Insoluble Spherical Particles Research Articles

A modified expression for the steady-state heterogeneous nucleation rate

A modified expression is derived to calculate the steady-state rate of heterogeneous nucleation on an insoluble spherical particle. For the first time, this modified expression comprehensively considers three factors used in previous expressions, i.e., two mechanisms of cluster growth, the self-consistent expression for the equilibrium number density of clusters, and the effect of line tension. The effects of the three factors are analyzed, and the comparisons of predicted and measured critical supersaturations are presented to validate the advantage of the modified expression and investigate the contributions of the three factors to heterogeneous nucleation. The results show that all the three factors especially the line tension in previous expressions should be considered, which promote the heterogeneous nucleation process. It is also found that the predicted data of the modified expression are much closer to the experimental data than those of the previous expressions.

A kinetic model for heterogeneous condensation of vapor on an insoluble spherical particle

A kinetic model is developed to describe the heterogeneous condensation of vapor on an insoluble spherical particle. This new model considers two mechanisms of cluster growth: direct addition of water molecules from the vapor and surface diffusion of adsorbed water molecules on the particle. The effect of line tension is also included in the model. For the first time, the exact expression of evaporation coefficient is derived for heterogeneous condensation of vapor on an insoluble spherical particle by using the detailed balance. The obtained expression of evaporation coefficient is proved to be also correct in the homogeneous condensation and the heterogeneous condensation on a planar solid surface. The contributions of the two mechanisms to heterogeneous condensation including the effect of line tension are evaluated and analysed. It is found that the cluster growth via surface diffusion of adsorbed water molecules on the particle is more important than the direct addition from the vapor. As an example of our model applications, the growth rate of the cap shaped droplet on the insoluble spherical particle is derived. Our evaluation shows that the growth rate of droplet in heterogeneous condensation is larger than that in homogeneous condensation. These results indicate that an explicit kinetic model is benefit to the study of heterogeneous condensation on an insoluble spherical particle.

Heterogeneous condensation on insoluble spherical particles: Modeling and parametric study

A full heterogeneous condensation model is developed to describe the water vapor condensation on an insoluble spherical particle. The new model divides the whole process of the heterogeneous condensation into three stages: nucleation, transition and growth, and considers the conservation of mass and energy of system. The model is incorporated with the population balance equation and results in a numerical method, and validated by comparison with the experimental data. In addition, two new criteria are proposed to evaluate the ability of heterogeneous condensation. The effects of particle properties and initial conditions on the whole process of heterogeneous condensation are then evaluated. It is found that the relations of the condensation ability with the wetting degree, the particle size or the initial saturation are all different from the monotonous tendency as found in the classical heterogeneous condensation theory. The parametric study suggests that a stronger ability of heterogeneous condensation can be achieved with a medium value of the wetting degree, the particle size, the initial saturation or the initial temperature.

Preparation and characterization of polysilsesquioxane particles containing UV-absorbing groups

Organotrialkoxysilanes (OTAS) containing bulky UV chromophores were polymerized under basic conditions to prepare insoluble spherical polysilsesquioxane (PSQ) particles potentially useful as UV blocking ingredients in sunscreens. The OTAS used in this study were 3-aminopropyltrimethoxysilyl-p-methoxycinnamamide (APTMSMCA), 3-aminopropyltriethoxysilyl-p-ethoxycinnamamide (APTESMCA), 3-aminopropyltrimethoxysilyl-p-N,N′-dimethylaminobezamide (APTMSDMABA), and 3-aminopropyltriethoxysilyl-p-N,N′-dimethylaminobenzamide (APTESDMABA). Mixtures of insoluble spherical particles, soluble solids, and insoluble monolithic solids were produced in various yields depending on the reaction conditions and the nature of the chromophore. The molar extinction coefficients of PSQ particles were 1/2 to 1/4 of those of corresponding unreacted chromophores and OTAS. The λ max and extinction coefficients of the PSQ particles varied according to their sizes. In vitro sun protection factor (SPF) values of petrolatum containing 10 wt% of the particles were between 10 and 21. The photostability of polyAPTMSMCA and polyAPTMSDMABA particles were significantly poorer than those of APTMSMCA and APTMSDMABA. Copolymerization of APTMSDMABA and methyltrimethoxysilane (MTMS) significantly improved the photostability. The particles dispersed in water and silicon oil showed photomechanical effects under UV light that were most likely caused by heat released during the relaxation process.

Morphology of a solidifying interface near a spherical particle: disjoining pressure effects.

Numerical simulations were conducted to determine the morphology of a solid-liquid interface near an insoluble spherical particle. The model accounts for the undercoolings due to the front's curvature and to the nonretarded van der Waals interactions. Our numerical results show that, in the near-contact region, the interface profile develops a sharp peak whose curvature has a logarithmic singularity. This is in agreement with the asymptotic analysis of a previously published equation for the interface profile.

Asymptotic analysis of particle engulfmemt.

An asymptotic analysis is conducted on the interaction between an insoluble spherical particle and an advancing solid-liquid interface when the particle is in the near-contact region (gap thickness is much smaller than the particle's radius). The analysis considers only thermal effects in a pure substance. The interface equilibrium temperature includes the undercooling effects due to the front curvature and to the long-range intermolecular forces in the thin melt film behind the particle. An expression for the crystal-particle gap thickness is derived and used to calculate the threshold value for the front velocity V(T) which separates pushing from engulfment.

Preparation of Spherical and Porous Chitosan Particles by Suspension Evaporation with O/W/O Multiple Emulsions

Porous spherical particles of chitosan were prepared by conventional suspension evaporation with modification. Aqueous chitosan solution was dispersed in decahydronaphthalene as the suspension medium with a nonionic surfactant as the emulsifier. O/w/o multiple emulsions consisting of aqueous chitosan particles containing decahydronaphthalene and dispersed in decahydronaphthalene were obtained. Chitosan precipitated as insoluble spherical particles by the gradual removal of water with heating. Particle porosity was related to microemulsions formation, the cloud point of the emulsifier and chemical structure of the acid used.

The influence of insoluble spherical particles on the stability of a planar solidifying interface

The doping of a binary substance with a small volume fraction of second phase inclusions is used in the solidification processing of metal matrix composites to improve the material properties of the final cast. In this paper, we investigate the morphological stability of a planar solidifying front that is grown from a melt containing a small volume fraction of insoluble particles. For ( φ/ k)≪1, we demonstrate that the presence of the particles modifies the solutal distribution coefficient as follows: k eff =k+( 3 2 ) (k−1)φ where φ≪1 is the volume fraction of particles and k is the segregation coefficient in the absence of particles. The concentration far away from the interface, c ∞, is chosen as the control parameter. A linear stability analysis of the planar interface reveals that the presence of the particles has a destabilizing influence. The threshold parameters for the onset of the Mullins–Sekerka instability are also altered. The dependence of the critical values of the concentration and corresponding wavenumber is calculated for a Pb–Sn alloy. For φ⩽0.01, it is found that c ∞*≈0.005695–0.01906 φ and α*≈14.69–11.81 φ.

On the Interaction of Insoluble Spherical Particles with a Solidifying Interface in the Presence of Morphological Instabilities

AbstractThe interaction of a dilute suspension of spherical particles with a moving solidifying front is investigated analytically. The front emerges during the unidirectional solidification of a dilute binary alloy. A linear stability analysis of the planar interface reveals that the presence of the particles has a destabilizing effect, i.e. the critical value of the control parameter, taken here to be the concentration faraway from the interface, for the onset of the Mullins-Sekerka instability is lowered due to the particles' presence.

Cloud Nucleation on Insoluble Particles

Abstract The theory of heterogeneous nucleation on partially-wettable insoluble spherical particles as developed by Fletcher is used to obtain relations readily applicable in the meteorologically important limit of low supersaturation ratio S. Taking 1.03 as the probable absolute maximum value of S in natural clouds, it is found that activation of a particle demands that the contact angle θ be less than 12°. Data from surface chemistry indicate that this θ-limit separates airborne particulates into a small class of active nucleating substances and a remaining broad class of nonactive cases. However, roughness effects (Wenzel's rule) may shift some from the latter to the former class, a trend possibly offset under special conditions (e.g., over industrial areas) by adsorption of non-wetting layers. A simple physical basis for understanding nucleation enhancement in terms of reduced size of the critical embryo is suggested, and a rule for predicting the approximate size-limits for activation of fully wettab...