María I. Cabrera

Mathematical modeling of drug delivery from torus-shaped single-layer devices.

A mathematical modeling of controlled release of drug from torus-shaped single-layer devices is presented. Analytical solutions based on the pseudo-steady state approximation are derived. The reliability and usefulness of the model are ascertained by comparison of the simulation results with matrix-type vaginal ring experimental release data reported in the literature. A good agreement between the model prediction and the experimental data is observed. An analysis of the effect of the variation in torus design parameters on the solute release is also presented. The model is applicable only to torus-shaped single-layer systems wherein the initial load of drug is higher than its solubility in the polymer.

Modeling of dispersed-drug delivery from planar polymeric systems: optimizing analytical solutions.

Analytical solutions for the case of controlled dispersed-drug release from planar non-erodible polymeric matrices, based on Refined Integral Method, are presented. A new adjusting equation is used for the dissolved drug concentration profile in the depletion zone. The set of equations match the available exact solution. In order to illustrate the usefulness of this model, comparisons with experimental profiles reported in the literature are presented. The obtained results show that the model can be employed in a broad range of applicability.

Photochemical decomposition of 2,4-dichlorophenoxy acetic acid (2,4-D) in aqueous solution. I. Kinetic study

The intrinsic kinetics of the photochemical decomposition of 2,4-dichlorophenoxyacetic acid in aqueous solution has been studied using light of 253.7 nm. Experiments were carried out in a well stirred batch reactor irradiated from its bottom by means of a tubular lamp and a parabolic reflector. Results were analyzed in terms of a very simple kinetic expression. Absorbed radiation effects were duly quantified by means of a one-dimensional radiation field model. This approach incorporates a variable absorption coefficient that is a function of the 2,4-D conversion. The decomposition kinetics can be properly represented with a point valued equation of the following form: RD, λ = − Φ D,λ e λ (y).

Euflabella N. Igen.: Complex Horizontal Spreite Burrows in Upper Cretaceous–Paleogene Shallow-Marine Sandstones of Antarctica and Tierra Del Fuego

Abstract Fine-grained sandstones and siltstones of Late Cretaceous to Eocene age in Antarctica and Tierra del Fuego yield an association of well-known shallow-marine trace fossils. Among them stick out complex spreite burrows, which are formally described as Euflabella n. igen. and subdivided into five ichnospecies with different burrowing programs and occurrences. As shown by concentrations of diatoms, radiolarians, foraminifers, and calcispheres in particular backfill lamellae, the unknown trace makers lived on fresh detritus from the surface as well as the burrowed sediment. In some ichnospecies, vertical sections show that the spreite is three-dimensionally meandering in upward direction and that upper laminae tend to rework the upper backfill of the folds underneath. This could mean a second harvest, after cultivated bacteria had time to ferment refractory sediment components, which the metazoan trace maker had been unable to digest before.

Photochemical decomposition of 2,4-dichlorophenoxy acetic acid (2,4-D) in aqueous solution. II. Reactor modeling and verification

An annular flow photoreactor for the direct photolysis of 2,4-dichlorophenoxyacetic acid has been developed, mathematically modeled and experimentally verified in a bench scale apparatus. The model employs a very simple kinetic equation that was previously obtained in a well stirred tank, batch laboratory reactor. Reasonably good agreement has been obtained between model predictions and experimental results. The observed errors are mainly due to the fact that the kinetics of this very complex reaction have been modeled in terms of just one single concentration.

Mathematical modeling of drug delivery from one-layer and two-layer torus-shaped devices with external mass transfer resistance.

A mathematical modeling of controlled release of drug from one-layer and two-layer torus-shaped devices with external mass transfer resistance is presented. Analytical solutions based on the pseudo-steady state approximation are derived. The validity of the equations is established in two stages. In the first stage, the validity of the models derived for more complex systems is determined by comparison with profiles predicted by the simplest model, in asymptotic cases. In the second stage, the reliability and usefulness of the models are ascertained by comparison of the simulation results with vaginal rings experimental release data reported in the literature. In order to measures quantitatively the fit of the theoretical models to the experimental data, the pair-wise procedure is used. A good agreement between the prediction of the models and the experimental data is observed. The models are applicable only to torus-shaped systems in where the initial load of drug is higher than its solubility in the polymer.

Selective Preparation of Key Intermediates for the Synthesis of Gemini Surfactants by Phase-Transfer Catalysis

A comparison of liquid-liquid and solid-liquid PTC for the selective synthesis of diglycidyl ether from protected pentaerythritol and epichlorohydrin is presented. Solid-liquid PTC was found to be more useful than liquid-liquid PTC because the use of water or other solvents can be avoided and higher yields and selectivity are achieved. It was proved that etherification takes place in the solid phase-organic phase system even in the absence of the phase-transfer catalyst. However, the use of tetrabutylammonium bisulfate as catalyst is essential due to its crucial effect on the enhancement of the rate of etherification and on the improvement of the selectivity to diglycidyl ether, which is higher than 98%.

Solving design equations for a hollow fiber bioreactor with arbitrary kinetics

Abstract An approach for solving the hollow fiber bioreactor design equations is presented. The original set of differential mass balance equations is cast into an equivalent system of integral equations by generating the appropriate Green’s functions. Mathematical features common to all hollow fiber bioreactors (HFBRs) operating with laminar flow are imbedded in the corresponding Green’s functions on the lumen side, and thus separated from specific aspects arising from mass transport through the permeable wall. On the spongy matrix side, the appropriate Green’s functions are expressed in terms of the mass transfer properties without involving any chemical kinetic parameters; this avoids repetitive computational effort when treating different reaction kinetics. The derived integral equations are numerically solved on an appropriately transformed coordinate system. The numerical method is well suited for problems where steep gradients of concentration cause an inaccurate numerical integration and low rates of convergence if the equations are solved with a uniform rectangular grid on the original coordinate system. The effectiveness of the proposed approach for the simulation of HFBRs with power-law, Michaelis–Menten and zero-order kinetics is demonstrated. The method is readily extendible to treat problems with chemical kinetics described by any arbitrary functional form.

THE LAMINAR FLOW TUBULAR REACTOR WITH HOMOGENEOUS AND HETEROGENEOUS REACTIONS II. Application to Reactor Modeling Involving Free Radical Reactions

The simulation of the complex polychlorination of methane in a non-isothermal photoreactor with laminar flow regime shows the usefulness of the integral equations deduced in Part I of this contribution. Improved iterative schemes for numerical solution have been implemented by using the particular equations proposed for species having slow, very fast and instantaneous reaction regimes. From such integral equations, in a mathematically consistent form, deviations in the fields of predicted concentrations with and without the application of the local steady-state approximation for homogeneous reactions involving atomic and free radical species have been obtained. Similarly the fields of predicted concentrations applying the usual assumption of negligible wall reactions for the same highly reactive intermediate species has been compared with the reaction mechanisms that includes the wall reactions. A comprehensive analysis of the validity of these simplifying assumptions is presented.

THE LAMINAR FLOW TUBULAR REACTOR WITH HOMOGENEOUS AND HETEROGENEOUS REACTIONS I. Integral Equations for Diverse Reaction Rate Regimes

Design equations for non-isothermal Laminar Flow Tubular Reactors (LFTRs) with homogeneous and heterogeneous - at the reactor wall - reactions with arbitrary kinetic equations have been satisfactorily treated transforming the original P.D.E. problem into a system of integral equations. The kernels of the integral operators are related to an eigenvalue problem which does not depend on the kinetic equations; this avoids repetitive computational effort in the treating of different reaction kinetics. To render a more efficient numerical treatment and according to the governing reaction rate regime, modified expressions of the general solution were obtained was follows: (i) a solution with kernels depending only on the diffusion and convective times was obtained for a low reaction regime; (ii) another solution with kernels including the reaction lime, besides the diffusion and convective ones, was necessary for a fast reaction regime and (iii) the local quasi-steady-state approximation was obtained as limiting case of solution (ii) for a instantaneous reaction regime.