Peterson Equation Research Articles

Prediction of Net Steady-State Wear Coefficient in an Al-Al2O3(P)/Steel System with an Integrated Wear Model

Experimental pin-on-disc wear tests were carried out previously on three types of commercial A6061 aluminum-based matrix composites (MMCs) reinforced with 10, 15 and 20% alumina particles, respectively, against steel disc, with both the moving-pin technique developed at Nanyang Technological University and the conventional pin-on-disc technique. An integrated wear model was established, with the transient wear volume described by an exponential equation while the steady-state wear by a revised Archard equation. A wear coefficient equation was formulated by using the transient wear data to model the standard wear coefficients of both the transient wear and the steady-state wear successfully. In this study, a new equation was developed from the previous model to predict the net steady-state wear coefficient. With a F A value of 0.999 or 0.9999, the average deviation from the measured values was about 26%. F A was an exponential function used in the transient wear equation. On the other hand, Peterson's equation was also found suitable for modeling the steady-state wear of the three types of aluminium-based matrix composites. However it lacked some of the features the newly proposed equation could provide.

Pseudo‐first‐order kinetic studies of the sorption of acid dyes onto chitosan

AbstractThe adsorption of five acid dyes onto chitosan, derived through the deacetylation of crab‐shell chitin, from aqueous solutions was studied. The equilibrium isotherms were measured and analyzed with the Langmuir, Freundlich, and Redlich–Peterson equations; the results correlated well with the Langmuir equation. Kinetic studies were also performed in an agitated batch adsorber to study the effect of the initial dye concentration and the mass of chitosan. The kinetics were analyzed with the pseudo‐first‐order rate equation, and the rate constants were determined. The first‐order kinetic model correlated the experimental concentration and time data at short times and even up to 60% of the total adsorption period in a number of systems. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 1633–1645, 2004

Adsorption of acid dyes on chitosan—equilibrium isotherm analyses

The ability of chitosan, derived from deacetylated crab shell chitin, to remove acid dyes from effluent solution by adsorption has been studied. Equilibrium isotherms for the adsorption of five acid dyes, Acid Green 25 (AG25), Acid Orange 10 (AO10), Acid Orange 12 (AO12), Acid Red 18 (AR18) and Acid Red 73 (AR73), on chitosan were measured experimentally. Results were analysed by the Langmuir, Freundlich and Redlich–Peterson (R–P) equation using a linearised correlation coefficient. The Langmuir isotherm gave the best correlation for the adsorption of AG25, AR18, AR73 and AO12 while the composite Freundlich isotherm gave excellent correlation for AO10. The equilibrium data were then analysed using five different non-linear error analysis methods and two significant findings were obtained. Firstly, the order of isotherm selection was changed showing that the R–P equation had the lowest error values for all five acid dye-chitosan isotherms. Secondly, the values of the individual isotherm constants changed with the error methodology selected.

Equilibrium studies for the sorption of lead from effluents using chitosan

The sorption of lead ions from aqueous solution onto chitosan has been studied. Equilibrium studies have been carried out to determine the capacity of chitosan for lead ions. The effects of solution pH and chitosan particle size on the sorption capacity have been studied. The experimental data were analyzed using three equilibrium isotherm correlations, namely, Langmuir, Freundlich and Redlich–Peterson equations. The linear correlation coefficients were determined for each isotherm and the Freundlich provided the best fit. In addition, error functions have been used to determine the alternative single component equilibrium isotherm parameters by non-linear regression due to the inherent bias in using the correlation coefficient from the linearization. This technique enables the “best fit” isotherm parameters to be used in the equilibrium equations for the sorption of lead ions on chitosan within the limits and assumptions of the various error analysis methods.

Equilibrium Studies of the Sorption of Cu(II) Ions onto Chitosan

Chitosan is a polymer that can be obtained from the shells of seafood such as prawns, crabs, and lobsters. Chitosan has free amino groups, which can attract metal ions, and has been used as an adsorbent for the removal of metal ions from effluents. In this research, the sorption of copper ions from solution onto chitosan at two pHs has been investigated. DSC, TGA, surface area, SEM, and NMR studies have been used to report the pure physical states of chitosan and the chitosan–copper complex. The experimental isotherm data were analyzed using the Langmuir, Freundlich, and Redlich–Peterson equations. Correlation coefficients were determined for each isotherm analysis. Error functions have been used to determine the alternative single component parameters by nonlinear regression due to the inherent bias in using the correlation coefficient resulting from linearization. The error function method provided the best parameters for the isotherm equations in this system and is demonstrated for error comparison purposes.

Interaction of Carboxylic Acids with Chitosan: Effect of pK and Hydrocarbon Chain Length

Sorption of acetic, propionic, butyric, valeric, and isovaleric acid on chitosan and cross-linked chitosan was studied in aqueous solutions and water/ethanol mixtures. Langmuir, Freundlich, and Redlich–Peterson equations were used to fit experimental isotherms of sorption. Correlation between maximum sorption and the pK value of every carboxylic acid was found for sorption on chitosan in aqueous solutions, while sorption in water/ethanol mixtures was mainly determined by structure and the hydrocarbon chain length of the carboxylic acid. Slight molecular-sieves effect was found for carboxylic acids sorption on cross-linked chitosan.

Adsorption Isotherms of Aspartame on Commercial and Chemically Modified Divinylbenzene−Styrene Resins at Different Temperatures

The equilibria of adsorption of aspartame in an aqueous solution on a commercial resin and three chemically modified Amberlite XAD-2 resins were measured at different temperatures within the range (0 to 35) °C. The functional groups, introduced by nucleophilic substitution in the aromatic rings of the divinylbenzene−styrene matrix, were bromine (−Br), bromoethyl (−CH2CH2Br), and chloromethyl (−CH2Cl). All of the isotherms showed a nonlinear and favorable shape with decreasing adsorption capacity as the temperature increased. The chloromethylated resin, and, to a lesser degree, the bromoethylated resin, increased the adsorption capacity for aspartame compared to Amberlite XAD-2. At 35 °C, the chloromethyl resin showed up to a 280% higher saturation capacity than the commercial adsorbent. The experimental equilibrium data were fitted to the Langmuir, Freundlich, Langmuir−Freundlich, Redlich−Peterson, and Toth models. Toth and Langmuir−Freundlich isotherms provided very good fittings for all of the resins over the temperature range studied, whereas the Langmuir and Redlich−Peterson equations were less accurate, although the average errors were, in general, below 10% with respect to the measured values.

Adsorption isotherms of phenols from water onto macroreticular resins

The amounts of equilibrium adsorption of phenol and 4-chlorophenol from water on non-ionic macroreticular resins were measured in the temperature range 288–318 K. It was shown that the isotherm data could not be fit by any conventional two- or three-parameter equation including the Langmuir, Freundlich, BET, and Redlich–Peterson equations over the entire range of concentration (1–32 mol m −3). They were well fit by combined BET equation or its modified form with the Freundlich or Langmuir equation, depending on the types of solutes and the resins. Such different fitting results could be related to the solute–resin interactions owing to the relatively wide pore size distribution of the resins. The effect of temperature on adsorption equilibrium was also discussed.

Adsorption behavior of reactive dyes from aqueous solutions on chitosan

The capability of the use of chitosan for removing vinyl sulfone and chlorotriazine reactive dyes from aqueous solutions was examined, including equilibrium and dynamic studies. Experiments were performed as a function of dye concentration, and the amount and particle size of chitosan. It was shown that the adsorption capacities of chitosan were comparatively high for the three investigated dyes. The equilibrium data could be best fitted by the Redlich–Peterson equation over the entire concentration range (50–500 g m−3). A comparison of the adsorption capacity among such adsorbents as chitin and powdered activated carbon was made. Two rate parameters were finally obtained to describe the adsorption process on a quantitative basis. These parameters could be well correlated to the amount and particle size of dry chitosan. ©1997 SCI

A method of predicting the fatigue life curve for misaligned welded joints

The effects of material properties, manner of loading, geometric shape, value of misalignment, residual stress, stress ratio and short crack in notch root of misaligned welded joint on the fatigue life are considered respectively. By means of Peterson's equation and Topper's equation and the concept of the worst-case fatigue notch factor, two estimating equations of effective stress concentration factors have been adopted. A method for predicting the fatigue life curve of misaligned welded joints for middle range of cycle numbers is developed. As an example of application of the method, the fatigue life curves of several misaligned welded joints made of low-alloy structural steel are predicted. Good agreement between the predicting and experimental results is achieved. This method has significance for engineering applications.

A new approach to the prediction of fatigue notch reduction factor Kf

Abstract From the point of view of energy, a fundamental relationship of local stress-strain at a notch is derived. Defining K f , the fatigue notch reduction factor, in terms of such factors as cyclic behaviour of material, plastic deformation of notch root and theoretical stress concentration factor, an equation for K f taking into consideration comprehensively is proposed, and verified by the results of experimental K f and then compared with the values of K f predicted from the Neuber-Kuhn and Peterson equations.

Solid Difusion in the pores of cellulose membrane

The diffuson kinetics of dye molecules (C.I. Direct Yellow 12) adsorbed in porous cellulose membrane is investigated. A solid diffusion model with concentration-dependent diffusivity (SDCDD model) is utilized to fit the experimental uptake curves (UCs) and concentration profiles (CPs). The experimental equilibrium data are well fitted by the Freundlich as well as the Redlich—Peterson model. On the basis of the Redlich—Peterson isotherm equation, the SDCDD model is able to simulate the experimental UCs and CPs for a wide variety of conditions. The simulations reveal a high sensitivity of the SDCDD model to variations in the course of the sorption isotherm. This property entails that the Freundlich model, although equivalent to the Redlich—Peterson equation with respect to fitting the equilibrium data, is not able to reflect the concentration dependence of CPs. The SDCDD model (in association with the Redlich—Peterson isotherm) is demonstrated to be the necessary alternative of the parallel diffusion model proposed by Yoshida .

Argon ion excitation by relativistic electrons: I. Collision cross sections and deposition efficiencies

Calculations of the electron impact excitation cross sections and deposition efficiencies for singly ionized argon with electrons of energies up to and including relativistic values have been made using the first Born approximation and the generalized oscillator formalism. Deposition efficiencies for fast electrons were generated from the Peterson and Green integral equation. Cross sections and efficiencies were produced for 29 transitions from the ground state configuration of Arii to excited energy levels with (Ne)3s23p44sand (Ne)3s23p43dconfigurations and for 40 transitions between excited energy levels from 4sand 3dto 4porbitals. Efficiencies are constant for electron energies above 1 keV to 10 MeV. Electrons ejected from inner shells contribute up to 12% of the efficiency of the transition for electrons above 10 keV.

The effects of change of work on the work decrement.

Based on results secured with a Whipple A cancellation and Peterson equations tests the author concludes that change of work does not entirely eliminate the decrement, but it lessens it to a large extent. Results are presented showing practice effects on decrements in different work intervals, as well as in continuous work. (PsycINFO Database Record (c) 2012 APA, all rights reserved)