Buckling and post-buckling of extensible rods revisited: A multiple-scale solution

An exact non-linear formulation of the equilibrium of elastic prismatic rods subjected to compression and planar bending is presented, electing as primary displacement variable the cross-section rotations and taking into account the axis extensibility. Such a formulation proves to be sufficiently general to encompass any boundary condition. The evaluation of critical loads for the five classical Euler buckling cases is pursued, allowing for the assessment of the axis extensibility effect. From the quantitative viewpoint, it is seen that such an influence is negligible for very slender bars, but it dramatically increases as the slenderness ratio decreases. From the qualitative viewpoint, its effect is that there are not infinite critical loads, as foreseen by the classical inextensible theory. The method of multiple (spatial) scales is used to survey the post-buckling regime for the five classical Euler buckling cases, with remarkable success, since very small deviations were observed with respect to results obtained via numerical integration of the exact equation of equilibrium, even when loads much higher than the critical ones were considered. Although known beforehand that such classical Euler buckling cases are imperfection insensitive, the effect of load offsets were also looked at, thus showing that the formulation is sufficiently general to accommodate this sort of analysis. (c) 2008 Elsevier Ltd. All rights reserved.

Numerical solution of the two-phase expansion of a metastable flashing liquid jet using the dispersion-controlled dissipative scheme

This paper presents a study of the stationary phenomenon of superheated or metastable liquid jets, flashing into a two-dimensional axisymmetric domain, while in the two-phase region. In general, the phenomenon starts off when a high-pressure, high-temperature liquid jet emerges from a small nozzle or orifice expanding into a low-pressure chamber, below its saturation pressure taken at the injection temperature. As the process evolves, crossing the saturation curve, one observes that the fluid remains in the liquid phase reaching a superheated condition. Then, the liquid undergoes an abrupt phase change by means of an oblique evaporation wave. Across this phase change the superheated liquid becomes a two-phase high-speed mixture in various directions, expanding to supersonic velocities. In order to reach the downstream pressure, the supersonic fluid continues to expand, crossing a complex bow shock wave. The balance equations that govern the phenomenon are mass conservation, momentum conservation, and energy conservation, plus an equation-of-state for the substance. A false-transient model is implemented using the shock capturing scheme: dispersion-controlled dissipative (DCD), which was used to calculate the flow conditions as the steady-state condition is reached. Numerical results with computational code DCD-2D vI have been analyzed. Copyright (C) 2009 John Wiley & Sons, Ltd.

Computer-Assisted Numerical Analysis for Oxygen and Carbon Dioxide Mass Transfer in Blood Oxygenators

A two-dimensional numeric simulator is developed to predict the nonlinear, convective-reactive, oxygen mass exchange in a cross-flow hollow fiber blood oxygenator. The numeric simulator also calculates the carbon dioxide mass exchange, as hemoglobin affinity to oxygen is affected by the local pH value, which depends mostly on the local carbon dioxide content in blood. Blood pH calculation inside the oxygenator is made by the simultaneous solution of an equation that takes into account the blood buffering capacity and the classical Henderson-Hasselbach equation. The modeling of the mass transfer conductance in the blood comprises a global factor, which is a function of the Reynolds number, and a local factor, which takes into account the amount of oxygen reacted to hemoglobin. The simulator is calibrated against experimental data for an in-line fiber bundle. The results are: (i) the calibration process allows the precise determination of the mass transfer conductance for both oxygen and carbon dioxide; (ii) very alkaline pH values occur in the blood path at the gas inlet side of the fiber bundle; (iii) the parametric analysis of the effect of the blood base excess (BE) shows that V(CO2) is similar in the case of blood metabolic alkalosis, metabolic acidosis, or normal BE, for a similar blood inlet P(CO2), although the condition of metabolic alkalosis is the worst case, as the pH in the vicinity of the gas inlet is the most alkaline; (iv) the parametric analysis of the effect of the gas flow to blood flow ratio (Q(G)/Q(B)) shows that V(CO2) variation with the gas flow is almost linear up to Q(G)/Q(B) = 2.0. V(O2) is not affected by the gas flow as it was observed that by increasing the gas flow up to eight times, the V(O2) grows only 1%. The mass exchange of carbon dioxide uses the full length of the hollow-fiber only if Q(G)/Q(B) > 2.0, as it was observed that only in this condition does the local variation of pH and blood P(CO2) comprise the whole fiber bundle.

Surface tension of flotation solution and its influence on the selectivity of the separation between apatite and gangue minerals

This work presents and discusses the influence of the surface tension (gamma(LV)) of methanol/water mixtures on the flotation response of apatite versus gangue minerals conditioned with flotation reagents (75 g/t cornstarch and 100 g/t Berol 867) at pH 10.6. Berol 867 is a collector composed of sodium alkyl sarcosinate plus nonionic surfactant. The highest Schulz efficiency of separation (recovery of apatite minus recovery of gangue) was achieved at approximate to 51.0 mN/m. The critical surface tension of wettability (gamma(C)) of apatite was found to occur at 34.7 mN/m when determined by means of gamma flotation experiments, , and it was 33.9 mN/m when determined by Zisman`s approach.

A contribution to the exact modal solution of in-plane beam structures

The exact vibration modes and natural frequencies of planar structures and mechanisms, comprised Euler-Bernoulli beams, are obtained by solving a transcendental. nonlinear, eigenvalue problem stated by the dynamic stiffness matrix (DSM). To solve this kind of problem, the most employed technique is the Wittrick-Williams algorithm, developed in the early seventies. By formulating a new type of eigenvalue problem, which preserves the internal degrees-of-freedom for all members in the model, the present study offers an alternative to the use of this algorithm. The new proposed eigenvalue problem presents no poles, so the roots of the problem can be found by any suitable iterative numerical method. By avoiding a standard formulation for the DSM, the local mode shapes are directly calculated and any extension to the beam theory can be easily incorporated. It is shown that the method here adopted leads to exact solutions, as confirmed by various examples. Extensions of the formulation are also given, where rotary inertia, end release, skewed edges and rigid offsets are all included. (C) 2008 Elsevier Ltd. All rights reserved.

Evidences of the evolution from solid solution to surface segregation in Ni-doped SnO(2) nanoparticles using Raman spectroscopy

Ni-doped SnO(2) nanoparticles, promising for gas-sensing applications, have been synthesized by a polymer precursor method. X-ray diffraction (XRD) and transmission electron microscopy (TEM) data analyses indicate the exclusive formation of nanosized particles with rutile-type phase (tetragonal SnO(2)) for Ni contents below 10 mol%. The mean crystallite size shows a progressive reduction with the Ni content. Room-temperature Raman spectra of Ni-doped SnO(2) nanoparticles show the presence of Raman active modes and modes activated by size effects. From the evolution of the A(1g) mode with the Ni content, a solubility limit at similar to 2 mol% was estimated. Below that content, Raman results are consistent with the occurrence of solid solution (ss) and surface segregation (seg.) of Ni ions. Above similar to 2 mol% Ni, the redshift of A(1g) mode suggests that the surface segregation of Ni ions takes place. Disorder-activated bands were determined and their integrated intensity evolution with the Ni content suggest that the solid-solution regime favors the increase of disorder; meanwhile, that disorder becomes weaker as the Ni content is increased. Copyright (C) 2010 John Wiley & Sons, Ltd.

Selective corrosion of 550 degrees C aged Cu10Ni-3Al-1.3Fe alloy in NaCl aqueous solution

This work studied the electrochemical behavior of a solution treated or 550 degrees C aged Cu10Ni-3Al-1.3Fe alloy, in 0.01 M NaCl aqueous solution, through potentiodynamic polarization in both stagnant condition or under erosion process. Results showed the occurrence of a passivity break potential (E(pb)), related to the beginning of the denickelification process, which occurred as a localized attack under stagnant electrolyte. Under erosion conditions localized denickelification was not observed, despite of the presence of E(pb). This could indicate that selective corrosion of Ni, which caused the observed E(pb), occurred as a dissolution-redeposition process, with removal of the Cu deposits during erosion process. (C) 2011 Elsevier Ltd. All rights reserved.

Degradation of Poly(ethylene glycol) in Aqueous Solution by Photo-Fenton and H(2)O(2)/UV Processes

This article reports experimental results obtained in a laboratory-scale photochemical reactor on the photodegradation of poly(ethylene glycol) (PEG) in aqueous solutions by means of the photo-Fenton and H(2)O(2)/UV processes. Dilute water solutions of PEG were fed to a batch reactor, mixed with pertinent reactants, and allowed to react under different conditions. Reaction progress was evaluated by sampling and analyzing the concentration of the total organic carbon (TOC) in solution as a function of the reaction time. Organic acids formed during oxidation were determined by HPLC analyses. The main acids detected in both processes were acetic and formic. Glycolic acid was detected only in the photo-Fenton process, and malonic acid was detected only in the H(2)O(2)/UV treatment, indicating that different reaction paths occur in these processes. The characteristics of both processes are discussed, based on the evolution of the TOC-time curves and the concentration profiles of the monitored organic acids. The experimental results constitute a contribution to the design of industrial processes for the treatment of wastewaters containing soluble polymers with similar properties.

Coalescence of Water Droplets in Crude Oil Emulsions: Analytical Solution

In petroleum refineries, water is used in desalting units to remove the salt contained in crude oil. Typically, 7% of the volume of hot crude oil is water, forming a water-and-oil emulsion. The emulsion flows between two electrodes and is subjected to an electric field. The electrical forces promote the coalescence of small droplets of water dispersed in crude oil, and these form bigger droplets. This paper calculates the forces acting on the droplets, highlighting particularly the mechanisms proposed for droplet-droplet coalescence under the influence of an applied electric field. Moreover, a model is developed in order to calculate the displacement speed of the droplets and the time between droplet collisions. Thus, it is possible to simulate and optimize the process by changing the operational variables (temperature, electrical field, and water quantity). The main advantage of this study is to show that it is feasible to increase the volume of water recycled in desalting processes, thus reducing the use of freshwater and the generation of liquid effluents in refineries.

Use of SECM to study the electrochemical behavior of DIN 1.4575 superferritic stainless steel aged at 475 degrees C

In order to lower the excessive costs of metallic prosthesis materia Is alternatives to Ti and Ti alloys have been searched. in this study, the corrosion resistance of the DIN 1.4575 superferritic stainless steel, either solution annealed or solution annealed and aged at 475 degrees C for periods varying from 100 to 1080 h, was investigated by electrochemical impedance spectroscopy (EIS) and potentiodynamic polarization methods in Hanks` solution. The solution annealed and the aged for 1080 h samples were also tested using scanning electrochemical microscopy (SECM) in a 0.1 mol/L NaCl solution at 25 degrees C. The EIS results showed that the corrosion resistance of the DIN 1.4575 steel decreases with heat treatment time at 475 degrees C probably due to alpha prime formation. Besides the diminution of the overall impedance values, the low frequency limit of the Nyquist diagrams show a progressive change from an almost capacitive response to a resistive behavior as the heat treatment time increases. Pitting corrosion resistance also decreased with aging time at 475 degrees C.

New Analytic Solution Related to the Richards, Philip, and Green-Ampt Equations for Infiltration

Based on physical laws of similarity, an analytic solution of the soil water potential form of the Richards equation was derived for water infiltration into a homogeneous sand. The derivation assumes a similarity between the soil water retention function and that of the soil water content profiles taken at fixed times. The new solution successfully described soil water content profiles experimentally measured for water infiltrating downward, upward, and horizontally into a homogeneous sand and agrees with that presented by Philip in 1957. The utility of this analysis is still to be verified, but it is expected to hold for soils that have a narrow pore-size distribution before wetting and that manifest a sharp increase of water content at the wetting front during infiltration. The effect of van Genuchten`s parameters alpha and n on the application of the solution to other porous media was investigated. The solution also improves and provides a more realistic description of the infiltration process than that pioneered by Green and Ampt in 1911.

New Analytic Solution of Boltzmann Transform for Horizontal Water Infiltration into Sand

The use of the Boltzmann transform function, lambda(theta), to solve the Richards equation when the diffusivity, D, is a function of only soil water content,., is now commonplace in the literature. Nevertheless, a new analytic solution of the Boltzmann transform lambda(h) as a function of matric potential for horizontal water infiltration into a sand was derived without invoking the concept or use of D(theta). The derivation assumes that a similarity exists between the soil water retention function and the Boltzmann transform lambda(theta). The solution successfully described soil water content profiles experimentally measured for different infiltration times into a homogeneous sand and agrees with those presented by Philip in 1955 and 1957. The applicability of this solution for all soils remains open, but it is anticipated to hold for soils whose air-filled pore-size distribution before wetting is sufficiently narrow to yield a sharp increase of water content at the wetting front during infiltration. It also improves and provides a versatile alternative to the well-known analysis pioneered by Green and Ampt in 1911.

Distribution and storage characterization of soil solution for drip irrigation

The increased use of marginal quality water with drip irrigation requires sound fertigation practices that reconcile environmental concerns with viable crop production objectives. We conducted experiments to characterize dynamics and patterns of soil solution within wet bulb formed by drip irrigation. Time-domain reflectometry probes were used to monitor the distribution of potassium nitrate (KNO(3)) and water distribution from drippers discharging at constant flow rates of 2, 4 and 8 L h(-1) in soil-filled containers. Considering results from different profiles, we observed greater solute storage near the dripper decreasing gradually towards the wetting front. About half of the applied KNO(3) solution (48%) was stored in the first layer (0-0.10 m) for all experiments, 29% was stored in the next layer (0.10-0.20 m). Comparing different dripper flow rates, we observed higher solution storage for 4 L h(-1), with 45, 53 and 47% of applied KNO(3) solution accumulating in the first layer (0-0.10 m) for dripper flow rates of 2, 4 and 8 L h(-1), respectively. The results suggest that based on the volume and frequency used in this experiment, it would be advantageous to apply small amounts of solution at more frequent intervals to reduce deep percolation losses of applied water and solutes.

Modeling of transpiration reduction in van Genuchten-Mualem type soils

We derive an analytic expression for the matric flux potential (M) for van Genuchten-Mualem (VGM) type soils which can also be written in terms of a converging infinite series. Considering the first four terms of this series, the accuracy of the approximation was verified by comparing it to values of M estimated by numerical finite difference integration. Using values of the parameters for three soils from different texture classes, the proposed four-term approximation showed an almost perfect match with the numerical solution, except for effective saturations higher than 0.9. Including more terms reduced the discrepancy but also increased the complexity of the equation. The four-term equation can be used for most applications. Cases with special interest in nearly saturated soils should include more terms from the infinite series. A transpiration reduction function for use with the VGM equations is derived by combining the derived expression for M with a root water extraction model. The shape of the resulting reduction function and its dependency on the derivative of the soil hydraulic diffusivity D with respect to the soil water content theta is discussed. Positive and negative values of dD/d theta yield concave and convex or S-shaped reduction functions, respectively. On the basis of three data sets, the hydraulic properties of virtually all soils yield concave reduction curves. Such curves based solely on soil hydraulic properties do not account for the complex interactions between shoot growth, root growth, and water availability.

Nickel adsorption in two Oxisols and an Alfisol as affected by pH, nature of the electrolyte, and ionic strength of soil solution

Background, aim, and scope The retention of potentially toxic metals in highly weathered soils can follow different pathways that variably affect their mobility and availability in the soil-water-plant system. This study aimed to evaluate the effects of pH, nature of electrolyte, and ionic strength of the solution on nickel (Ni) adsorption by two acric Oxisols and a less weathered Alfisol. Materials and methods The effect of pH on Ni adsorption was evaluated in surface and subsurface samples from a clayey textured Anionic `Rhodic` Acrudox ( RA), a sandy-clayey textured Anionic `Xantic` Acrudox (XA), and a heavy clayey textured Rhodic Kandiudalf (RK). All soil samples were equilibrated with the same concentration of Ni solution (5.0 mg L(-1)) and two electrolyte solutions (CaCl(2) or NaCl) with different ionic strengths (IS) (1.0, 0.1 and 0.01 mol L(-1)). The pH of each sample set varied from 3 to 10 in order to obtain sorption envelopes. Results and discussion Ni adsorption increased as the pH increased, reaching its maximum of nearly pH 6. The adsorption was highest in Alfisol, followed by RA and XA. Competition between Ni(2+) and Ca(2+) was higher than that between Ni(2+) and Na(+) in all soil samples, as shown by the higher percentage of Ni adsorption at pH 5. At pH values below the intersection point of the three ionic strength curves (zero point of salt effect), Ni adsorption was generally higher in the more concentrated solution (highest IS), probably due to the neutralization of positive charges of soil colloids by Cl(-) ions and consequent adsorption of Ni(2+). Above this point, Ni adsorption was higher in the more diluted solution (lowest ionic strength), due to the higher negative potential at the colloid surfaces and the lower ionic competition for exchange sites in soil colloids. Conclusions The effect of ionic strength was lower in the Oxisols than in the Alfisol. The main mechanism that controlled Ni adsorption in the soils was the ionic exchange, since the adsorption of ionic species varied according to the variation of pH values. The ionic competition revealed the importance of electrolyte composition and ionic strength on Ni adsorption in soils from the humid tropics. Recommendations and perspectives The presence of NaCl or CaCl(2) in different ionic strengths affects the availability of heavy metals in contaminated soils. Therefore, the study of heavy metal dynamics in highly weathered soils must consider this behavior, especially in soils with large amounts of acric components.