A dimensionless study of the evaporation and drying stages in spray pyrolysis

An original dimensionless study of the pure evaporation and precipitation stages of a spray pyrolysis process has been performed. An estimation of the evaporation time is proposed and the influence of the main processing parameters has been investigated. For operating conditions corresponding to industrial requirements, the main limiting step of the evaporation stage is thermal transfer from the column walls to the gas, not mass or thermal transfer at the droplet surface. Therefore, gas and liquid temperatures remain equal and constitutive equations can be greatly simplified. Moreover, in these conditions, neither solute concentration nor temperature gradients exist inside micronic droplets. Some data from the literature have been modelled and show the large range of validity of the equations and explanations proposed. Finally, with the assumptions made here, the dimensionless study of the precipitation stage shows that the presence of a crust can increase the drying time four-fold. However, a filled particle can still be formed

Limit distributions for large P\'{o}lya urns

We consider a two-color P\'{o}lya urn in the case when a fixed number $S$ of balls is added at each step. Assume it is a large urn that is, the second eigenvalue $m$ of the replacement matrix satisfies $1/2<m/S\leq1$. After $n$ drawings, the composition vector has asymptotically a first deterministic term of order $n$ and a second random term of order $n^{m/S}$. The object of interest is the limit distribution of this random term. The method consists in embedding the discrete-time urn in continuous time, getting a two-type branching process. The dislocation equations associated with this process lead to a system of two differential equations satisfied by the Fourier transforms of the limit distributions. The resolution is carried out and it turns out that the Fourier transforms are explicitly related to Abelian integrals over the Fermat curve of degree $m$. The limit laws appear to constitute a new family of probability densities supported by the whole real line.Comment: Published in at http://dx.doi.org/10.1214/10-AAP696 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multifluid eulerian modelling of a silicon fluidized bed chemical vapor deposition process : analysis of various kinetic models

Using the multifluid Eulerian code MFIX, the silicon Fluidized Bed Chemical Vapor Deposition process from silane (SiH4) has been modelled under transient conditions. In order to constitute an experimental database, a preliminary experimental study has been performed using a bed of Geldart’s group B particles. After a detailed analysis and comparison of the kinetic models available in the literature, four of them have been implemented in the MFIX code and two hydrodynamic models have been tested. 3-D simulations have shown that a strong interaction exists between the bed hydrodynamics, heat and reactive mass transfers and that Si deposition from silane mainly occurs in the dense zones of the bed whereas the unsaturated species silylene (SiH2) forms in bubbles and slugs and leads to Si deposition mainly at their periphery; its contribution to deposition can be locally as high as that of SiH4. The average contribution of SiH2 to deposition increases with the inlet concentration of silane and can reach 30%. The kinetic models derived from the law of Furusawa et al. and from the data compiled by Buss et al. and the hydrodynamic model based on the true granular energy equation and the Princeton solid phase stress model have revealed to be the most appropriate ones for the conditions tested

Smoothing equations for large P\'olya urns

Consider a balanced non triangular two-color P\'olya-Eggenberger urn process, assumed to be large which means that the ratio sigma of the replacement matrix eigenvalues satisfies 1/2<sigma <1. The composition vector of both discrete time and continuous time models admits a drift which is carried by the principal direction of the replacement matrix. In the second principal direction, this random vector admits also an almost sure asymptotics and a real-valued limit random variable arises, named WDT in discrete time and WCT in continous time. The paper deals with the distributions of both W. Appearing as martingale limits, known to be nonnormal, these laws remain up to now rather mysterious. Exploiting the underlying tree structure of the urn process, we show that WDT and WCT are the unique solutions of two distributional systems in some suitable spaces of integrable probability measures. These systems are natural extensions of distributional equations that already appeared in famous algorithmical problems like Quicksort analysis. Existence and unicity of the solutions of the systems are obtained by means of contracting smoothing transforms. Via the equation systems, we find upperbounds for the moments of WDT and WCT and we show that the laws of WDT and WCT are moment-determined. We also prove that WDT is supported by the whole real line and admits a continuous density (WCT was already known to have a density, infinitely differentiable on R\{0} and not bounded at the origin)

Support and density of the limit mm-ary search trees distribution

The space requirements of an $m$-ary search tree satisfies a well-known phase transition: when $m\leq 26$, the second order asymptotics is Gaussian. When $m\geq 27$, it is not Gaussian any longer and a limit $W$ of a complex-valued martingale arises. We show that the distribution of $W$ has a square integrable density on the complex plane, that its support is the whole complex plane, and that it has finite exponential moments. The proofs are based on the study of the distributional equation W\egalLoi\sum_{k=1}^mV_k^{\lambda}W_k, where $V_1, ..., V_m$ are the spacings of $(m-1)$ independent random variables uniformly distributed on $[0,1]$, $W_1, ..., W_m$ are independent copies of W which are also independent of $(V_1, ..., V_m)$ and $\lambda$ is a complex number

Digital search trees and chaos game representation

In this paper, we consider a possible representation of a DNA sequence in a quaternary tree, in which on can visualize repetitions of subwords. The CGR-tree turns a sequence of letters into a digital search tree (DST), obtained from the suffixes of the reversed sequence. Several results are known concerning the height and the insertion depth for DST built from i.i.d. successive sequences. Here, the successive inserted wors are strongly dependent. We give the asymptotic behaviour of the insertion depth and of the length of branches for the CGR-tree obtained from the suffixes of reversed i.i.d. or Markovian sequence. This behaviour turns out to be at first order the same one as in the case of independent words. As a by-product, asymptotic results on the length of longest runs in a Markovian sequence are obtained

Variable length Markov chains and dynamical sources

Infinite random sequences of letters can be viewed as stochastic chains or as strings produced by a source, in the sense of information theory. The relationship between Variable Length Markov Chains (VLMC) and probabilistic dynamical sources is studied. We establish a probabilistic frame for context trees and VLMC and we prove that any VLMC is a dynamical source for which we explicitly build the mapping. On two examples, the ``comb'' and the ``bamboo blossom'', we find a necessary and sufficient condition for the existence and the unicity of a stationary probability measure for the VLMC. These two examples are detailed in order to provide the associated Dirichlet series as well as the generating functions of word occurrences.Comment: 45 pages, 15 figure

Crystallization of microscopic Y2O3 powders by different techniques of fluidization at high temperature

Ahigh temperature fluidized bed reactor (HTFBR)working at 900 to 1200 ◦Chas been developed to crystallize microscopic yttria (Y2O3) powders synthesized by spray pyrolysis. Such crystallization is classically performed in crucible or in moving belt furnaces. In order to demonstrate the advantages of the fluidized bed process over the conventional static mode treatments, a comparative study of the main characteristics of particles after heat treatment in a crucible and in the HTFBR has been performed. The high interparticle forces existing in such Geldart group C powders made it necessary to activate their fluidization. Following previous results, two activated fluidization processes were studied: addition of coarse powders to fine particles and vibrated fluidization. The hydrodynamic behavior of these fluidized beds was analyzed through pressure drop measurements. Convenient fluidization conditions were obtained for the two activated fluidization processes, leading to isothermal beds. The size distribution, the crystallinity and the outer morphology of particles before and after thermal treatments were analyzed and compared for the three processes tested. Some pre-sintering phenomena occurred at 1200 ◦C, which were clearly more intense in crucible than in activated fluidization. The crystallinity of the samples treated was equivalent for the three methods of thermal treatment. The interest of fluidization processes to post-treat microscopic particles is thus fully demonstrated

Comparability of Health Care Responsiveness in Europe using anchoring vignettes from SHARE

The aim of this paper is to measure and to correct for the potential incomparability of responses to the SHARE survey on health care responsiveness. A parametric approach based on the use of anchoring vignettes is applied to cross-sectional data (2006-07) in ten European countries. More than 6,000 respondents aged 50 years old and over were asked to assess the quality of health care responsiveness in three domains: waiting time for medical treatment, quality of the conditions in visited health facilities, and communication and involvement in decisions about the treatment. Chopit models estimates suggest that reporting heterogenity is influenced by both individual (socio-economic, health) and national characteristics. Although correction for differential item functioning does not considerably modify countries ranking after controlling for the usual covariates, about two thirds of the respondents' self-assessments have been re-scaled in each domain. Our results suggest that reporting heterogenity tends to overestimate health care responsiveness for "time to wait for treatment", whereas it seems to underestimate people's self-assessment in the two other domains.Anchoring Vignettes, Cross-Country Comparison, Chopit Model

Y2O3:Eu micronic particles synthesised by spray pyrolysis: Global modelling and optimisation of the evaporation stage

There are a number of some major advantages to be gained in processing micronic europium-doped yttrium oxide Y2O3 particles for phosphor applications using spray pyrolysis. In order to maximise production rates, it is tempting to use relatively dense sprays, but then coalescence occurs increasing final particle diameters, which must be prevented. Moreover, the influence of the operating conditions on the process behaviour is poorly understood. A complete one-dimensional model of the evaporation stage of micronic water/Y(NO3)3 droplets considering only the evaporation process and then both evaporation and gravity-induced coalescence phenomena has been established. Calculations of pure evaporation have shown that the amounts of evaporated water and droplet compositions depend only on the local temperature and not on the thermal history of the spray. Coupled calculations have shown that, in comparison with evaporation, coalescence plays a minor role on droplet diameter, but non-negligible as the increase of the final mean droplet diameter due to coalescence reaches up to 10% at low flow rates in the operating conditions tested. Injecting a preheated air flow directly into the nebuliser is a promising method to minimise coalescence effects: optimal operating conditions for which coalescence is completely insignificant were obtained by simulation