scholarly journals III. On certain ternary alloys. Part V. Determination of various critical curves, and their tie-lines and limiting points

1892 ◽  
Vol 50 (302-307) ◽  
pp. 372-395 ◽  
Keyword(s):  
Graphical Representation ◽  
Conjugate Point ◽  
Critical Curve ◽  
Ternary Mixtures ◽  
Ternary Alloys ◽  
Conjugate Points ◽  
Critical Curves ◽  
Tie Lines ◽  
Tie Line

The triangular method of graphical representation suggested by Sir G. G. Stokes, and described in Part IV (‘Roy. Soc. Proc.,’ vol. 49, p. 174), substantially amounts to the tracing out of a curve (“ critical curve”) which shall express the saturation of the solvent C with a mixture in given variable proportions of the other two constituents, A, B ; the variation being such that any given point on the curve is related to some other point (“ conjugate point ”) in a way given by the consideration that all mixtures of the three constituents, A, B, C, represented by points lying on the line (“ tie-line ”) joining these two conjugate points (“ ideal ” alloys, or mixtures), will separate into two different ternary mixtures corresponding with the two points respectively ; whereas any mixture of the same constituents, repre­sented by a point lying outside the critical curve, will form a “ real ” alloy, or mixture, not separating spontaneously into two different fluids but existing as a stable homogeneous whole.

Ternary mixtures of phosphonium ionic liquids + organic solvents + water

2008 ◽  
Vol 80 (6) ◽  
pp. 1325-1335 ◽  
Author(s):  
Shahana A. Chowdhury ◽  
Janet L. Scott ◽  
Douglas R. MacFarlane
Keyword(s):  
Ionic Liquids ◽  
Organic Solvents ◽  
Ternary Phase ◽  
Single Phase ◽  
Ternary Mixtures ◽  
Green Solvents ◽  
Ternary Phase Diagrams ◽  
Tie Lines ◽  
Extraction Processes ◽  
Tie Line

Ionic liquids (ILs) and water are both potentially green solvents that are useful in a variety of extraction processes. This report presents the ternary phase diagrams and tie-line data of trihexyl(tetradecyl)phosphonium dicyanamide [P6,6,6,14][DCA], phosphonium bis(2,4,4-trimethylpentyl)phosphinate [P6,6,6,14][((CH3)3C5H8)2PO2], and 1-ethyl-3-methylimidazolium ethylsulfate [emim][C2H5SO4] ILs in organic solvents (ethanol, acetonitrile, toluene) and water. [P6,6,6,14][DCA] and [P6,6,6,14][((CH3)3C5H8)2PO2] tended to yield emulsions when combined with water and ethanol, while [emim][C2H5SO4] combined with toluene and water provided two clear phases of reasonable viscosity. The compositions of the ternary mixtures were determined to obtain the tie-lines. A noticeable difference was observed for the tie-lines of the same IL (e.g., [P6,6,6,14][DCA]) with different organic solvents (ethanol and acetonitrile) and water mixtures. In all cases, the addition of ethanol eventually produced a single phase.

Phase Equilibria of the Nickel-Aluminium-Chromium System at 1150°C

2006 ◽  
Vol 522-523 ◽  
pp. 103-110 ◽  
Author(s):  
Yuri Kitajima ◽  
Shigenari Hayashi ◽  
Toshio Narita
Keyword(s):  
Phase Equilibria ◽  
Ternary Alloys ◽  
Diffusion Couples ◽  
X Ray Diffraction ◽  
Β Phase ◽  
Third Phase ◽  
Tie Lines ◽  
Cr System ◽  
And Diffusion

Phase equilibria in the Ni-Al-Cr system at 1150°C were investigated by using annealed ternary alloys and diffusion couples. The phase constitutions, microstructures, and tie-lines were determined by conventional techniques, including X-ray diffraction, scanning electron microscopy and electron probe microanalysis. The solubility limits of Cr was found to be about 9at.% in the γ’ and 17at.% in the β phase. The size of second or third phase precipitates in the alloys was found to affect the determination of the tie-lines by the micro probe analysis.

ON CRITICAL CURVES IN TWO-DIMENSIONAL ENDOMORPHISMS

2001 ◽  
Vol 11 (03) ◽  
pp. 821-839 ◽  
Author(s):  
J. C. CATHALA
Keyword(s):  
Critical Curve ◽  
Two Dimensional ◽  
Curve Segment ◽  
Fundamental Properties ◽  
Critical Curves ◽  
Parameter Variations ◽  
Noninvertible Maps

Properties of the critical curves of noninvertible maps are studied using the representation of the plane in the form of sheets. In such a representation, every sheet is associated with a well-defined determination of the inverse map which leads to a foliation of the plane directly related to fundamental properties of the map. The paper describes the change of the plane foliation occurring in the presence of parameter variations, leading to a modification of the nature of the map by crossing through a foliation bifurcation. The degenerated map obtained at the foliation bifurcation is characterized by the junction of more than two sheets on a critical curve segment. Examples illustrating these situations are given.

Influence of temperature on the liquid-to-liquid extraction of ethanol from (water + ethanol + 1,2-dichloroethane)

1992 ◽  
Vol 70 (8) ◽  
pp. 2310-2313 ◽  
Author(s):  
Horacio N. Sólimo ◽  
José L. Zurita
Keyword(s):  
Experimental Data ◽  
Conjugate Points ◽  
Liquid Equilibrium ◽  
Experimental Conditions ◽  
Influence Of Temperature ◽  
Equilibrium Data ◽  
Tie Lines ◽  
Influence Of Temperature On ◽  
Tie Line ◽  
System Water

To evaluate the influence of temperature on the extraction of ethanol from aqueous solutions with 1,2-dichloroethane, liquid–liquid equilibrium data for the system water + ethanol + 1,2-dichloroethane were obtained at 298.15, 308.15, and 318.15 K. The binodal curves were determined by the cloud-point method, and conjugate points on the tie-lines were obtained by correlating the refractive index of these curves as a function of composition. The tie-line data at each temperature were satisfactorily correlated using the method of Othmer and Tobias, and the plait-point coordinates were estimated. The experimental data were also compared to values calculated by the UNIFAC group contribution method for the activity coefficients using the isoactivity conditions as restraint equations, and with the NRTL and UNIQUAC models. The UNIFAC method proved to be more accurate than the NRTL and UNIQUAC equations fitted to the experimental data. Under the experimental conditions used, ethanol extraction by 1,2-dichloroethane appears to be independent of the temperature.

scholarly journals V. On certain ternary alloys. Part VI. Alloys containing aluminium, together with lead (or bismuth) and tin (or silver)

1893 ◽  
Vol 52 (315-320) ◽  
pp. 11-27 ◽  
Keyword(s):  
Ternary Alloys ◽  
Conjugate Points ◽  
Critical Curves ◽  
Mutual Relations

The experiments described in the previous five papers* have shown inter alia that when the critical curves are delineated deduced with lead (or bismuth) as heavier immiscible metal, zinc as lighter ditto, and tin (or silver) as “solvent,” the curves where bismuth is substituted for lead lie inside , and those where silver is substituted for tin outside , the original curves; and, further, that in certain cases the formation of definite atomic compounds between particular pairs of metals leads to marked results as regards the mutual relations of the various pairs of conjugate points.

Systematic errors in equilibrium composition of ternary liquid-liquid systems and their effect on the calculated number of theoretical stages of countercurrent extraction

1988 ◽  
Vol 53 (6) ◽  
pp. 1172-1180
Author(s):  
Ján Dojčanský ◽  
Soňa Bafrncová ◽  
Július Surový
Keyword(s):  
Equilibrium Composition ◽  
Systematic Errors ◽  
Liquid Equilibrium ◽  
Countercurrent Extraction ◽  
Liquid Systems ◽  
Equilibrium Concentrations ◽  
Line Slope ◽  
Tie Line ◽  
Calculated Number

The influence of magnitude of systematic errors in the determination of ternary liquid-liquid equilibrium concentrations on the accuracy of the calculated number of theoretical stages of countercurrent extraction is evaluated on using five hypothetical systems differing in the extent of mutual solubility of components, tie-line slope, and type of binodal curve.

Comparative Study for the Assay of Plant Derived Chemicals in Pharmaceutical Formulation Using Methods Dependent on Factorized Spectra

2021 ◽  
Author(s):  
Nesma M Fahmy ◽  
Adel M Michael
Keyword(s):  
Pharmaceutical Formulations ◽  
Pharmaceutical Formulation ◽  
Ternary Mixtures ◽  
Ratio Method ◽  
The Novel ◽  
Naturally Occurring ◽  
Accuracy And Precision ◽  
Validation Parameters ◽  
Significant Difference

Abstract Background Modern built-in spectrophotometer software supporting mathematical processes provided a solution for increasing selectivity for multicomponent mixtures. Objective Simultaneous spectrophotometric determination of the three naturally occurring antioxidants—rutin(RUT), hesperidin(HES), and ascorbic acid(ASC)—in bulk forms and combined pharmaceutical formulation. Method This was achieved by factorized zero order method (FZM), factorized derivative method (FD1M), and factorized derivative ratio method (FDRM), coupled with spectrum subtraction(SS). Results Mathematical filtration techniques allowed each component to be obtained separately in either its zero, first, or derivative ratio form, allowing the resolution of spectra typical to the pure components present in Vitamin C Forte® tablets. The proposed methods were applied over a concentration range of 2–50, 2–30, and 10–100 µg/mL for RUT, HES, and ASC, respectively. Conclusions Recent methods for the analysis of binary mixtures, FZM and FD1M, were successfully applied for the analysis of ternary mixtures and compared to the novel FDRM. All were revealed to be specific and sensitive with successful application on pharmaceutical formulations. Validation parameters were evaluated in accordance with the International Conference on Harmonization guidelines. Statistical results were satisfactory, revealing no significant difference regarding accuracy and precision. Highlights Factorized methods enabled the resolution of spectra identical to those of pure drugs present in mixtures. Overlapped spectra of ternary mixtures could be resolved by spectrum subtraction coupled FDRM (SS-FDRM) or by successive application of FZM and FD1M.

Determination of the Workspace of a Three-Degrees-of-Freedom Parallel Manipulator Using a Three-Dimensional Computer-Aided-Design Software Package and the Concept of Virtual Chains1

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Andrew Johnson ◽  
Xianwen Kong ◽  
James Ritchie
Keyword(s):  
Computer Aided Design ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Workspace Analysis ◽  
Computer Aided ◽  
Aided Design

The determination of workspace is an essential step in the development of parallel manipulators. By extending the virtual-chain (VC) approach to the type synthesis of parallel manipulators, this technical brief proposes a VC approach to the workspace analysis of parallel manipulators. This method is first outlined before being illustrated by the production of a three-dimensional (3D) computer-aided-design (CAD) model of a 3-RPS parallel manipulator and evaluating it for the workspace of the manipulator. Here, R, P and S denote revolute, prismatic and spherical joints respectively. The VC represents the motion capability of moving platform of a manipulator and is shown to be very useful in the production of a graphical representation of the workspace. Using this approach, the link interferences and certain transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

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