Population balances for particulate processes—a volume approach

Population balance models have been used in chemical engineering since the 1960s and have evolved to become the most important tools for design and control of particulate processes. In this paper we show that the intrinsic particle parameter that determines changes in the process and should thus be included in the population balance is the particle volume. The basic population that is modeled should be the mass distribution, or the volume distribution if the density is constant. The population balance thus describes the change of the volume distribution of volume with time. Furthermore, we suggest that the “birth” and “death” terms that are often used to describe discrete events in particulate processes can almost always be replaced by a rate of change term.To design and control existing and future processes, a multi-dimensional population balance model is required. We propose a volume-based model in which the particle properties that are modeled are the volumes of solid, liquid, and air, respectively. In the most general case the model will consist of a properties vector and a distribution tensor. Depending on the complexity of the process, one or more of the properties may be omitted from the model. This is shown in three examples of increasing complexity: comminution, sintering, and granulation.     

Development of high-performance liquid chromatography criteria for determination of grades of commercial olive oils. Part I. The normal ranges for the triacylglycerols

Criteria for authentic olive oils were developed from isocratic high-performance liquid chromatography analyses of 99 olive oils from the major Mediterranean producers in the 1983–1986 crop years. Authentic olive oils include extra virgin, virgin and pure or refined oils, but exclude all reesterified and adulterated oils. The extra virgin through pure grades will have a combined area for the LOO (C_18:2C_18:1C_18:1), LOP (C_18:2C_18:1C_16:0), OOO (C_18:1C_18:1C_18:1), POO (C_16:0C_18:1C_18:1), POP (C_16:0C_18:1C_18:1), and SOO (C_18:0C_18:1C_18:1) peaks between 82.0 and 92.6% of the total area (L, linoleic; O, oleic; P, palmitic; S, stearic). Authentic oils will have ratios of LOO/LOP and OOO/POO that coincide with a line defined by OOO/POO=0.7844(LOO/LOP)+0.0968; correlation coefficient is 0.885. Authentic oils will not have a trilinolein (LLL) peak over 0.5% in area. Neither triolein (OOO) nor any other single peak suffices to characterize an olive oil sample as one of the authentic grades.     

Synthetic hydrogels: 3. Hydroxyalkyl acrylate and methacrylate copolymers: surface and mechanical properties

The surface and mechanical properties of copolymers of hydroxyalkyl acrylates and methacrylates have been examined by a variety of techniques. This work is complementary to earlier parts of this series which describe the effect of copolymer structure on water binding properties. Water structure has been demonstrated to exert a profound effect upon mechanical properties whether measured in compression or in tension. In particular, water that is characterized by differential scanning calorimetry as ‘freezing’ water is observed to have a marked plasticizing effect upon the gel, whereas ‘non-freezing’ water has little such effect. Similarly, the ‘freezing’ water produces a more marked effect on thermally induced transitions. Two distinct transition points are observed as a result of its presence. One corresponds to the freezing point of water and the other to a glass transition temperature, whose value depends upon the proportion of ‘freezing’ or ‘plasticizing’ water in the gel. Several predictive and direct measurement techniques have been used to study the surface properties of the copolymers in both hydrated and dehydrated states. Taken together they have established a sound understanding of the way in which polar and dispersive components of surface free energy vary as a function of copolymer composition and water content. Use of protein adsorption and fibroblast cell interaction techniques demonstrate that biological phenomena respond to changes at a molecular level which current macroscopic surface energy techniques are unable to discern.     

Preparation of segmented, high molecular weight, aliphatic poly(ether-urea) copolymers in isopropanol. In-situ FTIR studies and polymer synthesis

The use of isopropanol (IPA) as the reaction solvent for the preparation of high molecular weight segmented polyether-urea copolymers based on cycloaliphatic diisocyanates was investigated. Reactivity of IPA with bis(4-isocyanatohexyl)methane (HMDI) and isophorone diisocyanate (IPDI) was studied between 0 and 40 °C using in-situ FTIR spectroscopy. HMDI, which has secondary isocyanate groups, shows a very slow reaction with a large excess of IPA at 0 and 23 °C. Analysis of the kinetic data indicates an activation energy of 51 kJ/mol for the reaction between HMDI and IPA. As expected, IPDI, which has both a primary and a secondary isocyanate (NCO) group, reacts faster with IPA compared with HMDI, which only has secondary NCO groups. However, the rate of reaction of IPDI with IPA at 0 °C is extremely slow (approximately 1% consumption of isocyanate in 60 min) thus allowing the use of IPA as the reaction solvent for polyether-urea synthesis. Preparation of high molecular weight, high-strength HMDI and IPDI based polyether-urea segmented copolymers in IPA has been demonstrated. Thermal analysis and stress-strain analyses were used to characterize the products.     

Crystallization studies of semi-crystalline polymers under oscillatory shear using the rheometrics mechanical spectrometer

A method has been developed on the Rheometrics mechanical spectrometer using the eccentric rotating disks mode to study the crystallization kinetics of different semi-crystalline polymers (polyethylene, polypropylene, poly(butylene terephthalate) and Nylon 11) under oscillatory shear. Dynamic shear moduli (storage G′ and loss G″), loss tangent (tan δ), and dynamic viscosity (η′) were simultaneously, monitored during the crystallization process. The onset and completion of crystallization were characterized by the initial rise and final levelling off of G′, while the peak time, of crystallization (t_p) is calculated from the time elapsed between the onset and peak of crystallization which is indicated by the G″ or η′ maximum. In the case of polypropylene, going from a low frequency of ?0.1 rad/s, to higher frequencies of up to 10 rad/s, there is a monotonic decrease in peak time of crystallization (t_p) together with a progressive decrease in spherulitic morphology. The observed acceleration in crystallization is due predominantly to the increase in nucleation rate and orientation of chains in melt crystalline aggregate. The progressive disappearance of the spherulitic morphology is attributed to the disruption of the spherulite superstructure at higher frequencies of shear.     

Direct Measurement of Transformation Zone Strains in Toughened Zirconia

Residual strains responsible for crack tip shielding have been measured within transformation zones surrounding cracks in Mg-PSZ. Two techniques were used for strain measurement: moiré interferometry and high-resolution image matching. Both methods provide maps of differential in-plane displacements within the specimen surface intersected by the crack, the latter method with the higher resolution. The results are compared with finite-element analysis to assess surface relaxation effects, and the measured strains are used to evaluate the crack tip shielding stress intensity factor. Calculations based on the assumption that the unconstrained transformation strain is hydrostatic dilatation yielded results that were significantly smaller than the measured toughness increases.     

Determination of Both Mesopores and Macropores in Three-Dimensional Ordered Porous Materials by Nitrogen Adsorption

Three-dimensionally ordered silica structures containing both mesopores and macropores are created using polystyrene coacervate spheres with a diameter of ca. 146 nm. The close-packed polystyrene coacervate spheres are intercalated with tetraethyl orthosilicate. The spheres are removed by calcination leaving an inverse silica replica with a spherical macropore cavity diameter of 110 nm. Due to the nature of these porous structures, pores leading into the macropore cavity are in the mesopore regime, 40 nm in diameter. The nitrogen adsorption data described in the following paper gives a pore size for both the macropore cavity and the mesopore openings leading into the cavity. The pore sizes as determined by nitrogen sorption are in good agreement with the pore sizes observed by scanning electron microscopy. Mercury intrusion porosimetry results confirm the size of the mesopore openings leading into the macropore cavity, however due to destruction of the sample upon intrusion, extrusion results can not be obtained to determine main cavity diameters. As a result, nitrogen sorption may be a viable option for determining pore sizes with these three-dimensionally ordered materials containing both mesopores and macropores.     

The stability and unfolding of an IgG binding protein based upon the B domain of protein A from Staphylococcus aureus probed by tryptophan substitution and fluorescence spectroscopy

The stability and unfolding of an immunoglobulin (Ig) G bindingprotein based upon the B domain of protein A (SpAB) from Staphylococcusaureus were studied by substituting tryptophan residues at strategiclocations within each of the three a-helical regions (al-a3)of the domain. The role of the C-terminal helix, a3, was investigatedby generating two protein constructs, one corresponding to thecomplete SpAB, the other lacking a part of ct3; the Trp substitutionswere made in both one-and two-domain versions of each of theseconstructs. The fluorescence properties of each of the single-tryptophanmutants were studied in the native state and as a function ofguanidine-HCl-mediated unfolding, and their IgG binding activitieswere determined by a competitive enzyme-linked immunosorbentassay. The free energies of folding and of binding to IgG foreach mutant were compared with those for the native domains.The effect of each substitution upon the overall structure andupon the IgG binding interface was modelled by molecular graphicsand energy minimization. These studies indicate that (i) 3 contributesto the overall stability of the domain and to the formationof the IgG binding site in l and 2, and (ii) al unfolds first,followed by 2 and 3 together.     

Diffusion of organic penetrants through low density polyethylene (LDPE) films: Effect of size and shape of the penetrant molecules

The diffusion coefficient at zero penetrant concentration D₀ of dichloromethane, chloroform, carbon tetrachloride, cyclohexane, benzene, o-xylene, m-xylene, and p-xylene, and n-hexane in LDPE were measured at 25°C, using the desorption method. The D₀ values obtained in this way are correlated with the size, shape, and chemical nature of the penetrant molecules. The temperature dependence of the diffusion coefficients of toluene and n-hexane in LDPE are also reported in the limited temperature range of 25–45°C. It indicates that, in spite of a size larger than that of toluene, n-hexane has a lower activation energy of diffusion.     

Use of the 15N natural abundance technique to quantify biological nitrogen fixation by woody perennials

Biological nitrogen fixation (BNF) associated with trees and shrubs plays a major role in the functioning of many ecosystems, from natural woodlands to plantations and agroforestry systems, but it is surprisingly difficult to quantify the amounts of N₂ fixed. Some of the problems involved in measuring N₂ fixation by woody perennials include: (a) diversity in occurrence, and large plant-to-plant variation in growth and nodulation status of N₂-fixing species, especially in natural ecosystems; (b) long-term, perennial nature of growth and the seasonal or year-to-year changes in patterns of N assimilation; and (c) logistical limitations of working with mature trees which are generally impossible to harvest in their entirety. The methodology which holds most promise to quantify the contributions of N₂ fixation to trees is the so-called `¹⁵N natural abundance' technique which exploits naturally occurring differences in ¹⁵N composition between plant-available N sources in the soil and that of atmospheric N₂. In this review we discuss probable explanations for the origin of the small differences in ¹⁵N abundance found in different N pools in both natural and man-made ecosystems and utilise previously published information and unpublished data to examine the potential advantages and limitations inherent in the application of the technique to study N₂ fixation by woody perennials. Calculation of the proportion of the plant N derived from atmospheric N₂ (%Ndfa) using the natural abundance procedure requires that both the ¹⁵N natural abundance of the N derived from BNF and that derived from the soil by the target N₂-fixing species be determined. It is then assumed that the ¹⁵N abundance of the N₂-fixing species reflects the relative contributions of the N derived from these two sources. The ¹⁵N abundance of the N derived from BNF (B) can vary with micro-symbiont, plant species/provenance and growth stage, all of which create considerable difficulties for its precise evaluation. If the%Ndfa is large and the ¹⁵N abundance of the N acquired from other sources is not several ¹⁵N units higher or lower than B, then this can be a major source of error. Further difficulties can arise in determining the ¹⁵N abundance of the N derived from soil (and plant litter, etc.) by the target plant as it is usually impossible to predict which, if any, non-N₂-fixing reference species will obtain N from the same N sources in the same proportions with the same temporal and spatial patterns as the N₂-fixing perennial. The compromise solution is to evaluate the ¹⁵N abundance of a diverse range of neighbouring non-N₂-fixing plants and to compare these values with that of the N₂-fixing species and the estimate of B. Only then can it be determined whether the contribution of BNF to the target species can be quantified with any degree of confidence. This review of the literature suggests that while the natural abundance technique appears to provide quantitative measures of BNF in tree plantation and agroforestry systems, particular difficulties may arise which can often limit its application in natural ecosystems.