension for roughness height （RH） is introduced to characterize the degree of roughness or disorder of particle surface characters which significantly influence physical-chimerical processes in porous media. An analytical expression for the fractal dimension of RH on statistically self-similar fractal surfaces is derived and is expressed as a function of roughness parameters. The specific surface area （SSA） of porous materials with spherical particles is also derived, and the proposed fractal model for the SSA of particles with rough surfaces is expressed as a function of fractal dimension for RH and fractal dimension for particle size distribution, relative roughness of particle surface, and ratio of the minimum to the maximum particle diameters of spherical particles.     

Effect of surface conduction on the dynamics of induction charging of particles

The purpose of this paper is to investigate the dynamics of induction charging for spherical particles assuming finite volume and surface conductivities. It is assumed that the thickness of the surface layer is a small percentage of the particle radius. All results were obtained using COMSOL commercial software. The results show that the rate of charge accumulation is affected by the conductivity, permittivity and the contact area with the ground electrode. It is shown that the actual charging time constant for a material with fixed bulk properties can differ considerably from the relaxation time.     

Active thermophoresis and diffusiophoresis

Thermophoresis and diffusiophoresis respectively refer to the directed drift of suspended particles in solutions with external thermal and chemical gradients, which have been widely used in the manipulation of mesoscopic particles. We here study a phoretic-like motion of a passive colloidal particle immersed in inhomogeneous active baths, where the thermal and chemical gradients are replaced separately by activity and concentration gradients of the active particles. By performing simulations, we show that the passive colloidal particle experiences phoretic-like forces that originate from its interactions with the inhomogeneous active fluid, and thus drifts along the gradient field, leading to an accumulation. The results are similar to the traditional phoretic effects occurring in passive colloidal suspensions, implying that the concepts of thermophoresis and diffusiophoresis could be generalized into active baths.     

Active transport and cluster formation on 2D networks

We introduce a model for active transport on inhomogeneous networks embedded in a diffusive environment which is motivated by vesicular transport on actin filaments. In the presence of a hard-core interaction, particle clusters are observed that exhibit an algebraically decaying distribution in a large parameter regime, indicating the existence of clusters on all scales. The scale-free behavior can be understood by a mechanism promoting preferential attachment of particles to large clusters. The results are compared with a diffusion-limited aggregation model and active transport on a regular network. For both models we observe aggregation of particles to clusters which are characterized by a finite size scale if the relevant time scales and particle densities are considered.     

Depletion interactions in binary mixtures of repulsive colloids

Acceptance ratio method, which has been used to calculate the depletion potential in binary hard-sphere mixtures, is extended to the computation of the depletion potential of non-rigid particle systems. The repulsive part of the Lennard-Jones pair potential is used as the direct pair potential between the non-rigid particles. The depletion potential between two big spheres immersed in a suspension of small spheres is determined with the acceptance ratio method through the application of Monte Carlo simulation. In order to check the validity of this method, our results are compared with those obtained by the Asakura-Oosawa approximation, and by Varial expansion approach, and by molecular dynamics simulation. The total effective potential and the depth of its potential well are computed for various softness parameters of the direct pair potential.     

The comparison between the Mie theory and the Rayleigh approximation to calculate the EM scattering by partially charged sand

The Mie theory and Rayleigh approximation are two basic methods to study the EM scattering of uncharged spherical particle, and when the particle radius is much smaller than the incident wavelength, they are equivalent, but whether the Rayleigh approximation is still equivalent to Mie theory when we use them to calculate the EM scattering of small charged particle, there is still no any report published to discuss this problem. In this paper we make some comparisons between Mie theory and Rayleigh approximation to solve the EM scattering of partially electrification spherical particles. The results showed that the Mie theory would be more suitable to calculate the scattering of charged spherical particles.     

Measurements of Silica Aggregate Particle Growth Using Light Scattering and Thermophoretic Sampling in a Coflow Diffusion Flame

The evolution of silica aggregate particles in a coflow diffusion flame has been studied experimentally using light scattering and thermophoretic sampling techniques. An attempt has been made to calculate the aggregate number density and volume fraction using the measurements of scattering cross section from 90° light scattering with combination of measuring the particle size and morphology from the localized sampling and a TEM image analysis. Aggregate or particle number densities and volume fractions were calculated using Rayleigh–Debye–Gans and Mie theory for fractal aggregates and spherical particles, respectively. Using this technique, the effects of H₂ flow rates on the evolution of silica aggregate particles have been studied in a coflow diffusion flame burner. As the flow rate of H₂ increases, the primary particle diameters of silica aggregates have been first decreased, but, further increase of H₂ flow rate causes the diameter of primary particles to increase and for sufficiently larger flow rates, the fractal aggregates finally become spherical particles. For the cases of high flame temperatures, the particle sizes become larger and the number densities decrease by coagulation as the particles move up within the flame. For cases of low flame temperatures, the primary particle diameters of aggregates vary a little following the centerline of burner and for the case of the lowest flame temperature in the present experiments, the sizes of primary particles even decrease as particles move upward.