Effects of polydispersity in quenched-annealed fluids: An integral equation approach

An extension of the replica Ornstein-Zernike (ROZ) equations for partly quenched polydisperse systems is presented. Explicit calculations have been performed for a monodisperse hard sphere fluid confined by a polydisperse hard sphere disordered matrix by using Percus-Yevick and hypernetted chain (HNC) approximations. The chemical potential of adsorbed fluid species has been evaluated. A numerical solution of the ROZ equations makes use of the orthonormal polynomials with the weight function corresponding to the distribution function of the diameters of matrix species. We have also compared the results of theoretical predictions with Monte Carlo simulation in a canonical ensemble. The result of this comparison suggests that the HNC approximation performs slightly better in predicting the structural properties of the system.     

The stability limit of the fluid phase of polydisperse sticky spheres

It has been shown by Stell (1991, J. statist. Phys., 63, 1203) that at low temperature mono-disperse sticky spheres collapse to form coexisting close-packed solid and infinitely dilute gases. We show that polydisperse sticky spheres also collapse and calculate the collapse temperature. The polydisperse spheres separate into fractions with narrower polydispersities which can then solidify. This is perhaps the first example of a single-peaked polydisperse mixture phase solidifying and separating. It implies that a mixture of polydisperse large hard spheres with much smaller hard spheres does not show fluid—fluid coexistence.     

Analytical model of equation of state for polydisperse fluid of adhesive spherical particles

An analytical model of the equation of state is presented for the polydisperse fluid of adhesive colloidal particles. The model is based on the mean-spherical approximation solution of the Ornstein-Zernike equation for a multicomponent hard sphere Yukawa fluid in which the Yukawa tails are sufficiently short range and strong. In particular, assuming that distributions of diameters and ‘charges’ of particles are described by the Schulz function, the analytical expressions for the compressibility and the pressure for the intrinsically polydisperse fluid are given in terms of simple functions of the packing fraction, the adhesion parameter and the Schulz distribution parameter.     

Phase equilibrium in nearly monodisperse fluids

The two-phase equilibrium and critical point conditions of a polydisperse fluid (a mixture with a continuous distribution of components) are solved by making power-series expansions about the properties of a single representative species.     

On multiple small-angle scattering

An analytical approach has been taken for analyzing the multiple scattering effects in small angle scattering (SAS) from both monodisperse and polydisperse systems. Two limiting regions, viz the Guinier region and the Porod region have been studied. A modified form of Guinier law has been deduced for the scattered intensity distribution in the region of small wave vector transfer, q. In the regionq(=|q|)→∞, it is shown that the effect of multiple scattering does not alter the Porod (q ⁻⁴) law. In the case of polydisperse systems, a correlation has been established between the size distribution of the inhomogeneities and the experimentally extractable parameters. The validity of the formalism has been examined by reinterpretation of the multiple SANS data (Hardman-Rhyne and Berk 1985) on polydisperse Al₂O₃ samples. This formalism is useful in characterizing the inhomogeneities from SAS measurements, particularly when thick samples are used.     

Polydisperse spherical colloidal silica particles:Preparation and application

A new industrial method has been developed to produce polydisperse spherical colloidal silica particles with a very broad particle size,ranging from 20-95 nm.The process uses a reactor in which the original seed solution is heated to 100 ℃,and then active silicic acid and the seed solution are titrated to the reactor continuously with a constant rate.The original seeds and the titrated seeds in the reactor will go through different particle growth cycles to form different particle sizes.Both the particles' size distribution and morphology have been characterized by dynamic light scattering(DLS)and the focus ion beam(FIB) system.In addition,the as-prepared polydisperse colloidal silica particle in the application of sapphire wafer's chemical mechanical polishing(CMP) process has been tested.The material removal rate(MRR) of this kind of abrasive has been tested and verified to be much faster than traditional monodisperse silica particles.Finally,the mechanism of sapphire CMP process by this kind of polydisperse silica particles has been investigated to explore the reasons for the high polishing rate.     

Wetting transitions in polydisperse fluids

The properties of the coexisting bulk gas and liquid phases of a polydisperse fluid depend not only on the prevailing temperature but also on the overall parent density. As a result, a polydisperse fluid near a wall will exhibit density-driven wetting transitions inside the coexistence region. We propose a likely topology for the wetting phase diagram, which we test using Monte Carlo simulations of a model polydisperse fluid at an attractive wall, tracing the wetting line inside the cloud curve and identifying the relationship to prewetting.     

Numerical investigation of the effects of polydisperse water sprays on extinction conditions of counterflow methane non-premixed flames

Water, sprayed in the form of tiny droplets, has emerged as a potential fire suppressant after the halon compounds such as trifluorobromomethane (CF₃Br, Halon 1301) were banned by the Montreal protocol. The size distribution of the water droplet plays a crucial role in the effectiveness of the water spray in fire suppression. A numerical investigation of the influence of size distribution of a polydisperse water spray on extinction of counterflow diffusion flames is presented in this paper. This study uses laminar finite rate model with reduced CHEMKIN chemistry for numerical simulations. The discrete phase, namely the water spray, is simulated using Lagrangian Discrete Phase Modelling approach. In this work, the polydispersity of water spray is taken into account in the numerical simulation by a suitable Rosin–Rammler distribution. Results obtained from numerical simulation are validated with the experimental results reported in the literature. This study demonstrates that the representation of the polydisperse spray by a monodisperse spray (with droplet diameter same as the SMD of the polydisperse spray) in numerical simulations is not always justified and it leads to deviation from the experimental results. The effects of number mean diameter and spread parameter on the efficacy of flame suppression are investigated for polydisperse sprays. A comprehensive comparison is done between the effectiveness of monodisperse and polydisperse water sprays. An optimum droplet diameter is obtained for monodisperse sprays for which the effectiveness of the spray is maximum. The effects of evaporation Damköhler number and Stokes number of water droplets on flame suppression have also been explained.     

Effects of sintering on microstructure and dielectric response in YCrO<Subscript>3</Subscript> nanoceramic

Effects of sintering on pore morphology and dielectric response have been investigated. Pore structure has been probed by small angle neutron scattering (SANS). It has been observed that the size distribution becomes less polydisperse with a slight modification in the distribution as sintering temperature is increased. Dielectric response in the frequency range 0.02–1000 kHz is significantly altered by modification of pore structure because of sintering. A transition from non-Debye type to near-Debye type response has been observed as the sintering temperature is increased.      

Effective interaction between two giant spheres suspended in a size polydisperse hard-sphere fluid

Analytic expressions for the Laplace transform of the interaction energy and force between two exceedingly large hard spheres at infinite dilution in a polydisperse hard-sphere suspending fluid are presented. The equations are based on the Percus–Yevick approximation for the many-component suspending fluid, supplemented by the hypernetted chain approximation for the correlation function of the suspended spheres. By applying the Derjaguin approximation, the energy and force results for two spheres are related to the energy per unit area and the disjoining pressure between two flat walls suspended in a polydisperse fluid. Numerical results for the representative Schultz distributions of the diameters of the species comprising the suspending fluid are presented and discussed.     

Structure and thermodynamic properties of a polydisperse fluid in contact with a polydisperse matrix

We present expressions that allow the determination of the structural and thermodynamic properties of a polydisperse liquid mixture in contact with a polydisperse matrix; polydispersity of the fluid and of the matrix are described by distribution functions f ^f(σ) and f m (σ), where σ and σ characterize the size of the fluid and of the matrix particles. The formalism is based on the replica trick (to describe the properties of a fluid in contact with a matrix) and on the expansion of size-dependent functions in terms of orthogonal polynomials associated with the distribution functions f _f(σ) and f _m (σ). In our expressions structural and thermodynamic properties are calculated from coefficient functions (of these expansions) which are obtained from a numerical solution of the generalized replica Ornstein-Zernike equations, solved along with a suitable closure relation.     

Bulk and shear viscosities of a polydisperse hard-sphere fluid

The bulk and shear viscosity expressions for a multicomponent hard-sphere mixture in the Enskog transport theory are generalized to the polydisperse limit. The effect of polydispersity is expressed in terms of correction factors to the monodisperse fluid results. These correction factors have been evaluated for both a log-normal size distribution with the mass-size relation of a power-law form and a log-normal mass distribution with fixed particle size, which is the continuous limit of isotopes.     

Polydispersity exponent in homogeneous droplet growth

The homogeneous growth of D-dimensional hyperspherical droplets on a d-dimensional surface produces a bimodal distribution in the sizes of the droplets, with a roughly monodispersed distribution of larger droplets superimposed on a highly polydisperse distribution of smaller ones. The polydisperse regime is characterized by an exponent, which also determines the total droplet density. The exponent is evaluated, and it is deduced that d = 3 represents an upper critical dimensionality.     

Small-angle neutron scattering contrast variation on magnetite-myristic acid-benzene magnetic fluid

A magnetic fluid with magnetite dispersed in D-benzene and stabilized by myristic acid is investigated using the contrast variation technique in small-angle neutron scattering. The results obtained are interpreted within a new approach to the basic functions for polydisperse multicomponent and superparamagnetic systems. Myristic acid is considered an alternative to oleic acid, which is commonly used in these fluids. The parameters characterizing the particle size distribution function and the thickness of the myristic acid layer are determined. The data obtained are in good agreement with the results derived from previous investigations with the use of polarized neutrons.     

Light-scattering by optically soft randomly oriented spheroids

In the framework of the Rayleigh–Gans–Debye approximation and anomalous diffraction approaches, the light scattering characteristics of randomly oriented spheroids have been investigated. It has been proved that the system of randomly oriented spheroids is equivalent to the system of polydisperse spherical particles that have the same values of volume and surface area as nonspherical particles. The power law size distribution meeting these requirements has been obtained.     

Calibration and numerical simulation of Nanoparticle Surface Area Monitor (TSI Model 3550 NSAM)

TSI Nanoparticle Surface Area Monitor (NSAM) Model 3550 has been developed to measure the nanoparticle surface area deposited in different regions of the human lung. It makes use of an adjustable ion trap voltage to match the total surface area of particles, which are below 100 nm, deposited in tracheobronchial (TB) or alveolar (A) regions of the human lung. In this paper, calibration factors of NSAM were experimentally determined for particles of different materials. Tests were performed using monodisperse (Ag agglomerates and NaCl, 7–100 nm) and polydisperse particles (Ag agglomerates, number count mean diameter below 50 nm). Experimental data show that the currents in NSAM have a linear relation with a function of the total deposited nanoparticle surface area for the different compartments of the lung. No significant dependency of the calibration factors on particle materials and morphology was observed. Monodisperse nanoparticles in the size range where the response function is in the desirable range can be used for calibration. Calibration factors of monodisperse and polydisperse Ag particle agglomerates are in good agreement with each other, which indicates that polydisperse nanoparticles can be used to determine calibration factors. Using a CFD computer code (Fluent) numerical simulations of fluid flow and particle trajectories inside NSAM were performed to estimate response function of NSAM for different ion trap voltages. The numerical simulation results agreed well with experimental results.     

Characterisation of Particle Size for Polydisperse Powders aerosolised and detected by light scattering

This paper describes a study to determine the most appropriate particle size parameter for polydisperse powders dispersed as aerosol and detected by light scattering. It is relevant to many areas of engineering research. By means of calculations of the intensity of light scattered from particles of different sizes, it has been shown that the surface median aerodynamic diameter (SMAD) is an appropriate measure for polydisperse aerosolised powders. The microscope-based procedure for obtaining the SMAD is described, as well as its implementation for narrowly-graded polydisperse powders of fused alumina of type which have been widely used in studies of particle transport in wind tunnels. It was shown that for the fused alumina powders examined, SMAD = 1.25 x (PASMAD), where PASMAD is the projected area surface median aerodynamic diameter.     

Effective dielectric constant of dilute polydisperse suspensions of spheres

We study the effective dielectric constant of a dilute, polydisperse suspension of spheres embedded in a uniform background. We consider a frequency region where the dipole polarizability of individual spheres exhibits a resonance. We evaluate the effective dielectric constant to second order in the volume fraction employing the dipole approximation, which in previous work has been shown to be applicable in resonance. We apply our results to suspensions of spheres with identical and uniform dielectric constant, assuming a log-normal distribution of sphere radii.     

Density-functional theory for polymer fluids with molecular weight polydispersity

We develop a density-functional theory for polydisperse polymer fluids satisfying the Schulz-Flory distribution. The resulting equations are remarkably simple and quickly solved, the computational effort scaling with the polydispersity index, rather than the average molecular weight. Equilibrium, or "living", polymers enter naturally as very polydisperse samples. We illustrate the importance of polydispersity on colloid stability by investigating interactions between adsorbing and nonadsorbing surfaces. Significant free energy barriers are present in monodisperse samples, but these diminish as the degree of polydispersity increases.     

Carbide precipitates in solution-quenched PH13-8 Mo stainless steel: A small-angle neutron scattering investigation

This paper deals with the small-angle neutron scattering (SANS) investigation on solution-quenched PH13-8 Mo stainless steel. From the nature of the variation of the functionality of the profiles for varying specimen thickness and also from the transmission electron microscopy (TEM), it has been established that the small-angle scattering signal predominantly originates from the block-like metallic carbide precipitates in the specimen. The contribution due to double Bragg reflection is not significant in the present case. The single scattering profile has been extracted from the experimental profiles corresponding to different values of specimen thickness. In order to avoid complexity and non-uniqueness of the multi-parameter minimization for randomly oriented polydisperse block-like precipitate model, the data have been analyzed assuming randomly oriented polydisperse cylindrical particle model with a locked aspect ratio.