Seven Years of Membranes: Feature Paper 2017

For the last seven years, Membranes has provided an outstanding platform for the publication of articles at the forefront of research in the areas of membrane fabrication, characterization and application. This Special Issue, entitled “Seven Years of Membranes: Feature Paper 2017,” celebrates this achievement. The articles included in this Special Issue, written by prominent researchers in the field, provide an authoritative and up-to-date account of the advances in membrane science and technology. They describe new methods for the fabrication of organic, inorganic and mixed matrix membranes and their utilization in improving the efficiency of membrane-based separation processes, such as membrane distillation, nanofiltration, ultrafiltration, reverse osmosis, and gas permeation. A number of articles are focused on water treatment, which, because of its significance to sustainable development, is one of the main areas of membrane research and application. These articles report novel techniques for the clean-up of contaminated waters, and the desalination of industrial effluents, brackish water and seawater

Mathematical modelling of a flow-injection system with a membrane separation module

A mathematical model for a flow-injection system with a membrane separation module based on the axially dispersed plug flow model was developed. It takes into account the geometrical dimensions and dispersion properties of the main sections of the manifold, the mass transfer in the channels of the separation module and the characteristics of the membrane (thickness and diffusion coefficient within it). The model was solved analytically in the Laplace domain. The inverse transformation was found to give satisfactory results for reactor Peclet numbers less than 120. Otherwise a numerical solution based on the implicit alternating-direction finite difference method was preferred. The adequacy of the model was confirmed experimentally on a flow-injection manifold with a parallel-plate dialysis module. The unknown flow and membrane parameters were determined by curve fitting. The membrane parameters were determined also by steady-state measurements. Fairly good agreement between the dynamic and steady-state results and with results given in the literature was observed, which, together with other experimental results, supported the validity of the model and showed that it can be used successfully for the mathematical description and optimization of flow-injection systems with membrane separation modules. In this connection, the influence of the reactor parameters and the sample volume on the performance of such a system were investigated and conclusions for improving its sensitivity and sample throughput were drawn. Other possible applications of the model are in membrane technology for characterizing of various membranes and in process engineering for investigating the mass transfer in different dialysers

Application of Laplace transforms for the solution of transient mass- and heat-transfer problems in flow systems

A fast numerical technique for the solution of partial differential equations describing timedependent two- or three-dimensional transport phenomena is developed. It is based on transforming the original time-domain equations into the Laplace domain where numerical integration is performed and by subsequent numerical inverse transformation the final solution can be obtained. The computation time is thus reduced by more than one order of magnitude in comparison with the conventional finite-difference techniques. The effectiveness of the proposed technique is demonstrated by illustrative examples

Analysis of transient laminar mass-transfer in a parallel-plate dialyzer

Mass transfer under laminar flow conditions is discussed on the basis of the Navier-Stokes equations and the axially dispersed plug-flow model. By fitting the results with these two approaches, relationships can be derived for predicting the mass-transfer coefficient and the Peclet number in a parallel-plate laminar flow system with on impermeable wall and an opposite wall at which the concentration is uniform. This single-stream relationship can be utilized for calculating the mass-transfer coefficients in both channels of a co-current parallel-plate dialyser. It is shown that the Peclet number in the axially dispersed plug-flow model derived for a parallel-plate flow where both sides are impermeable gives better results when applied to the co-current dialyser than the single-stream relationship. The results obtained allow the mathematical modelling of process and analytical flow-through manifolds incorporating a dialysis module

Mathematical modelling of the chronoamperometric response of an array of rectangular microelectrodes

A general mathematical model describing the response of an array of flat amperometric electrodes with arbitrary size and spatial distribution at the bottom of a measuring cell with rectangular walls and finite dimensions is outlined. It is based on the three-dimensional diffusion equation with initial and boundary conditions corresponding to the physical situation which was numerically solved by the implicit alternating-direction finite-difference method. The accuracy of the numerical solution was confirmed by theoretical and experimental results obtained by other authors. By comparing the chronoamperometric curves of the individual electrodes and by examining the spatial concentration distribution in the measuring cell conclusions can be drawn concerning the mutual influence of the individual electrodes for a given geometry of the array and the dimensions of the measuring cell. This will allow the designing of arrays and selecting the proper measuring cell dimensions resulting in minimal sensor interferences. Chronoamperometric curves show the time required for attaining quasi steady state and the corresponding current value. Illustrative examples are presented