Thermodynamic model for equilibrium solubility of gibbsite in concentrated NaOH solutions

The thermodynamic properties of the most important NaOH-NaAI（OH）4-H20 system in Bayer process for alumina production were investigated. A theoretical model for calculating the equilibrium constant of gibbsite dissolved in sodium hydroxide solution was proposed. New Pitzer model parameters and mixing parameters for the system NaOH-NaAI（OH）4-H20 were yielded and tested in the temperature range of 298.15-373.15 K. The results show that the proposed model for calculating the equilibrium constant of gibbsite dissolution is applicable and accurate. The obtained Pitzer model parameters of β（0）（NaAl（OH）4）、β（1）（NaAl（OH）4）和CΦ（NaAl（OH）4）,Al（OH）4 for NaAI（OH）4, the binary mixing parameter of θ（OH-Al（OH）4-） with OH-, and the ternary mixing parameter of ψ（Na＋OH-Al（OH）4-） for AI（OH）4- with OH- and Na＋ are temperature-dependent. The prediction of the equilibrium solubility of gibbsite dissolved in sodium hydroxide solution was feasible in the temperature range of 298.15-373.15 K.

Equilibrium concentration of lithium ion in sodium aluminate solution

Excess lithium in alumina is significantly bad for aluminum reduction.In this study,the concentration variation of lithium ion in sodium aluminate solution with addition of synthetic lithium aluminate was investigated.Elevating temperature,increasing caustic soda concentration,reducing alumina concentration or raising molar ratioαk improved equilibrium concentration of lithium ion in sodium aluminate solution.Agitation speed had a minimal effect on lithium ion concentration.Over 0.65 g/L lithium ion equilibrium concentration was observed in digestion process,whereas 35 mg/L lithium ion concentration remained in solution after precipitation time of 9 h.Moreover,equilibrium concentration decreased sharply from digestion of boehmite or diaspore to seed precipitation,about 95%lithium was precipitated into red mud(bauxite residue)and aluminum hydroxide.This study provides a valuable perspective in removal or extraction of lithium from sodium aluminate solution in alumina refineries.

POSITIVE EQUILIBRIUM SOLUTIONS OF SEMILINEAR PARABOLIC EQUATIONS

The author studies semilinear parabolic equations with initial and periodic boundary value conditions. In the presence of non-well-ordered sub- and super-solutions： ＂subsolution ≮ supersolution＇, the existence and stability/instability of equilibrium solutions are obtained.

EXISTENCE RESULTS FOR GLOBALLY EFFICIENT SOLUTIONS OF VECTOR EQUILIBRIUM PROBLEMS VIA A GENERALIZED KKM PRINCIPLE

The aim of this article is to present new existence results for globally efficient solutions of a strong vector equilibrium problem given by a sum of two functions via a generalized KKM principle, and to establish the connectedness of the solutions set.

L^2 ASYMPTOTIC FOR THE EQUILIBRIUM SOLUTION OF THE F-M EQUATIONS IN THE SPACE-PERIODIC CASE

The L2 exponetial asymptotical stability for the equilibrium solution of the F-M equations in the space-periodic case (n=2) is considered. Under some assumptions on the external force, it can be shown that the weak solution of F-M equations with initial and boundary conditions in space-periodic case approaches the stationary solution of the system exponetially when time t goes to infinite.

NONTRIVIAL EQUILIBRIUM SOLUTIONS FOR A SEMILINEAR REACTION-DIFFUSION SYSTEM

By the degree theory on positive cone together with the technique of a priori estimate, the nontrivial equilibrium solutions of a strong nonlinearity and weak coupling reaction diffusion system and the structure of the equilibrium solutions are discussed.

Influence of Fluoride Addition on the Composition of Solutions in Equilibrium with Acid Soils

Atmospheric emissions of fluoride from an aiuminium smelter-alumina refinery located on the northern coast of Galicia, NW Spain, increase the content of fluorine in soils and vegetation in the vicinity of the complex. The effects of the addition of fluoride solutions on the chemical properties of soil samples from the area surrounding the complex were investigated in laboratory experiments. Addition of fluoride to soils resulted in increases in pH and concentrations of Fe, A1, and organic matter in the equilibrium solutions and decreases in concentrations of Ca, Mg, and K. No consistent effects were observed on the Cu, Mn, or Zn concentrations. Most of the A1 in solution was bound to organic matter. Within the fraction ＂labile aluminium＇, the concentration of A1-OH complexes decreased and the A1-F complexes increased, especially A1F3 and A1F4^-, which are less toxic than Al^3＋ and A1-OH species.

SWELLING EQUILIBRIUM OF NONIONIC POLYACRYLAMIDE HYDROGEL IN AQUEOUS SALT SOLUTIONS

A series of nonionic polyacrylamide hydrogels, using acrylamide as monomer and N,N＇-methylene diacrylamide as crosslinking agent, were prepared by the free radical polymerization in aqueous solution. Swelling equilibria for the gels were carried out in aqueous solutions of NaCl, KCI, CaCl2, Na2HPO4 and K2HPO4 with concentration ranging from 10^-3 to 5mol/kgH2O at 25 ℃. Experimental results revealed that the chlorides and phosphates cause a different behavior at higher salt concentration. The swelling ratio increases with increasing concentration of chlorides salts, while decreases with the increased phosphates salt concentration. The phenomena seem to be related to the different interactions of chloride and hydrogen phosphate ions with the network groups. Furthermore, the effects of different concentration of crosslinking agent and total monomers on gel swelling performance were also investigated.

V-L EQUILIBRIUM OF WEAK ELECTROLYTE SOLUTION OF THE NH_3-CO2-H_2O,NH_3-H_2S-H_2O AND NH_3-SO_2-H_2O SYSTEM

In this paper we have systematically studied V-L equilibrium in ternary aqueous solutions containingvolatile electrolytes by introducing a ternary interaction term into Edwards generalized molecular thermody-namic model and optimizing several adjustable parameters.The program PARA9 with flexible functions ofdoing a series of calculations has been developed and carried out on a TQ-16 computer.It can be usedeither for directly calculating the V-L equilibrium or for optimizing the adjustable parameters.For the sys-toms（NH3-CO3-H2O3,NH3-H2S-H2O and NH3-SO2-H2O）satisfactory results have been obtained withrelative mean deviation of 5-10%.Besides,several sets of adjustable parameters and valuable information ofactivity coefficients,equilibrium concentrations of ions and molecules in solutions are obtained.

Upper and Lower Semicontinuity of Solution Sets for Parametric Generalized Vector Quasi-equilibrium Problems

In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.

Measurements of zinc oxide solubility in sodium hydroxide solution from 25 to 100 °C

The solubility of zinc oxide in sodium hydroxide solution was measured in a closed polytetrafluoroethylene vessel from 25 to 100 ℃. The ZnO solubility was determined by employing the method of isothermal solution saturation. The results show that only ZnO solid exists in the equilibrium state in the low concentration alkali regions, and the solubility of zinc oxide is almost invariable with temperature. With the increase of alkali concentration, equilibrium solid turns from ZnO to NaZn（OH）3 suddenly, this mutation is called invariant point. The alkali concentration of the invariant points increases with increasing temperature, but the solubility of NaZn（OH）3 decreases with increasing alkali concentration at the same temperature. At the same Na2O concentration, the higher the temperature is, the higher the solubility of NaZn（OH）3 is.

Equilibrium Swelling and Solute Diffusion Characteristics of Poly (Methacrylic Acid co-Poloxamer) Hydrogels

Poly(methacrylic acid co-poloxamer) hydrogel networks were synthesized by free radical solution polymerization and their equilibrium swelling and solute permeation properties were characterized. These gels exhibited pH dependant swelling and solute diffusivity due to the formation or disruption of hydrogen bonded complexation between methacrylic acid (MAA) and etheric (EO). In neutral and basic conditions (above the swelling transition pH), the copolymer swelling was greatly higher than acid condition. In complexed hydrogels, the diffusion coefficients of vitamin B12 (VB12) were in the range of 10-10 to 10-7 cm2s-1; While in uncomplexed hydrogels, the values were about 210-6 cm2s-1. The comonomer composition and synthesis conditions have great effect on the structure, and thereby, swelling and solute diffusion characteristics of the resultant hydrogels. For the copolymers with composition of less than or more than 1:1 MAA/EO molar ratio, the plot of lnD vs 1/H-1 followed two different linear equations of 慺ree volume theory? respectively.

Zinc isotope fractionation under vaporization processes and in aqueous solutions

Equilibrium Zn isotope fractionation was inves- tigated using first-principles quantum chemistry methods at the B3LYP/6-311G level. The volume variable cluster model method was used to calculate isotope fractionation factors of sphalerite, smithsonite, calcite, anorthite, for- sterite, and enstatite. The water-droplet method was used to calculate Zn isotope fractionation factors of Zn^2＋-bearing aqueous species; their reduced partition function ratio factors decreased in the order [Zn（H2O）6]^2＋ 〉 [ZnCl（H2O）5]^ ＋ 〉 [ZnCl2（H2O）4] 〉 [ZnCl3（H20）2]^-〉 ZnCl4]^2-. Gas- eous ZnCl2 was also calculated for vaporization processes. Kinetic isotope fractionation of diffusional processes in a vacuum was directly calculated using formulas provided by Richter and co-workers. Our calculations show that in addition to the kinetic isotope effect of diffusional processes, equilibrium isotope fractionation also contributed nontriv- ially to observed Zn isotope fractionation of vaporization processes. The calculated net Zn isotope fractionation of vaporization processes was 7-7.5‰, with ZnCl2 as the gas- eous species. This matches experimental observations of the range of Zn isotope distribution of lunar samples. Therefore, vaporization processes may be the cause of the large distri- bution of Zn isotope signals found on the Moon. However, we cannot further distinguish the origin of such vaporization processes; it might be due either to igneous rock melting inmeteorite bombardments or to a giant impact event. Fur- thermore, isotope fractionation between Zn-bearing aqueous species and minerals that we have provided helps explain Zn isotope data in the fields of ore deposits and petrology.

A Modified Mixing Rule for PSRK Model and Application for the Prediction of Vapor-Liquid Equilibria of Polymer Solutions

To extend the PSRK (predictive Soave-Redlich-Kwong equation of state) model to vapor-liquid equilibria of polymer solutions, a new EOS-gE mixing rule is applied in which the term ∑ xi ln(b/bi) in the PSRK mixing rule for the parameter a, and the combinatorial part in the original universal functional activity coefficient (UNIFAC) model are cancelled. To take into account the free volume contribution to the excess Gibbs energy in polymer solution, a quadratic mixing rule for the cross co-volume bij with an exponent equals to 1/2 is applied[bij1/2= 1/2(bi1/2+bj1/2)]. The literature reported Soave-Redlich-Kwong equation of state (SRK EOS) parameters ofpure polymer are employed. The PSRK model with the modified mixing rule is used to predict the vapor-liquid equilibrium (VLE) of 37 solvent-polymer systems over a large range of temperature and pressure with satisfactory results.

On the positive nonoscillatory solutions of the difference equation Xn＋1=α＋（xn-k/xn-m）^p

The aim of this paper is to show that the following difference equation：Xn＋1=α＋（xn-k/xn-m）^p, n=0,1,2,…,where α 〉 -1, p 〉 O, k,m ∈ N are fixed, 0 ≤ m 〈 k, x-k, x-k＋1,…,x-m,…,X-1, x0 are positive, has positive nonoscillatory solutions which converge to the positive equilibrium x=α＋1. It is interesting that the method described in the paper, in some cases can also be applied when the parameter α is variable.

ON THE MULTIPLE SOLUTIONS TO A THREE-COEFFICIENT SPECTRAL MODEL OF WIND-DRIVING OCEAN CURRENT EQUATION

In this paper,a research on the problem of multiple solutions of the three-coefficient low-spectrum model for the quasi-geostrophic ocean current equation with forcing and dissipation terms is carried out.The state of the ocean current under wind conditions such as those of typhoon is discussed carefully and the rela- tions between the multiple solutions and the coefficients R and ε are analyzed.It is seen that in an approxi- mate triangular region with the Rossby-coefficient R less than 0.5,and the friction-coefficient ε less than 0.22, there exist three equifibrium solutions,among which two are stable and one is unstable.For the former,the coefficient A or B in the expansion is rather large,while for the latter,A or B is relatively small.They respectively imply how much the ocean energy is fed back from the wind stress and the solution with a large A is much more stable than that with a larger B.

The Optimal Solution of the Model with Physical and Human Capital Adjustment Costs

We prove that the model with physical and human capital adjustment costs has optimal solution when the production function is increasing return and the structure of vetor fields of the model changes substantially when the prodution function from decreasing return turns to increasing return. And it is shown that the economy is improved when the coefficients of adjustment costs become small. Key words optimal solution - nonzero equilibrium - adjustment costs CLC number O 29 Foundation item: Supported by the National Natural Science Foundation of China (79970104)Biography: RAO Lan-lan (1978-), female, Master candidate, research direction: mathematical economy.

The Problem of Periodic Solution for Dynam icalSystem s (Ⅱ)

In this paper,we consider the dynamical system which are from general Hemilton systems under a disturbance,we use theories in Liapunov stability and show that there are not any periodic solutions in some a neighborhood of the equilibrium points of the dynamical systems.

Membrane Potentials Across Hybrid Charged Mosaic Membrane in Organic Solutions

Membrane potentials across hybrid charged mosaic membrane in organic solutions were measured. Equilibrium swelling degree （SD） and fixed charge density in both organic solutions and water were also determined. Ethylene glycol, ethanol, n-propanol and glycerol were used as organic solutes; meanwhile 0.001mol-dm^-3 aqueous KCl solution was utilized as a strong electrolyte to measure the electrical difference. Equilibrium swelling degree indicated that it could be affected by the density of organic solutes; while it enhanced with the increasing density of these solutes. The measurement of fixed charge density showed that the membrane had the maximal absolute value in water among these solvents whether for cationic or anionic groups; the difference of dielectric constant between the water and the organic solutes might be responsible for these change trends. It was confirmed that membrane potentials increased with both the increasing concentration of the organic solutions and the elevated pH values. These results demonstrated that the characteristics of the hybrid charged mosaic membrane could be highly impacted by the properties of the organic solutes. A theoretical modal for charged membranes in ternary ion systems of weak electrolyte can be used to explain the above-mentioned phenomena.

Periodic Solutions for Functional Differential Inclusion with Nonconvex Right Hand Sides

In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform boundedness and ultimate boundedness are only assumed to the solutions with bounded initial functions. On the other hand, the dissipativity is sought on a suitable bounded convex subset of the state space of solutions. This becomes difficult for the systems with infinite delay since in this case the subset is probably not forward invariant for the orbits of solutions. These are also considerable even for the usual functional differential equations with infinite delay. As an application, we answer an open problem on the existence of an equilibrium state for multivalued permanent systems.