Influence of ultrafiltration membrane characteristics on adsorptive fouling with dextrans

This paper presents a detailed investigation of fouling mechanisms for ultrafiltration membranes with polysaccharides obtained by studying membrane–solute (static adsorption) and membrane–solute–solute interactions (ultrafiltration (UF)). Two polyethersulfone (PES) membranes and one stabilized cellulose (cellulosic) membrane with a nominal cut-off of 10 kg/mol and dextrans with average molar mass (M) of 4, 10 and 15 kg/mol were used. The membranes before and after static adsorption of dextran were characterized by captive bubble contact angle and tangential streaming potential measurements as well as ultrafiltration sieving curves for polyethylene glycols. Significant water flux reductions (4–15%), which also correlated with dextran molar mass, and changes of the other membrane characteristics occurred after static dextran adsorption for the PES membranes. An empirical model to describe the correlation between the relative water flux reduction and the concentration of solute had also been proposed. In contrast, no significant changes could be detected for the cellulosic membrane. Significant membrane–solute interactions had also been confirmed in the ultrafiltration experiments with dextrans where irreversible fouling had been observed for the PES but not for the cellulosic membranes. The results provide fundamental information for a better understanding of fouling by polysaccharides. In particular, it had been confirmed that hydrophilic and neutral dextrans can significantly foul PES membranes via adsorption to the surface of the membrane polymer. On this basis, methods for control of this fouling can be properly developed

Solitons in a parametrically driven damped discrete nonlinear Schr\"odinger equation

We consider a parametrically driven damped discrete nonlinear Schr\"odinger (PDDNLS) equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental discrete bright solitons. We show that there are two types of onsite discrete soliton, namely onsite type I and II. We also show that there are four types of intersite discrete soliton, called intersite type I, II, III, and IV, where the last two types are essentially the same, due to symmetry. Onsite and intersite type I solitons, which can be unstable in the case of no dissipation, are found to be stabilized by the damping, whereas the other types are always unstable. Our further analysis demonstrates that saddle-node and pitchfork (symmetry-breaking) bifurcations can occur. More interestingly, the onsite type I, intersite type I, and intersite type III-IV admit Hopf bifurcations from which emerge periodic solitons (limit cycles). The continuation of the limit cycles as well as the stability of the periodic solitons are computed through the numerical continuation software Matcont. We observe subcritical Hopf bifurcations along the existence curve of the onsite type I and intersite type III-IV. Along the existence curve of the intersite type I we observe both supercritical and subcritical Hopf bifurcations.Comment: to appear in "Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations in Nonlinear Systems", B.A. Malomed, ed. (Springer, Berlin, 2012

Drying a liquid paint layer

Subject of this study is the free boundary problem of a liquid layer that is dried by evaporation. Using a Stefan type problem, we model the diffusion driven drying of a layer of liquid paint consisting of resin and solvent. The effect of a small perturbation of the flat boundary is considered. We include the discussion of evaporation constant as a free parameter. For both small and big wavenumber, the high speed of evaporation can lead to instability. We first recognize this instability in the linearized equation. Using numerical calculations, we show that the instability also happens in the full equation

Josephson tunneling of dark solitons in a double-well potential

We study the dynamics of matter waves in an effectively one-dimensional Bose-Einstein condensate in a double well potential. We consider in particular the case when one of the double wells confines excited states. Similarly to the known ground state oscillations, the states can tunnel between the wells experiencing the physics known for electrons in a Josephson junction, or be self-trapped. As the existence of dark solitons in a harmonic trap are continuations of such non-ground state excitations, one can view the Josephson-like oscillations as tunnelings of dark solitons. Numerical existence and stability analysis based on the full equation is performed, where it is shown that such tunneling can be stable. Through a numerical path following method, unstable tunneling is also obtained in different parameter regions. A coupled-mode system is derived and compared to the numerical observations. Regions of (in)stability of Josephson tunneling are discussed and highlighted. Finally, we outline an experimental scheme designed to explore such dark soliton dynamics in the laboratory.Comment: submitte

Caravan Awnings: a Geometrical Problem

Two questions regardingthe design of caravan awnings were posed by a company.The company wishes to produce awnings with a pretty appearance. When an awning is attached to a caravan, some wrinkles could appear. We developed some methods to avoid the wrinkles. The problem is restricted to awnings which are made from one piece of cloth

Variational approximations to homoclinic snaking

We investigate the snaking of localised patterns, seen in numerous physical applications, using a variational approximation. This method naturally introduces the exponentially small terms responsible for the snaking structure, that are not accessible via standard multiple-scales asymptotic techniques. We obtain the symmetric snaking solutions and the asymmetric 'ladder' states, and also predict the stability of the localised states. The resulting approximate formulas for the width of the snaking region show good agreement with numerical results.Comment: 4 pages, 3 figures, submitte