Rane L. Curl

Estimating the Fraction Dose Absorbed from Suspensions of Poorly Soluble Compounds in Humans: A Mathematical Model

A microscopic mass balance approach has been developed to predict the fraction dose absorbed of suspensions of poorly soluble compounds. The mathematical model includes four fundamental di-mensionless parameters to estimate the fraction dose absorbed: initial saturation (Is), absorption number (An), dose number (Do), and dissolution number (Dn). The fraction dose absorbed (F) increases with increasing Is, An, and Dn and with decreasing Do. At higher Dn and lower Do, the fraction dose absorbed reaches the maximal F, which depends only on An. The dissolution number limit on F can appear at both lower Do and lower Dn. Likewise, at higher Do and Dn, the fraction dose absorbed reaches a Do limit. Initial saturation makes a significant difference in F at lower Do and Dn. It is shown that the extent of drug absorption is expected to be highly variable when Dn and Do are approximately one. Furthermore, by calculating these dimensionless groups for a given compound, a formulation scientist can estimate not only the extent of drug absorption but also the effect, if any, of particle size reduction on the extent of drug absorption.

Molybdenum nitride catalysts: I. Influence of the synthesis factors on structural properties

Effects of the synthesis parameters on the structural properties of molybdenum nitride catalysts, prepared by the temperature-programmed reaction of MoO3 with NH3, have been examined. Molybdenum trioxide was heated in flowing NH3 through two linear heating segments (623 to 723 K then 723 to 973 K) with different space velocities in a 23 factorial design. The temperature limits for these heating segments were defined based on the results of in situ X-ray diffraction analysis of the gas-solid reaction. The resulting catalysts were characterized using BET surface area analysis, environmental scanning electron microscopy, ex situ X-ray diffraction, and oxygen chemisorption. The primary bulk phase present was γ-Mo2N. Some of the lower surface area catalysts also contained MoO2 and Mo, but there was no evidence of nitrides other than γ-Mo2N. The catalysts consisted of micrometersized, plate-like aggregates of nanometer-sized crystallites, and possessed surface areas ranging up to ≈140 m2/g depending on the synthesis and reduction conditions employed. Statistical analysis of the results revealed that the space velocity individually and the heating rates combined had the most significant effects on the structural properties. The production of catalysts with surface areas in excess of 50 m2/g required the use of slow heating rates during the first segment and high space velocities. We concluded that the key to producing the highest surface area Mo nitrides was channeling the reaction through HxMoO3 (x ≤ 0.34) and γ-Mo2OyN1-y intermediates. Passivation of the materials immediately following synthesis appeared to produce an oxynitride at the surface. Reduction of the passivated materials in H2 at temperatures up to 673 K caused a significant increase in the surface area and O2 uptake. The O2 uptake for the low and medium surface area catalysts varied linearly with the BET surface area and corresponded to an O:Mo stoichiometry of approximately 1:5. The oxygen site density for the highest surface area nitride was lower than those for the lower surface area catalysts, presumably due to differing surface structures.

Experimental and theoretical studies of dissolution roughness

Periodic dissolution patterns that result from the interaction of a soluble surface and an adjacent turbulent flow have been investigated experimentally and theoretically. They occur at a Reynolds number based on a characteristic wavelength and friction velocity of about 2200. Experimental results for the stable geometry, propagation, mass-transfer distribution, average mass-transfer correlation and friction factor are presented. An interpretation based upon the repetitive transitional nature of the flow structure is advanced to explain aspects of the origin and behaviour of this type of roughness.

Fractal dimensions and geometries of caves

Lengths of all caves in a region have been observed previously to be distributed hyperbolically, like self-similar geomorphic phenomena identified by Mandelbrot as exhibiting fractal geometry. Proper cave lengths exhibit a fractal dimension of about 1.4. These concepts are extended to other self-similar geometric properties of caves with the following consequences.Lengths of a cave is defined as the sum of sizes of passage-filling, linked modular elements larger than the cave-defining modulus. If total length of all caves in a region is a self-similar fractal, it has a fractal dimension between 2 and 3; and the total number of linked modular elements in a region is a self-similar fractal of the same dimension. Cave volume in any modular element size range may be calculated from the distribution.The expected conditional distribution of modular element sizes in a cave, given length and modulus, also is distributed hyperbolically. Data from Little Brush Creek Cave (Utah) agree and yield a fractal dimension of about 2.8 (like the Menger Sponge). The expected number of modular elements in a cave equals approximately the 0.9 power of length of the cave divided by modulus. This result yields an intriguing “parlor trick.” An algorithm for estimating modular element sizes from survey data provides a means for further analysis of cave surveys.

A mathematical model to describe drug release from thin topical applications

Summary Release of a thin topical application of a drug is modeled by transient diffusion between the application, the underlying stratum corneum, and a receptor. Cases treated include sudden contact of the application with drug-free stratum corneum, and initially equilibrated application and stratum comeum. The method of solution is the numerical inversion of the analytic Laplace Transform of the exact solution, which has speed, accuracy and convenience advantages over classical analytical or numerical methods for coupled linear partial differential equations. The algorithm for long-time solutions in the time domain is also found, although this has no computational advantage over the direct numerical transform inversion.

Caves as a Measure of Karst

The development of a statistical distribution of proper entrances among proper caves in a limestone karst is considered as a geomorphic process and described with stochastic geomorphic models. The models assume that entrances form and close independently at entrance sites and that the sites are randomly distributed among caves. Analysis of 820 caves in 10 regions on this basis finds that the best model is one assuming a proportional length dependence for mean site frequency on each cave. This model is used to obtain a constant which is characteristic of a karst and to predict the number and length distributions of entranceless caves and the length distribution of all caves in each region. The karst constant varies from about 0.0001 to 0.01

Topical Drug Delivery from Thin Applications: Theoretical Predictions and Experimental Results

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Dispersed phase mixing effects on second moments in dominantly first-order, backmix reactors

. Comparisons between the karst constants in the different regions suggest a correlation with the underlying karst processes and disclose an apparently unique karst situation in County Clare, Ireland. Predictions of complete length distributions of all caves show similarities not found in observed length distributions and support the conclusion that the proper interpretation of a cave region demands information about unobservable caves.