Cleaning of wastewater for the environment is an emerging issue for the living organism. The separation of oily wastewater, especially emulsified mixtures, is quite challenged due to a large amount of wastewater produced in daily life. In this review, the membrane technology for oily wastewater treatment is presented. In the first part, the global membrane market, the oil spill accidents and their results are discussed. In the second and third parts, the source of oily wastewater and conventional treatment methods are represented. Among all methods, membrane technology is considered the most efficient method in terms of high separation performance and easy to operation process. In the fourth part, we provide an overview of membrane technology, fouling problem, and how to improve the self-cleaning surface using functional groups for effectively treating oily wastewater. The recent development of surface-modified membranes for oily wastewater separation is investigated. It is believed that this review will promote understanding of membrane technology and the development of surface modification strategies for anti-fouling membranes.

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We introduce a discrete fracture network model of stationary Darcy flow in fractured rocks. We approximate the fractures by a network of planar circle disks, which is generated on the basis of statistical data obtained from field measurements. We then discretize this network into a mesh consisting of triangular elements placed in three-dimensional space. We use geometrical approximations in fracture planes, which allow for a significant simplification of the final triangular meshes. We consider two-dimensional Darcy flow in each fracture. In order to accurately simulate the channeling effect, we assign to each triangle an aperture defining its hydraulic permeability. For the discretization we use the lowest order Raviart-Thomas mixed finite element method. This method gives quite an accurate velocity field, which is computed directly and which satisfies the mass balance on each triangular element. We demonstrate the use of this method on a model problem with a known analytical solution and describe the generation and triangulation of the fracture network and the computation of fracture flow for a particular real situation.

The mixed-hybrid finite element discretization of Darcy's law and continuity equation describing the potential fluid flow problem in porous media leads to a symmetric indefinite linear system for the pressure and velocity vector components. As a method of solution the reduction to three Schur complement systems based on successive block elimination is considered. The first and second Schur complement matrices are formed eliminating the velocity and pressure variables, respectively, and the third Schur complement matrix is obtained by elimination of a part of Lagrange multipliers that come from the hybridization of a mixed method. The structural properties of these consecutive Schur complement matrices in terms of the discretization parameters are studied in detail. Based on these results the computational complexity of a direct solution method is estimated and compared to the computational cost of the iterative conjugate gradient method applied to Schur complement systems. It is shown that due to special block structure the spectral properties of successive Schur complement matrices do not deteriorate and the approach based on the block elimination and subsequent iterative solution is well justified. Theoretical results are illustrated by numerical experiments.

The antibacterial efficiency of nanofibre composite yarns with an immobilized antibacterial agent was tested. This novel type of nanofibrous composite material combines the good mechanical properties of the core yarn with the high specific surface of the nanofibre shell to gain specific targeted qualities. The main advantages of nanofibre covered composite yarns over the standard planar nanofibre membranes include high tensile strength, a high production rate, and their ability to be processed by standard textile techniques. The presented paper describes a study of the immobilization of an antibacterial agent and its interaction with two types of bacterial colonies. The aim of the study is to assess the applicability of the new composite nanomaterial in antibacterial filtration. During the experimental tests copper(II) oxide particles were immobilized in the polyurethane and polyvinyl butyral nanofibre components of a composite yarn. The antibacterial efficiency was evaluated by using both Gram-negativeEscherichia coliand Gram-positiveStaphylococcus gallinarumbacteria. The results showed that the composite yarn with polyvinyl butyral nanofibres incorporating copper(II) oxide nanoparticles exhibited better antibacterial efficiency compared to the yarn containing the polyurethane nanofibres. The nanofibre/nanoparticle covered composite yarns displayed good antibacterial activity against a number of bacteria.

Nanofibres are very promising for water remediation due to their high porosity and small pore size. Mechanical properties of nanofibres restrict the application of pressure needed water treatments. Various PAN, PVDF, and PVDF/PAN nanofibre layers were produced, and mechanical properties were improved via a lamination process. Low vacuum plasma treatment was applied for the surface modification of nanofibres. Atmospheric air was used to improve hydrophilicity while sulphur hexafluoride gas was used to improve hydrophobicity of membranes. Hydrophilic membranes showed higher affinity to attach plasma particles compared to hydrophobic membranes.

Markov processes play an important role in physics and the theory of open systems in particular. In this paper we study the asymptotic evolution of trace-nonincreasing homogenous quantum Markov processes (both types, discrete quantum Markov chains and continues quantum dynamical semigroups) equipped with a so-called strictly positive T -state in the Schrödinger and the Heisenberg picture. We derive a fundamental theorem specifying the structure of the asymptotic and uncover a rich set of transformations between attractors of quantum Markov processes in both pictures. Moreover, we generalize the structure theorem derived for quantum Markov chains to quantum dynamical semigroups showing how the internal structure of generators of quantum Markov processes determines attractors in both pictures. Based on these results we provide two characterizations of all asymptotic and stationary states, both strongly reminding in form the well-known Gibbs states of statistical mechanics. We prove that the dynamics within the asymptotic space is of unitary type, i.e. quantum Markov processes preserve a certain scalar product of operators from the asymptotic space, but there is no corresponding unitary evolution on the original Hilbert space of pure states.Finally simple examples illustrating the derived theory are given.

Preparing easily scaled up, cost-effective, and recyclable membranes for separation technology is challenging. In the present study, a unique and new type of modified polyvinylidene fluoride (PVDF) nanofibrous membrane was prepared for the separation of oil–water emulsions. Surface modification was done in two steps. In the first step, dehydrofluorination of PVDF membranes was done using an alkaline solution. After the first step, oil removal and permeability of the membranes were dramatically improved. In the second step, TiO2 nanoparticles were grafted onto the surface of the membranes. After adding TiO2 nanoparticles, membranes exhibited outstanding anti-fouling and self-cleaning performance. The as-prepared membranes can be of great use in new green separation technology and have great potential to deal with the separation of oil–water emulsions in the near future.