Computational Analysis of Mixing and Scale-Up in Emulsion Polymerization Reactors

Summary: A hybrid multi-zonal/computational fluid dynamics (CFD) framework is currently being developed to aid in the scale-up of high solid content latex production and processing. Poly3D, a commercial laminar CFD code tailored to modelling the mixing of non-Newtonian fluids, has been coupled to a population balance model via a customized interface. CFD is used to generate flow fields inside a series of reactors; this information is then transferred to a multi-zone population balance model to assess the impact of non-homogenous mixing on the evolution of the latex particle size distribution (PSD) when concentrated latex suspension is altered via the addition of a coagulant. The rheological properties of high solid content latexes are sensitive to changes in the PSD, so the flow field is periodically updated if significant changes in the rheological properties of the latex are detected in any of the zones. The details of the models comprising the framework are presented and the utility of the framework is demonstrated.     

Optimal choice of threshold in Two Level Processor Sharing

We analyze the Two Level Processor Sharing (TLPS) scheduling discipline with the hyper-exponential job size distribution and with the Poisson arrival process. TLPS is a convenient model to study the benefit of the file size based differentiation in TCP/IP networks. In the case of the hyper-exponential job size distribution with two phases, we find a closed form analytic expression for the expected sojourn time and an approximation for the optimal value of the threshold that minimizes the expected sojourn time. In the case of the hyper-exponential job size distribution with more than two phases, we derive a tight upper bound for the expected sojourn time conditioned on the job size. We show that when the variance of the job size distribution increases, the gain in system performance increases and the sensitivity to the choice of the threshold near its optimal value decreases. The work was supported by France Telecom R&D Grant “Modélisation et Gestion du Trafic Réseaux Internet” no. 46129414.     

A stochastic approximation algorithm with multiplicative step size modification

An algorithm of searching a zero of an unknown function ϕ: ℝ → ℝ is considered: x _t = x _t−1 − γ _t−1 y _t , t = 1, 2, ..., where y _t = ϕ(x _t−1) + ξ _t is the value of ϕ measured at x _t−1 and ξ _t is the measurement error. The step sizes γ _t > 0 are modified in the course of the algorithm according to the rule: γ _t = min{uγ _t−1, } if y _t−1 y _t > 0, and γ _t = dγ _t−1, otherwise, where 0 < d < 1 < u, > 0. That is, at each iteration γ _t is multiplied either by u or by d, provided that the resulting value does not exceed the predetermined value . The function ϕ may have one or several zeros; the random values ξ _t are independent and identically distributed, with zero mean and finite variance. Under some additional assumptions on ϕ, ξ _t , and , the conditions on u and d guaranteeing a.s. convergence of the sequence {x _t }, as well as a.s. divergence, are determined. In particular, if P(ξ ₁ > 0) = P (ξ ₁ < 0) = 1/2 and P(ξ ₁ = x) = 0 for any x ∈ ℝ, one has convergence for ud < 1 and divergence for ud > 1. Due to the multiplicative updating rule for γ _t , the sequence {x _t } converges rapidly: like a geometric progression (if convergence takes place), but the limit value may not coincide with, but instead, approximate one of the zeros of ϕ. By adjusting the parameters u and d, one can reach arbitrarily high precision of the approximation; higher accuracy is obtained at the expense of lower convergence rate.      

Redox-photosensitized reaction of indene using photosensitive surfactant in emulsion: dependence on oil droplet size and surfactant charge

A redox-photosensitized reaction of indene 2 using a photosensitive surfactant 1a in an oil-in-water emulsion proceeded efficiently to give alcohol 3 as a major product and is strongly influenced by the oil droplet size and surfactant charge.     

Effect of the molecular weight and architecture on the size and glass transition of arborescent polyisobutylenes

This article discusses the characterization of arborescent (hyperbranched) polyisobutylenes (arb‐PIBs) by size exclusion chromatography and differential scanning calorimetry, in comparison with linear PIB standards. The radius of gyration (〈r〉^1/2 = R_z), measured from the angle dependence of light scattering of high‐molecular‐weight arb‐PIBs, was significantly larger than the hydrodynamic radius (R_h) from size exclusion chromatography/viscometry, and the R_h values were significantly smaller than R_h of linear PIBs. The glass‐transition temperature of arb‐PIBs having a branch molecular weight higher than the critical entanglement molecular weight was dependent on both the total number‐average molecular weight and BR up to BR ～ 15. A modified Fox–Flory equation is proposed to describe the effect of architecture on the thermal transition. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1770–1776, 2006     

Uranium colloid analysis by single particle inductively coupled plasma-mass spectrometry

Uranium single particle analysis has been performed by inductively coupled plasma-mass spectrometry (ICP-MS) and the performances are compared with that provided by scanning electron microsopy and single particle counting. The transient signal induced by the flash of ions due to the ionisation of an uranium colloidal particle in the plasma torch can be detected and measured for selected uranium ion masses (²³⁸U⁺, ²³⁵U⁺ or ²⁵⁴[²³⁸U¹⁶O]⁺) by the mass spectrometer. The signals recorded via time scanning are analysed as a function of particle size or fraction of the studied element or isotope in the colloid phase. The frequency of the flashes is directly proportional to the concentration of particles in the colloidal suspension. The feasibility tests were performed on uranium dioxide particles. The study also describes the experimental conditions and the choice of mass to detect uranium colloids in a single particle analysis mode.     

The effect of cationic disorder on the optical and electrochemical behavior of nanocrystalline ZnO preparedfrom peroxide precursors

The relation between particle size and the optical and electrochemical behavior of nanocrystalline ZnO was studied on materials prepared by the thermal decomposition of zinc peroxide. The formation of zinc oxide starts at 180°C and yields particles of characteristic size bigger than 10 nm. Smaller particles (r∼2–5 nm) may be prepared at reduced pressure and at a temperature of 150°C. The particle radius of synthesized nanocrystals increases proportionally to synthesis temperature. Regardless of actual particle size, synthesized ZnO samples show cationic disorder, with Zn distributed between 2b and 2a sites. The fraction of “octahedrally” coordinated Zn in 2a position decreases with increasing synthesis temperature. Zn disorder causes a narrowing of band gap, which results in the “red shift” of the absorption edge in the UV–Vis spectra of prepared samples with respect to bulk ZnO. The effect of the disorder on the band gap width is partially compensated by quantum size effects when the characteristic particle size drops below 5 nm. A decrease in particle size results in an asymmetric shift of valence and conduction band edges, which can be assigned to uneven effective masses of electrons and holes in nanocrystalline ZnO. Prepared nanocrystalline samples were (photo)electrochemically active; their activity, however, decreases with particle size.

On the assortment optimization with endogenized market size

In this paper, we consider the joint effects of product substitution and market size endogenization. Under the substitution effects, a product’s demand may be cannibalized by other substitutable products; while the market size, measured by the number of customers who are interested in the products from the same category, may be largely influenced by the product offer set. We establish the computational complexity for the assortment problem under the joint effects, and develop a fully polynomial-time approximation scheme (FPTAS).     

Effect of temperature on adaptive evolution of phytoplankton cell size

We present a simple nutrient--phytoplankton model that incorporates adaptive evolution and allometric relations. This model allows us to examine the patterns and consequences of adaptive changes in the cell size of phytoplankton under the effect of changes in water temperature. A theoretical study reveals that the ecological reproductive index can be used to characterize the evolutionary dynamics of the nutrient--phytoplankton model. Numerical analysis suggests that phytoplankton should evolve toward the small sizes typical of picophytoplankton as the water temperature increases. This study provides a framework for studying the adaptive evolution of phytoplankton cell size in water ecosystem.     

Synthesis of Polyacrylic/Silica Nanocomposite Latexes using Static Mixer

Summary: Static mixers (Sulzer Chemtech; SMX) were used to prepare silica/ MMA-co-BA miniemulsions that were polymerized to produce nanocomposite latexes. Acceptable conditions for the formulation of polymerizable nanodroplets were found and subsequently used to produce silica/poly(MMA-co-BA) nanocomposites. The droplet size distribution of the resulting miniemulsions was narrow enough that it could be successfully polymerized. It was found that the droplet size depends on the silica content and increases with increasing the silica concentration. It was also shown that there is a relationship between the droplet size and the viscosity of the dispersed phase. The majority of droplets were nucleated upon polymerization when less than 15% silica was used. However, when the silica content exceeded 15%, the ratio of the number of particles in the final latex to the number of droplets (Np/Nd) increased to value much higher than 1 indicating the occurrence of homogeneous nucleation.