Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations. (C) 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:504-520, 2001.

(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

Diffusion modeling of percutaneous absorption kinetics: 3. Variable diffusion and partition coefficients, consequences for stratum corneum depth profiles and desorption kinetics

Stratum corneum (SC) desorption experiments have yielded higher calculated steady-state fluxes than those obtained by epidermal penetration studies. A possible explanation of this result is a variable diffusion or partition coefficient across the SC. We therefore developed the diffusion model for percutaneous penetration and desorption to study the effects of either a variable diffusion coefficient or variable partition coefficient in the SC over the diffusion path length. Steady-state flux, lag time, and mean desorption time were obtained from Laplace domain solutions. Numerical inversion of the Laplace domain solutions was used for simulations of solute concentration-distance and amount penetrated (desorbed)-time profiles. Diffusion and partition coefficients heterogeneity were examined using six different models. The effect of heterogeneity on predicted flux from desorption studies was compared with that obtained in permeation studies. Partition coefficient heterogeneity had a more profound effect on predicted fluxes than diffusion coefficient heterogeneity. Concentration-distance profiles show even larger dependence on heterogeneity, which is consistent with experimental tape-stripping data reported for clobetasol propionate and other solutes. The clobetasol propionate tape-stripping data were most consistent with the partition coefficient decreasing exponentially for half the SC and then becoming a constant for the remaining SC. (C) 2004 Wiley-Liss, Inc.

Methyl and ethyl chloride synthesis in microreactors

Methyl chloride is an important chemical intermediate with a variety of applications. It is produced today in large units and shipped to the endusers. Most of the derived products are harmless, as silicones, butyl rubber and methyl cellulose. However, methyl chloride is highly toxic and flammable. On-site production in the required quantities is desirable to reduce the risks involved in transportation and storage. Ethyl chloride is a smaller-scale chemical intermediate that is mainly used in the production of cellulose derivatives. Thus, the combination of onsite production of methyl and ethyl chloride is attractive for the cellulose processing industry, e.g. current and future biorefineries. Both alkyl chlorides can be produced by hydrochlorination of the corresponding alcohol, ethanol or methanol. Microreactors are attractive for the on-site production as the reactions are very fast and involve toxic chemicals. In microreactors, the diffusion limitations can be suppressed and the process safety can be improved. The modular setup of microreactors is flexible to adjust the production capacity as needed. Although methyl and ethyl chloride are important chemical intermediates, the literature available on potential catalysts and reaction kinetics is limited. Thus the thesis includes an extensive catalyst screening and characterization, along with kinetic studies and engineering the hydrochlorination process in microreactors. A range of zeolite and alumina based catalysts, neat and impregnated with ZnCl2, were screened for the methanol hydrochlorination. The influence of zinc loading, support, zinc precursor and pH was investigated. The catalysts were characterized with FTIR, TEM, XPS, nitrogen physisorption, XRD and EDX to identify the relationship between the catalyst characteristics and the activity and selectivity in the methyl chloride synthesis. The acidic properties of the catalyst were strongly influenced upon the ZnCl2 modification. In both cases, alumina and zeolite supports, zinc reacted to a certain amount with specific surface sites, which resulted in a decrease of strong and medium Brønsted and Lewis acid sites and the formation of zinc-based weak Lewis acid sites. The latter are highly active and selective in methanol hydrochlorination. Along with the molecular zinc sites, bulk zinc species are present on the support material. Zinc modified zeolite catalysts exhibited the highest activity also at low temperatures (ca 200 °C), however, showing deactivation with time-onstream. Zn/H-ZSM-5 zeolite catalysts had a higher stability than ZnCl2 modified H-Beta and they could be regenerated by burning the coke in air at 400 °C. Neat alumina and zinc modified alumina catalysts were active and selective at 300 °C and higher temperatures. However, zeolite catalysts can be suitable for methyl chloride synthesis at lower temperatures, i.e. 200 °C. Neat γ-alumina was found to be the most stable catalyst when coated in a microreactor channel and it was thus used as the catalyst for systematic kinetic studies in the microreactor. A binder-free and reproducible catalyst coating technique was developed. The uniformity, thickness and stability of the coatings were extensively characterized by SEM, confocal microscopy and EDX analysis. A stable coating could be obtained by thermally pretreating the microreactor platelets and ball milling the alumina to obtain a small particle size. Slurry aging and slow drying improved the coating uniformity. Methyl chloride synthesis from methanol and hydrochloric acid was performed in an alumina-coated microreactor. Conversions from 4% to 83% were achieved in the investigated temperature range of 280-340 °C. This demonstrated that the reaction is fast enough to be successfully performed in a microreactor system. The performance of the microreactor was compared with a tubular fixed bed reactor. The results obtained with both reactors were comparable, but the microreactor allows a rapid catalytic screening with low consumption of chemicals. As a complete conversion of methanol could not be reached in a single microreactor, a second microreactor was coupled in series. A maximum conversion of 97.6 % and a selectivity of 98.8 % were reached at 340°C, which is close to the calculated values at a thermodynamic equilibrium. A kinetic model based on kinetic experiments and thermodynamic calculations was developed. The model was based on a Langmuir Hinshelwood-type mechanism and a plug flow model for the microreactor. The influence of the reactant adsorption on the catalyst surface was investigated by performing transient experiments and comparing different kinetic models. The obtained activation energy for methyl chloride was ca. two fold higher than the previously published, indicating diffusion limitations in the previous studies. A detailed modeling of the diffusion in the porous catalyst layer revealed that severe diffusion limitations occur starting from catalyst coating thicknesses of 50 μm. At a catalyst coating thickness of ca 15 μm as in the microreactor, the conditions of intrinsic kinetics prevail. Ethanol hydrochlorination was performed successfully in the microreactor system. The reaction temperature was 240-340°C. An almost complete conversion of ethanol was achieved at 340°C. The product distribution was broader than for methanol hydrochlorination. Ethylene, diethyl ether and acetaldehyde were detected as by-products, ethylene being the most dominant by-product. A kinetic model including a thorough thermodynamic analysis was developed and the influence of adsorbed HCl on the reaction rate of ethanol dehydration reactions was demonstrated. The separation of methyl chloride using condensers was investigated. The proposed microreactor-condenser concept enables the production of methyl chloride with a high purity of 99%.

Influence of Edible Coating on the Drying and Quality of Papaya (Carica papaya)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Genesis of metasomatic sapphirine-corundum-spinel-bearing granulites in Sri Lanka

The goal of the present study is to understand the mechanism of mass transfer, the composition and the role of fluids during crustal metasomatism in high-temperature metamorphic terranes. A well constrained case study, a locality at Rupaha, Sri Lanka was selected. It is located in the Highland Complex of Sri Lanka, which represents a small, but important fragment of the super-continent Gondwana. Excellent exposures of ultramafic rocks, which are embedded in granulites, were found at 10 localities. These provide a unique background for understanding the metasomatic processes. The boundary between the ultramafic and the granulite rocks are lined with metasomatic reaction zones up to 50cm in width. Progressing from the ultramafics to the granulite host rock, three distinct zones with the following mineral assemblages can be distinguished: (1). phlogopite + spinel + sapphirine, (2). spinel + sapphirine and (3). corundum + biotite + plagioclase. In order to assess the P-T-t path, the peak metamorphism and the exhumation history were constrained using different thermobarometers, as well as a diffusion model of garnet zoning. A maximum temperature of 875 ± 20oC (Opx-Cpx thermometer) and at the peak pressure of 9.0 ± 0.1 kbar (Grt-Cpx-Pl-Qtz) was calculated for the silicic granulite. The ultramafic rocks recorded a peak temperature of 840 ± 70oC (Opx-Cpx thermometer) at 9 kbar. Coexisting spinel and sapphirine from the reaction zone yield a temperature of 820 ± 40oC. This is in agreement with the peak-temperatures recorded in the adjacent granulites and ultramafics rocks. The structural concordance of the ultramafic rocks with the siliceous granulite host rock further support the suggestion, that all units have experienced the same peak metamorphism. Diffusion modeling of retrograde zoning in garnets from mafic granulites suggests a three-step cooling history. A maximum cooling rate of 1oC/Ma is estimated during the initial stage of cooling, followed by a cooling rate of ~30oC/Ma. The outermost rims of garnet indicate a slightly slower cooling rate at about 10-15oC/Ma. The sequences of mineral zones, containing a variety of Al-rich, silica undersaturated minerals in the reaction zones separating the ultramafic rocks from the silica-rich rocks can be explained by a diffusion model. This involves the diffusion of Mg from ultramafic rocks across the layers, and K and Si diffuse in opposite direction. Chemical potential of Mg and Si generated continuous monotonic gradient, allowing steady state diffusional transport across the profile. The strong enrichment in Al, and the considerable loss of Si, during the formation of reaction bands can be inferred from isocon diagrams. Some Al was probably added to the reaction zones, while Si was lost. This is most likely due to fluids percolating parallel to the zones at the boundary of the rock units. This study has shown that not only pressure and temperature conditions but most importantly PH2O and the concentration of the chlorine and fluorine in aqueous fluids also control the mass transport in different geological environments.

Geochemistry of ODP Hole 183-1137A basalts

The Kerguelen Plateau and Broken Ridge in the southern Indian Ocean together represent one of the most voluminous large igneous provinces (LIPs) ever emplaced on Earth. A scientific objective of Ocean Drilling Program (ODP) Leg 183 was to constrain the post-melting magma evolution of Kerguelen Plateau magmas. In an effort to better understand this evolution, isotopic and trace element analysis of individual plagioclase crystals hosted within two Kerguelen Plateau basalts recovered from Elan Bank were undertaken. Previous whole-rock studies established that the two host basalts investigated in this study are samples of crustally contaminated (lower group) and relatively uncontaminated (upper group) basalt. Plagioclase phenocrysts from the uncontaminated basalt are dominantly normal zoned and exhibit a 87Sr/86SrI range of 0.704845-0.704985, which overlaps uncontaminated group whole-rock values previously reported. Plagioclase crystals from the contaminated basalt are dominantly reverse zoned and exhibit a 87Sr/86SrI range of 0.705510-0.705735, which all lie within contaminated group whole-rock values previously reported. There are no systematic within crystal core to rim variations in 87Sr/86SrI from either group, with the exception that contaminated group crystal rims have overall less radiogenic 87Sr/86SrI than other zones. These observations indicate that crustal assimilation occurred before the formation of Unit 10 plagioclase phenocrysts, which is supported by parent magma trace element abundance data inverted using carefully calculated partition coefficients. Trace element diffusion modeling indicates that the upper group basalt (Unit 4) experienced a more vigorous eruptive flux than the lower group basalt (Unit 10). We suggest that plagioclase phenocrysts in both the upper and lower group basalts originated from the shallowest section of what was likely a complex magma chamber system. We contend that the magmatic system contained regions of extensive plagioclase-dominated crystal mush. Crustal assimilation was not a significant ongoing process in this portion of the Elan Bank magmatic system. Both basalts exhibit compelling evidence for remobilization and partial resorption of crystalline debris (e.g., reverse zoned crystals, glomerocrysts). We suggest Unit 4 and 10 magmas ascended different sections of the Elan Bank magma system, where the Unit 10 magmas ascended a section of the magma system that penetrated a stranded fragment of continental crust.

Life Cycle of Deccan Trap Magma Chambers: A Crystal Scale Elemental and Strontium Isotopic Investigation

The Deccan Trap basalts are the remnants of a massive series of lava flows that erupted at the K/T boundary and covered 1-2 million km2 of west-central India. This eruptive event is of global interest because of its possible link to the major mass extinction event, and there is much debate about the duration of this massive volcanic event. In contrast to isotopic or paleomagnetic dating methods, I explore an alternative approach to determine the lifecycle of the magma chambers that supplied the lavas, and extend the concept to obtain a tighter constraint on Deccan’s duration. My method relies on extracting time information from elemental and isotopic diffusion across zone boundary in an individual crystal. I determined elemental and Sr-isotopic variations across abnormally large (2-5 cm) plagioclase crystals from the Thalghat and Kashele “Giant Plagioclase Basalts” from the lowermost Jawhar and Igatpuri Formations respectively in the thickest Western Ghats section near Mumbai. I also obtained bulk rock major, trace and rare earth element chemistry of each lava flow from the two formations. Thalghat flows contain only 12% zoned crystals, with 87Sr/86Sr ratios of 0.7096 in the core and 0.7106 in the rim, separated by a sharp boundary. In contrast, all Kashele crystals have a wider range of 87Sr/86Sr values, with multiple zones. Geochemical modeling of the data suggests that the two types of crystals grew in distinct magmatic environments. Modeling intracrystalline diffusive equilibration between the core and rim of Thalghat crystals led me to obtain a crystal growth rate of 2.03x10-10 cm/s and a residence time of 780 years for the crystals in the magma chamber(s). Employing some assumptions based on field and geochronologic evidence, I extrapolated this residence time to the entire Western Ghats and obtained an estimate of 25,000 – 35,000 years for the duration of Western Ghats volcanism. This gave an eruptive rate of 30 – 40 km3/yr, which is much higher than any presently erupting volcano. This result will remain speculative until a similarly detailed analytical-modeling study is performed for the rest of the Western Ghats formations.

Modeling the Diffusion of Energy Performance Contracting

The Portuguese Energy Policy considers the development of a commercially viable and competitive market for energy performance contracting (EPC) as a main mechanism to achieve the objectives of energy efficiency improvement. This paper proposes a study to investigate how to achieve widespread adoption of energy performance contracting by means of system dynamics modelling and simulation. To explore and gather insights on this question, a system dynamics model representing the system of the Portuguese EPC market at industry level will be created. The simulation of that model will provide a helpful basis for analysing and explaining the development of key variables, and accelerating learning on the managerial, organizational and political adaptation processes that foster the diffusion of EPC adoption. The first phase of this research project aims at identifying and analysing the key factors and critical cause-effect relations that drive the adoption of EPC. With this purpose, a qualitative content analysis on relevant documents was performed and a set of interviews was conducted. That data was analysed to capture the critical variables and its interrelation to formulate a preliminary representation of the system structure as stock and flow diagrams.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.

Modeling Information Diffusion in University Libraries: Assessing Peer Interaction Patterns as a Complex Dynamic System

This presentation was offered as part of the CUNY Library Assessment Conference, Reinventing Libraries: Reinventing Assessment, held at the City University of New York in June 2014.