Some effects of electrolytes on the swelling and shrinking processes of sodium polyacrylate-type super-absorbent gel were examined systematically, using several kinds of uni-univalent and di-univalent electrolyte solutions. A gel of this type goes through a maximum degree of swelling and then shrinks in electrolyte solutions. The reason was found to be that the sodium ions dissociated from the functional groups in the gel, –COONa, are exchanged easily with the other cations in the solution. The swelling and shrinking mechanism can be reasonably explained in terms of the electric force acting on the charged network of the gel. This is different from the previously proposed mechanism, which involves the osmotic pressure. The final degree of swelling is closely related to the selectivity of –COO– ion for the cation in the solution and to the cation concentration in the solution.
Parameters in residence time distribution (RTD) models are commonly estimated by least-squares curve-fit in the time domain. Two procedures suggested in the literature for this purpose involve (i) fixing τ (the mean residence time) as equal to μ (first moment of the experimental response) prior to curve-fitting and (ii) estimating τ along with other model parameters by curve-fitting. In this work these two procedures, i.e., curve-fitting with and without the constraint τ = μ, are compared. Four models in conjunction with eight sets of RTD data are considered. The results indicate that consistently better results are obtained when the constraint τ = μ is relaxed prior to curve-fitting. This is particularly so for models with fewer parameters like the dispersion model.
Hydrogenation of CO2 was conducted on iron catalyst under various reaction conditions to explore the catalytic behavior and the change of bulk phase composition. It was found by the use of Mössbauer spectroscopy that the metallic iron phase was transformed to a mixture of magnetite and carbides progressively during the course of reaction. The formation of Fe3O4 phase became more favorable under conditions which led to a high H2O partial pressure on the catalyst bed. On the other hand, the carburization of iron catalyst was enhanced at higher temperature, with χ-Fe5C2 phase being predominant over θ-Fe3C phase. Due to the fact that H2O produced in the Fischer–Tropsch reaction also contributes to the equilibrium of the reverse water–gas shift reaction, the common product H2O of these two steps plays a major role in suppression of overall CO2 conversion level.
Results by modification of the time transient method are presented, in which the superficial average velocity (streaming velocity) can be obtained in addition to molecular number density. The molecular number flux was thus obtained by the product of molecular number density and superficial average velocity. The results of analysis of molecular flow in a circular tube were newly studied. The study revealed that there was a distortion of molecular number density distribution affected by outer storage. It became clear that the jumps in molecular number density and superficial average velocity at inlet and outlet openings were induced by discontinuity of macroscopic transfer rate (molecular number flux) between the tube and the outer space. For a finite length tube, using Knudsen’s simple equation for a tube of infinite length, the transfer rate, i.e. the conductance, can be easily calculated by applying the slip distance.
The “pseudo-liquid phase” catalytic behavior of 12-tungstophosphoric acid was confirmed by studying the effect of catalyst particle size on the apparent rate of t-BuOH dehydration. The apparent rate of reaction strongly depended on the particle size, indicating strong diffusional effects in the pseudo-liquid phase. Based on the theory of Thiele with some modification and extension to pseudo-liquid phase catalysis, along with a knowledge of intrinsic reaction rate, diffusivity values were evaluated. The effective dilfusivity was found to lie in a range of 10–11–10–10 m2/s, which are very small values for diffusivity in gas phase, but close to that in liquid-filled pores. Due to the large temperature dependency of diffusivity, the effectiveness factor is smaller in the lower-temperature region—a sharp contrast to the usual diffusion-restricted gas–solid catalytic reaction in a microporous solid.
The particle growth properties in drying of an aqueous mixture of sodium orthophosphates were studied in a 0.078 m-ID × 0.84 m-high fluidized bed. Glass beads and sodium tripolyphosphate (STPP) particles were used as the initial seed particles. Particle growth was mainly governed by the agglomeration of product particles in beds of glass beads and STPP particles. Particle growth conversion decreased with increasing gas velocity and bed temperature but increased with an increase in feed solution concentration. The particle size distribution of products can be represented by the lognormal distribution function. A semiempirical correlation is proposed to predict the size distribution of product particles in the bed.
Determination of the equilibrium data was carried out in an apparatus which can circulate vapor and liquid phase alternately. The uncertainties in measurement were less than 50 mK in temperature and 8 kPa in pressure. The uncertainties in the equilibrium composition near 0.5 mole fraction were less than 0.009 mole fraction, and near 0.9 or 0.1 are less than 0.003. Simple consistency tests were applied to check the experimental data. Their results show the reliability of the present experimental data. Two equations of state, the P–R equation and the S–R–K equation, were used to correlate the vapor–liquid equilibrium relationships of these systems. It was found that both equations of state reproduce the experimental data satisfactorily by introducing the binary interaction parameter into the conventional mixing rule.
Bubble formation at an orifice submerged in highly viscous liquid was studied. The volume and shape of the bubble formed at an orifice and the pressure fluctuation in the gas chamber were measured experimentally. A revised nonspherical bubble formation model is proposed to describe the bubble formation mechanism and to estimate the bubble volume and shape and the pressure change in the gas chamber. The bubble volume, bubble shape and gas chamber pressure calculated by the present model agreed relatively well with the values obtained experimentally in a wide range of viscosity: μ = 0.001 to 1.1 Pas.
The continuous-phase mass transfer volumetric coefficient kLa in a liquid-liquid mixing vessel was measured by using the hydrolysis reaction of both n-amyl and n-hexyl acetates with sodium hydroxide. Droplet diameter was also observed by using a videorecorder via a microscope during the reaction period, allowing the continuous-phase mass transfer coefficient, kL, to be determined. The coefficient obtained was 2–5 times larger than that obtained from the correlation by Calderbank–MooYoung. Dimensionless correlation of the mass transfer coefficient with the droplet diameter and the power input per unit volume was confirmed experimentally to be close to that for the solid suspension system.
A new method is developed for the determination of mutual diffusivity of low-molecular weight materials in concentrated polymer solution far above the glass transition temperature. The most important feature of the present method is that the diffusivity of the monomer can be determined by consideration of the simultaneous diffusion and polymerization of the monomer. This method can be easily applied to systems containing non-reactive diffusant as well. The diffusivities of styrene monomer and ethylbenzene in molten polystyrene and their temperature dependency are determined over a temperature range from 423 to 523 K and a concentration range up to 3 wt% of diffusant. Treating the diffusivities as constant regardless of concentration over the experimental range of concentration, we correlate the diffusivities as
D = 6.97 × 10–2 exp(–42400/RT)
for styrene and
D = 1.17 × 102 exp(–72600/RT)
for ethylbenzene, where the units of D, R and T are cm2·s–1, J·mol–1·K–1 and K, respectively.
A two-stage membrane separation process composed of one step using a silicone rubber membrane hollow-fiber module and another step using a polyimide hollow-fiber module for effective separation of alcohol from a low-concentration alcohol–water solution was proposed and its effectiveness was experimentally confirmed. The first step is a pervaporation through the silicone rubber into a carrier gas, and the second is a gas-phase separation through the polyimide membrane. By use of these two steps in series, 99% and 1% solutions were separated from 5–10 mol% ethanol solution. This effective separation must be due to the high permeation rate of water vapor through the polyimide membrane, 200-fold that of ethanol vapor as shown by the experimental data.
A model for describing steam bubble formation at a submerged orifice in flowing liquid is developed. It is assumed that the bubble grows continuously in the radial direction, translates continuously in the vertical direction, and is surrounded by a thin liquid layer unaffected by the bulk liquid motion. The model allows fluctuation of pressure, temperature, and density of the vapor in a bubble in equilibrium with the liquid at the bubble wall. The temperature profile in the boundary layer is not limited to a quadratic function as assumed in Denekamp’s model6) but varies in accordance with the propagation of heat. The detachment criterion assumed is that the bubble neck is equal to zero for the first bubble of the pairing and equal to half of the bubble radius for the bubble containing the second bubble of the pairing. The prediction values from the present model using an explicit finite-difference technique are compared with experimental data in the literature. The results are in good agreement and show a significant improvement over Denekamp’s model.
For silicon CZ crystal growth, the effect of a radiation shield inserted in a furnace on the thermal stress field was studied theoretically by the finite-element method based on thermoelastic analysis. It is found that a radiation shield lowers the maximum (thermally induced) shear stress, since it reduces the temperature gradient, especially in the radial direction, in a crystal. There is an optimum location for placement of the radiation shield so as to realize the smallest shear stress. From the viewpoint of thermal stress, a radiation shield can allow a higher pull rate of defect-free crystal.
Theoretical and experimental studies of the shapes and terminal velocities of bubbles rising in quiescent Newtonian and non-Newtonian liquids were carried out. For non-Newtonian liquids, the power law model was adopted as the constitutive model. Numerical analysis by use of the finite element method can predict well the observed shapes and velocities of such bobbles. It is found experimentally and theoretically that as bubble diameter increases, the bubble deforms from a sphere to one of three types of ellipsoids, depending on the viscosity of the continuous phase: (1) more deformed at the front than at the rear, (2) symmetrical front to rear, and (3) more deformed at the rear than at the front, in both Newtonian and non-Newtonian liquids. Shape regime maps are proposed on the basis of the numerical simulations.
To provide a better theoretical basis for obtaining higher concentration of ethanol from a fermentation broth using near- or super-critical CO2 extraction, the vapor–liquid equilibria for the quaternary system of CO2, ethanol, water and an entratner were measured at 35.0°C and 10 MPa for various entrainer concentrations. Experiments were carried out for four entrainers: glycerol, ethylene glycol, 1,3-propanediol and propylene glycol. The experimental results demonstrated that the upper limit of ethanol composition for the CO2–ethanol–water ternary system could be raised by the addition of the above entrainers other than propylene glycol. It was also found that this effect of the entrainer could be estimated qualitatively from its solubility parameter value. The group parameter values of the GC-EOS by Jorgensen were redetermined using binary vapor–liquid equilibrium (VLE) data in order to improve the accuracy of prediction of the VLE of the CO2–ethanol–water and the CO2–ethanol–water-entrainer mixtures.
The solvent extraction of vanadium and molybdenum by tri-n-octylmethylammonium chloride (TOMAC) from neutral solutions was studied and it was found that vanadium was extracted preferentially by an anion exchange mechanism. The pentavalent vanadyl anion in the organic solution was found to be reduced to the form of tetra- or trivalent cations by contact with an aqueous solution containing a reduction agent such as L-ascorbic acid. This enables the vanadium to be stripped selectively by chemical reduction, with the molybdenum remaining in the organic phase. A separation efficiency of 1.64 × 104 was obtained for an aqueous solution containing initially equal concentrations of the two metals by single extraction followed by single selective stripping.
Three-dimensional numerical analysis of flow behaviour such as velocity components, shear rate and apparent viscosity of a highly viscous pseudoplastic Ellis liquid in stirred vessels was performed. The vessels used were geometrically similar, non-baffled ones of 0.2 to 0.8 m vessel diameter each with a 6-blade turbine, a paddle and an anchor-type stirring impeller. The analogy of flow fields in model and large-scale stirred vessels was investigated by applying the concept of representative shear rate to estimate the apparent viscosity of a power-law fluid proposed by Metzner et al. and Nagata. It was found that the normalized flow profiles of a pseudoplastic liquid in the scaled-up vessels were nearly consistent with those in the model vessel within the impeller blade region, while it was quantitatively shown that the deviation between the two profiles in the outer region of the impeller expands with increasing vessel diameter.
This paper presents an extended technique for predicting the mixing time of high-viscosity liquids in a mixer. The molecular diffusion and reaction between solutes each dissolved in the liquids are analyzed during the mixing. Concentration profiles are obtained by solving simultaneously the diffusion and reaction differential equation and a model equation representing the decrease of scale of segregation with time. The calculated mixing time is predicted as the elapsed time until the local maximum concentrations of the solute become less than a chosen criterion of mixing. Mixing experiments were carried out with helical screw/draft tube mixers and helical ribbon-impeller mixers filled with corn syrups prepared at various viscosities. The chemical reactions were the reduction of I2 to 2I– in the presence of either Na2S2O3 or Na2HPO4. It was found that the predicted mixing times were in fairly good agreement with those determined experimentally. The mixing time was found to depend mainly on the reaction rate of reactants as well as the operational conditions of the mixer.
Measurement of the extraction equilibria of samarium and europium in acetate media with dibutylmonothiophosphoric acid (HR) in toluene diluent was carried out at 303 K. It was found that lanthanide ions (Ln3+) are extracted according to the following equation.
Ln3+aq + 3HRorg ↔ LnR3,org + 3H+aq
The extraction equilibrium constants of the metals were obtained. The separation factor between the two metals was a very low 1.1. A synergistic extraction of the metals with the mixed extractant of dibutylmonothiophosphoric acid and 1,10-phenanthroline (phen) was also conducted to separate the metals efficiently. In this case, the lanthanide ions were extracted according to the following equation.
Ln3+aq + 3HRorg + phenorg ↔ LnR3·phenorg + 3H+aq
The extraction equilibrium constants were obtained, and from them the separation factor was calculated as 1.3. It was found that the factor is improved by the synergistic effect.