Analytical solutions for protective filters based on soil-retention and permeability criteria with respect to the phenomenon of soil boiling

For the successful performance of a granular filter medium, existing design guidelines, which are based on the particle size distribution (PSD) characteristics of the base soil and filter medium, require two contradictory conditions to be satisfied, viz., soil retention and permeability. In spite of the wider applicability of these guidelines, it is well recognized that (i) they are applicable to a particular range of soils tested in the laboratory, (ii) the design procedures do not include performance-based selection criteria, and (iii) there are no means to establish the sensitivity of the important variables influencing performance. In the present work, analytical solutions are developed to obtain a factor of safety with respect to soil-retention and permeability criteria for a base soil - filter medium system subjected to a soil boiling condition. The proposed analytical solutions take into consideration relevant geotechnical properties such as void ratio, permeability, dry unit weight, effective friction angle, shape and size of soil particles, seepage discharge, and existing hydraulic gradient. The solution is validated through example applications and experimental results, and it is established that it can be used successfully in the selection as well as design of granular filters and can be applied to all types of base soils.

Beta-structure of polypeptides in non-aqueous solutions. I. Spectral characteristics of the polypeptide backbone

The optical rotatory features of the beta-structure of the polypeptides in non-aqueous solutions and films cast from these solutions have been investigated. The beta-structure of poly-S-benzyl-L-cysteine, poly-S-carbobenzoxy-L-cysteine and poly-S-benzyl-L-cysteine, poly-S-carbobenzoxy-L-cysteine and poly-O-carbo-bands of their films. The optical rotatory dispersion (ORD) and circular dichroism (CD) spectra of these polypeptides are found to be very similar in both film and solution. In solvents promoting the beta-structure, the polypeptides are characterized by CD troughs in the n-pi* transition region of the peptide chromophore. The ORD spectra are found to be positive in sign throughout the visible and accessible ultraviolet regions and are interpreted in terms of the possible existence of a relatively much larger positive pi-pi* CD bands as compared with the negative n-pi* band. The rotatory data obtained in the non-aqueous solution are compared with those obtained for other poly peptides in aqueous solutions, with respect to the type and extent of beta-structure present.

Beta-structure of polypeptides in non-aqueous solutions. II. Side-chain orientation

The specific side-chain orientations of the phenyl group in the polypeptides poly-S-benzyl-L-cysteine, poly-S-carbobenzoxy-L-cysteine and poly-O-carbobenzoxy-L-serine in the beta-structure have been studied by spectral measurements in solutions. All the three polypeptides exhibit aromatic CD bands, indicating the asymmetric placement of the side-chain phenyl rings when the polypeptide backbone takes up the antiparallel beta-structure. Supporting evidence for this is derived from n.m.r. spectra of the polypeptides, which show upfield shift of the phenyl protons due to the stacking of the aromatic rings. Molecular model building studies reveal the stacking of alternate phenyl groups along the polypeptide chain.

Closed form solutions for element equilibrium and flexibility matrices of eight node rectangular plate bending element using integrated force method

Closed form solutions for equilibrium and flexibility matrices of the Mindlin-Reissner theory based eight-node rectangular plate bending element (MRP8) using integrated Force Method (IFM) are presented in this paper. Though these closed form solutions of equilibrium and flexibility matrices are applicable to plate bending problems with square/rectangular boundaries, they reduce the computational time significantly and give more exact solutions. Presented closed form solutions are validated by solving large number of standard square/rectangular plate bending benchmark problems for deflections and moments and the results are compared with those of similar displacement-based eight-node quadrilateral plate bending elements available in the literature. The results are also compared with the exact solutions.

Activities of oxygen and lead in Pb-Ag O solutions

The reversible e.m.f. of galvanic cells: stainlesssteel,Ir,Pb+PbO|CaO+ZrO2|Ag+Pb+PbO,Ir,stainlesssteel,I and Pt,Ni+NiO|CaO+ZrO2|O(Pb+Ag),Cermet,Pt,II incorporating solid oxide electrolytes were measured as a function of alloy composition. In lead-rich alloys, the temperature dependence of the e.m.f. of cell I was also investigated. Since the solubility of oxygen in the alloy is small, the relative partial molar properties of lead in the binary Ag + Pb system can be calculated from the e.m.f. of this cell. The Gibbs free energies obtained in this study are combined with selected calorimetric data to provide a complete thermodynamic discription of liquid Ag + Pb Alloys. The activity coefficient of oxygen in the whole range of Ag + Pb alloys at 1273 K have been obtained from the e.m.f. of cell II; and these are found to deviate positively from Alcock and Richardson's quasichemical equation when the average co-ordination number of all the atoms is assigned a value of 2.

Prediction of activities of oxygen in dilute quaternary solutions using binary data

Equations are developed for predicting the activity coefficients of oxygen dissolved in ternary liquid alloys. These are extensions of earlier treatments, and are based on a model in which each oxygen atom is assumed to make four bonds with neighboring metal atoms. It is also postulated that the strong oxygen-metal bonds distort the electronic configuration around the metal atoms bonded to oxygen, and that the quantitative reduction of the strength of bonds made by these atoms with all of the adjacent metal atoms is equivalent to a factor of approximately two. The predictions of the quasichemical equation which is derived agree satisfactorily with the partial molar free energies of oxygen in Ag-Cu-Sn solutions at 1200°C reported in literature. An extension of this treatment to multicomponent solutions is also indicated.

Thermodynamics of solid solutions of silver with indium and tin

A solid oxide galvanic cell and a gas-solid (View the MathML source) equilibration technique have been used to measure the activities of the solutes in the α-solid solutions of silver with indium and tin. The results are consistent with the information now available for the corresponding liquid alloys, the phase diagram and the heats of mixing of the solid alloy. When the results of this study are taken together with published data for the α-solid solutions in Ag + Cd system, it is found that the variation of the excess partial free energy of the solute with mole fraction can be correlated to the electron/atom ratio. The significant thennodynamic parameter that explains the Hume-Rothery findings in these alloys appears to be the rate of change of the excess partial free energy with composition near the phase boundary, and this in turn reflects the value of the solute-solute interaction energy.

Activities of indium in solid solutions of Cu+In, Au+In and Cu+Au+In alloys

Thin foils of Cu, Au and Cu + Au alloys embedded in indium sesquioxide were equilibrated with controlled streams of CO-CO2 mixtures. The equilibrium concentrations of indium in the foils were determined by neutron activation analysis. The corresponding chemical potentials of indium were calculated from the standard free energies of formation of carbon monoxide, carbon dioxide, and indium oxide. It was found that the size difference between the solute and the solvent does not make significant contributions to the solute—solute interaction energy in the α-phase. The chemical potential of indium at one at.% concentration is 8.6 Kcals more negative in gold than in copper at 900°K. The variation of this chemical potential with alloy composition in Cu + Au system was in good agreement with Alcock and Richardson's quasichemical equation. The agreement is strengthened by the accurate knowledge of the co-ordination number in these substitutional solid solutions from X-ray diffraction studies.

Chemical potential of germanium in its solid solutions with Cu, Ag and Au

Thin foils of copper, silver and gold were equilibrated with tetragonal GeO2 under controlled View the MathML source gas streams at 1000 K. The equilibrium concentration of germanium in the foils was determined by the X-ray fluorescence technique. The standard free energy of formation of tetragonal GeO2 was measured by a solid oxide galvanic cell. The chemical potential of germanium calculated from the experimental data and the free energies of formation of carbon monoxide and carbon dioxide was found to decrease in the sequence Ag + Ge > Au + Ge > Cu + Ge. The more negative value for the chemical potential of germanium in solid copper, compared to that in solid gold, cannot be explained in terms of the strain energy factor, electro-negativity differences or the vaporization energies of the solvent, and suggests that the d band and its hybridization with s electrons are an important factor in determining the absolute values for the chemical potential in dilute solutions. However, the variation of the chemical potential with solute concentration can be correlated to the concentration of s and p electrons in the outer shell.

Solute solute and solvent solute interactions in solid solutions of Cu+Sn, Au+Sn and Cu+Au+Sn alloys

The chemical potentials of tin in its α-solid solutions with Cu, Au and Cu + Au alloys have been measured using a gas-solid equilibration technique. The variation of the excess chemical potential of tin with its composition in the alloy is related to the solute-solute repulsive interaction, while the excess chemical potential at infinite dilution of the solute is a measure of solvent-solute interaction energies. It is shown that solute-solute interaction is primarily determined by the concentration of (s + p) electrons in the conduction band, although the interaction energies are smaller than those predicted by either the rigid band model or calculation based on Friedel oscillations in the potential function. Finally, the variation of the solvent-solute interaction with solvent composition in the ternary system can be accounted for in terms of a quasi-chemical treatment which takes into account the clustering of the solvent atoms around the solute.

Ion exchange equilibria between (Mn,Co)O solid solution and (Mn,Co)Cr2O4 and (Mn,Co)Al2O4 spinel solid solutions at 1100oC

The compositions of the (Mn,Co)O solid solution with rock salt structure in equilibrium with (Mn,Co)Cr2O4 and (Mn,Co)Al2O4 spinel solid solutions have been determined by X-ray diffraction measurements at 1100° C and an oxygen partial pressure of 10–10 atm. The ion exchange equilibria are quantitatively analysed, using values for activities in the (Mn,Co)O solid solution available in the literature, in order to obtain activities in the spinel solid solutions. The MnAl2O4-CoAl2O4 solid solution exhibits negative deviations from Raoult's law, consistent with the estimated cation disorder in the solid solution, while the MnCr2O4-CoCr2O4 solid solution shows slightly positive deviations. The difference in the Gibbs free energy of formation of the two pure chromites and aluminates derived from the results of this study are in good agreement with recent results obtained from solid oxide galvanic cells and gas-equilibrium techniques.

Activities and their relation to cation distribution in NiAl2O4 MgAl2O4 spinel solid solutions

The activity of NiAl2O4 in NiAl2O4MgAl2O4 solid solutions has been measured by using a solid oxide galvanic cell of the type, Pt, Ni + NiAl2O4 + Al2O3(α)/CaOZrO2/Ni + NixMg1−xAl2O4 + Al2O3(α). Pt, in the temperature range 750–1150°C. The activities in the spinel solid solutions show negative deviations from Raoult's law. The cation distribution in the solid solutions has been calculated using site preference energies independent of composition for Ni2+, Mg2+, and Al3+ ions obtained from crystal field theory and measured cation disorder in pure NiAl2O4 and MgAl2O4, and assumi g ideal mixing of cations on the tetrahedral and octahedral positions. The calculated values correctly predict the decrease in the fraction, α, of Ni2+ ions on tetrahedral sites for 1>x>0.25, observed by Porta et al. [J. Solid State Chem.11, 135 (1974)] but do not support their tentative evidence for an increase in α for x < 0.25. The measured excess free energy of mixing can be completely accounted for by using either the calculated or the measured cation distributions. This suggests that the Madelung energy is approximately a linear function of composition in the solid solutions. The composition of NiOMgO solid solutions in equilibrium with NiAl2O4MgAl2O4 solid solutions has been calculated from the results and information available in literature.

Electrochemical determination of activities in Cr2O3 Al2O3 solid solutions

The activity of Cr20~ in Cr20~-A12Oa solid solution has been determined in the temperature range 800~176 from electromotive force measurements on the solid oxide galvanic cell Pt,Cr + Cr2OJY~O~-ThO2/Cr + Cr~A12-xO~,Pt The activities of Cr203 and A120~ in the solid solution show both positive and negative deviations from Raoult's law. The heat and entropy of mixing of the solid Solution obtained from the temperature dependence of the emf can be expressed as AH = XCr203XA1203 [31,700Xcrzo3 -}- 37,470XA1203] J mole -I hS = -- 1.8R [Xcr2o3 In Xcr2o3 + XA12o3 In XAaos]The entropy of mixing is 10% lower than that predicted by the Temkin model.The large positive heat of mixing in the Cr2Os-A12Oa solid solution, however, suggests that this apparent: entropy discrepancy originates with the clustering of positive ions on the cation sublattice. The asymmetric miscibility gap exhibited in the CrzOa-A12Oa system below 900~ is consistent with the thermodynamic data trends recorded at the more elevated temperatures.