Experimental quantification and modelling of attrition of infant formulae during pneumatic conveying

Infant formula is often produced as an agglomerated powder using a spray drying process. Pneumatic conveying is commonly used for transporting this product within a manufacturing plant. The transient mechanical loads imposed by this process cause some of the agglomerates to disintegrate, which has implications for key quality characteristics of the formula including bulk density and wettability. This thesis used both experimental and modelling approaches to investigate this breakage during conveying. One set of conveying trials had the objective of establishing relationships between the geometry and operating conditions of the conveying system and the resulting changes in bulk properties of the infant formula upon conveying. A modular stainless steel pneumatic conveying rig was constructed for these trials. The mode of conveying and air velocity had a statistically-significant effect on bulk density at a 95% level, while mode of conveying was the only factor which significantly influenced D[4,3] or wettability. A separate set of conveying experiments investigated the effect of infant formula composition, rather than the pneumatic conveying parameters, and also assessed the relationships between the mechanical responses of individual agglomerates of four infant formulae and their compositions. The bulk densities before conveying, and the forces and strains at failure of individual agglomerates, were related to the protein content. The force at failure and stiffness of individual agglomerates were strongly correlated, and generally increased with increasing protein to fat ratio while the strain at failure decreased. Two models of breakage were developed at different scales; the first was a detailed discrete element model of a single agglomerate. This was calibrated using a novel approach based on Taguchi methods which was shown to have considerable advantages over basic parameter studies which are widely used. The data obtained using this model compared well to experimental results for quasi-static uniaxial compression of individual agglomerates. The model also gave adequate results for dynamic loading simulations. A probabilistic model of pneumatic conveying was also developed; this was suitable for predicting breakage in large populations of agglomerates and was highly versatile: parts of the model could easily be substituted by the researcher according to their specific requirements.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Molecular composition of biogenic secondary organic aerosols using ultrahigh resolution mass spectrometry: comparing laboratory and field studies

Numerous laboratory experiments have been performed in an attempt to mimic atmospheric secondary organic aerosol (SOA) formation. However, it is still unclear how close the aerosol particles generated in laboratory experiments resemble atmospheric SOA with respect to their detailed chemical composition. In this study, we generated SOA in a simulation chamber from the ozonolysis of α-pinene and a biogenic volatile organic compound (BVOC) mixture containing α- and β-pinene, Δ3-carene, and isoprene. The detailed molecular composition of laboratory-generated SOA was compared with that of background ambient aerosol collected at a boreal forest site (Hyytiälä, Finland) and an urban location (Cork, Ireland) using direct infusion nanoelectrospray ultrahigh resolution mass spectrometry. Kendrick Mass Defect and Van Krevelen approaches were used to identify and compare compound classes and distributions of the detected species. The laboratory-generated SOA contained a distinguishable group of dimers that was not observed in the ambient samples. The presence of dimers was found to be less pronounced in the SOA from the VOC mixtures when compared to the one component precursor system. The elemental composition of the compounds identified in the monomeric region from the ozonolysis of both α-pinene and VOC mixtures represented the ambient organic composition of particles collected at the boreal forest site reasonably well, with about 70% of common molecular formulae. In contrast, large differences were found between the laboratory-generated BVOC samples and the ambient urban sample. To our knowledge this is the first direct comparison of molecular composition of laboratory-generated SOA from BVOC mixtures and ambient samples.

Molecular composition of organic aerosols in central Amazonia: an ultra-high-resolution mass spectrometry study

The Amazon Basin plays key role in atmospheric chemistry, biodiversity and climate change. In this study we applied nanoelectrospray (nanoESI) ultra-high-resolution mass spectrometry (UHRMS) for the analysis of the organic fraction of PM2.5 aerosol samples collected during dry and wet seasons at a site in central Amazonia receiving background air masses, biomass burning and urban pollution. Comprehensive mass spectral data evaluation methods (e.g. Kendrick mass defect, Van Krevelen diagrams, carbon oxidation state and aromaticity equivalent) were used to identify compound classes and mass distributions of the detected species. Nitrogen- and/or sulfur-containing organic species contributed up to 60 % of the total identified number of formulae. A large number of molecular formulae in organic aerosol (OA) were attributed to later-generation nitrogen- and sulfur-containing oxidation products, suggesting that OA composition is affected by biomass burning and other, potentially anthropogenic, sources. Isoprene-derived organosulfate (IEPOX-OS) was found to be the most dominant ion in most of the analysed samples and strongly followed the concentration trends of the gas-phase anthropogenic tracers confirming its mixed anthropogenic–biogenic origin. The presence of oxidised aromatic and nitro-aromatic compounds in the samples suggested a strong influence from biomass burning especially during the dry period. Aerosol samples from the dry period and under enhanced biomass burning conditions contained a large number of molecules with high carbon oxidation state and an increased number of aromatic compounds compared to that from the wet period. The results of this work demonstrate that the studied site is influenced not only by biogenic emissions from the forest but also by biomass burning and potentially other anthropogenic emissions from the neighbouring urban environments.