Abraham Sagiv

Theoretical formulation of the diffusion through a slab-theory validation

A new theoretical approach to diffusion through a slab and its convection out of the slab is developed. The resulted general model is based on the following assumptions. The transport is a one-dimensional. The diffusion coefficient, the membrane thickness and the temperature are constants. The fluxes in or out of the slab are proportional to concentration differences at the slab interfaces with the concentrations in the two volumes of both sides of the slab. No restrictions are set on the size of the two volumes, on the solute concentrations either in the slab or in the two volumes, as well as on the stirring intensity (natural to perfect forced convection) of the solutions in the two volumes. The formulation in general is exact, except the initial condition. It has been approximately satisfied using the residual approximation method. The general model is validated by its reduction to special cases covering the whole range of its parameters. The general model is reduced to existing analytical studies and well agrees to existing data covering other parts of the parameter ranges. The generality of the model is useful in a wide variety of applications such as separation technology, conducting diffusion experiments, membrane material selection, packaging, pharmaceutical and agricultural applications, as well as other applications which obey the above restrictions underlying the general model.

Boron Removal Using Membranes

Boron is an important micronutrient for humans, animals, and plants, although the range between deficiency and excess is narrow. The use of desalinated water and the reuse of treated wastewater for irrigation may result in excess boron. In aqueous environments boron is mainly present as boric acid, which at natural pH of water is mostly undissociated and insufficiently rejected by desalination membranes.

Initial burst measures of release kinetics from fiber matrices.

AbstractA comprehensive axisymmetric diffusion model of drug release from a fiber is developed to account for both the initial burst (IB) phenomenon as well as the later diffusion-dominated release. This model is an enhancement over previous models in that a set of four IB parameters are calculated, which both describe the initial burst phenomenon as well as improve the fit for the diffusion-dominated release phase. This model is also an enhancement over previous models in allowing: finite dissolution volumes, finite stirring levels of the medium, and user-specified initial drug dispersion within the device. Five different drug release data sets are used to verify the model and to derive values for the IB parameters. Two of the data sets are from experiments conducted in this study, and the other three sets are from previously published data. These data sets were selected to cover a wide range of possibilities, i.e., from nearly 0% to nearly 100% of the total drug release during IB, yet the model handles all cases equally well.

Modeling Remineralization of Desalinated Water by Micronized Calcite Dissolution

A widely used process for remineralization of desalinated water consists of dissolution of calcite particles by flow of acidified desalinated water through a bed packed with millimeter-size calcite particles. An alternative process consists of calcite dissolution by slurry flow of micron-size calcite particles with acidified desalinated water. The objective of this investigation is to provide theoretical models enabling design of remineralization by calcite slurry dissolution with carbonic and sulfuric acids. Extensive experimental results are presented displaying the effects of acid concentration, slurry feed concentration, and dissolution contact time. The experimental data are shown to be in agreement within less than 10% with theoretical predictions based on the simplifying assumption that the slurry consists of uniform particles represented by the surface mean diameter of the powder. Agreement between theory and experiment is improved by 1-8% by taking into account the powder size distribution. Apart from the practical value of this work in providing a hitherto lacking design tool for a novel technology. The paper has the merit of being among the very few publications providing experimental confirmation to the theory describing reaction kinetics in a segregated flow system.