Mathematical analysis of viscometric (polymer) flow fields in capillaries: Taylor dispersion revisited

A general formulation for capillary flow of two miscible fluids – one a dilute plug of polymer fluid inserted into a fully developed Poiseuille flow of the other, a Newtonian stream – is examined for its long time behavior. Phenomenologically, the system evolves from an initial state, that of a plug within the boundaries of sharp, well defined fronts inside a Newtonian stream, to a more homogenized state in the very long time scale. This problem was addressed by G.I. Taylor but with regard to a system of two Newtonian fluids, leading to the well-known results commonly described as `Taylor axial dispersion'. In this paper, a general and systematic perturbation analysis is presented from which Taylor's result is recovered as a special case of a more general solution which applies to fluids incorporating elastic properties. In particular, the influence of viscoelasticity and (polymer) diffusivity on the observed pressure profile in the capillary conduit is examined. This effect is clearly separated out for small Peclet number flows using asymptotic and numerical analysis. The results identify the influence of fluid viscosity, elasticity, and diffusivity on the observed pressure profile and form the basis for the improved characterization of polymeric elasticity using capillaries – a finding that is of significant scientific and commercial interest. These results were obtained by the authors as a class of observations resulting from the perturbation analysis of forced-flow capillary devices in viscoelastic fluid property investigation.     

Uses of Ozone in a Three-Phase System for Water Treatment: Ozone Adsorption

A new technique of using ozone for water treatment is presented. This new technique consists of using a three-step-process composed firstly of ozone adsorption on an appropriate adsorbent, secondly water treatment, and thirdly regeneration of the adsorbent. Results regarding ozone adsorption (the first step) are presented in this paper. Different types of silica gel and a type of TiO₂ have been tested for ozone adsorption. It was found that the physical characteristics of the silica gel affect its capacity for ozone. Titanium dioxide has shown ozone decomposition instead of adsorption as it contains Lewis acid sites. An exponential decrease of the silica gel capacity with its moisture content has been found. Linear isotherms in the range of ozone concentrations less than 100?g/m³ NTP have been found. A particle diffusion model with linear equilibrium isotherm has been used to model the breakthrough curves in fixed bed columns.     

Kinetic investigation of the carbothermal reduction of an Iranian clay

The kinetics of the carbothermal reduction of clay under argon atmosphere has been investigated by the X-ray diffraction method. The clay-carbon (excess) mixture was formed into 2 cm diameter disks of different thicknesses. Experimental data evidences the significant effect of sample thickness on the reaction rate at 1400 °C. Decreasing thickness promotes mullite dissociation and formation of SiC and alumina powders. Mathematical modeling of the reaction system showed the gas diffusion in the Knudsen regime through the pellet to be the rate controlling step. Diffusivity of CO and reacted core tortuosity factor have been calculated.     

Tannins/melamine–urea–formaldehyde (MUF) resins substitution of chrome in leather and its characterization by thermomechanical analysis

A new sulfonated melamine–urea–formaldehyde (MUF) resin of relatively low melamine content, prepared according to a sequential formulation, has been shown to be highly effective when coupled with different natural vegetable tannins to produce leather with the same good characteristics of leather prepared with chrome salts. In particular, the antishrinkage effectiveness of the leather prepared according to the new approach is comparable to that obtained with chrome tanned leathers. The comparison of the traditional leather shrinkage temperatures test method with a new thermomechanical analysis (TMA) test method in tension yields thermograms presenting three major modulus of elasticity (MOE) peaks. These are closely connected to molecular level phenomena determining the shrinkage temperature of leather. The three determining parameters appear to be as follows: (1) The average value of the temperatures at which the three MOE peaks occur: the higher the value of this average, the lower is the shrinkage of leather. (2) The average of maximum MOE values of the TMA peaks: the higher this average is, the better is the leather in regard to antishrinkage effectiveness. This means the leather maximum MOE at each peak is a measure of the resistance to the contraction force induced by heat. (3) The relative intensity of the first TMA peak in relation to the second: the higher the value of the MOE for the first TMA peak is in relation to the second peak, the lower the leather shrinkage appears to be. However, it has not been possible to better define or quantify this latter effect. This new TMA test method in tension has also yielded a mathematical relationship correlating the thermogram peak temperatures and MOE averages with the traditional shrinkage temperature to a high degree of confidence. A previous TMA test method, in compression, has proven to yield more problematic and finally not very reliable results when one needs to apply it to a wide variety of different cases. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1889–1903, 2003     

Efficient model reduction in non-linear dynamics using the Karhunen-Loève expansion and dual-weighted-residual methods

 We look at the task of computing the time-evolution of a non-linear system for a long time, in our case under random external influences. Our specific example is the fatigue evaluation of a wind turbine. To facilitate such a computation, we look at a reduction of the computational effort by projecting everything on a low-dimensional basis. In this case we take the Karhunen-Loève basis generated from running the model a little while under the random loading. It is important that the error which is caused by this reduction process can be controlled. We estimate the error by dual or adjoint methods. This in turn allows the process of model reduction to be performed adaptively. Dedicated to the memory of Prof. Mike Crisfield, for his cheerfulness and cooperation as a colleague and friend over many years.     

Thermal Generation of Residual Stress Fields for Purpose of Distortion Minimization

Thermal treatments of steel components with the goal of hardening often result in distortion by releasing the residual stresses which were brought into the specimen during the preceding processing steps. The goal of the presented work is the minimization of this distortion. By generating definite residual stress fields and investigating the resulting distortion, the distortion mechanism can be observed in detail. A flexible and reproducible way to generate such residual stress fields inside a specimen is by means of local thermal treatment with a laser beam. Computer simulations as well as experiments were carried out using an idealized tooth of a gearwheel (finger sample) as a model system. The deformation of the samples due to the laser heat treatment and the stress fields generated inside the samples were determined with respect to different process parameters.     

Oil Spill Cleanup from Sea Water by Sorbent Materials

Three sorbents were compared in order to determine their potential for oil spill cleanup. Polypropylene nonwoven web, rice hull, and bagasse with two different particle sizes were evaluated in terms of oil sorption capacities and oil recovery efficiencies. Polypropylene can sorb almost 7 to 9 times its weight from different oils. Bagasse, 18 to 45 mesh size, follows polypropylene as the second sorbent in oil spill cleanup. Bagasse, 14 to 18 mesh size, and rice hull have comparable oil sorption capacities, which are lower than those of the two former sorbents. It was found that oil viscosity plays an important role in oil sorption by sorbents. All adsorbents used in this work could remove the oil from the surface of the water preferentially.     

Dental amalgam – the effect of the technology of alloy powder preparation on the corrosion behaviour and the release of mercury

Dental amalgams are based on a broad spectrum of materials differing in their chemical composition, metallurgical treatment, and in the way the initial alloys powders are prepared. In addition to their chemical composition, amalgams based on various powders differ in both their microstructure and the amount of mercury needed for preparation. All these facts may affect electrochemical processes occurring during their interaction with oral fluids, and also mercury release. While verifying the effect of the technology used for the preparation of the high‐copper ternary alloy powder on the properties of resulting amalgams, this study aimed at the mechanism of their interaction with a model saliva solution as well as mercury release was included. Measurements were done in a model saliva solution using standard electrochemical methods and exposition measurements. The interaction of individual types of amalgams with artificial saliva did not reveal any significant differences. The free corrosion potential of all these amalgams in an aerated solution settled in the range of values in which tin oxidation, resulting in a layer of insoluble corrosion producsts, turned out to be the dominant anodic process. The rate of mercury release was the lowest for amalgams based on a gas‐atomized alloy. The highest rate of mercury release, and also its dependence on time, was exhibited by lathe‐cut powder based amalgam. In addition to different volume fraction of the Ag‐Hg phase and the level of its tin alloying, this different behaviour may be explained by differences in the rate at which a layer of tin corrosion products acting as a barrier to mercury release is formed.