Fractional Curves Research Articles

Radiation loss in the flash method for thermal diffusivity

The boundary radiation heat loss method is investigated for the flash method in measuring thermal diffusivity. Present correction procedures for heat loss are tested experimentally using AXM−5Q (POCO) graphite. In addition, a new method for radiation loss correction is presented based solely on the heating portion of the temperature rise curve. Using the new method, corrections of 35% can be made within a ±3% error. The thermal diffusivity results calculated using the adiabatic expression for various portions of the fractional rise curve and for various heat losses are also presented.

Selection of Size Ratio of Intervals in Matrices for the Simulation of Closed-circuit Grinding Systems

In the matrix simulation of closed-circuit grinding systems, selection of appropriate size ratio of intervals in matrices is quite important.Some examples demonstrating how the inappropriate selection of size ratio of intervals affects the calculated results of steady-state flow-rate and size distribution of fine products are presented.According to these results, calculated flow-rate of fine products P/flow-rate of classifier feed F and the calculated cumulative undersize of fine products cp(x) converge to their limiting values with the reduction of size ratio of intervals; the sign and the extent of error of estimation in case of higher values of size ratio are, however, not so simply determined.It has been found that the principal part of the estimating error in case of matrix simulation of closed-circuit grinding systems with large size ratio of intervals is induced from the ‘error of representation’ of classification matrix. Accordingly, the following precautions should be taken.i) In making conversion of fractional recovery curves of classifier into elements of classification matrices, some appropriate conversion method in which the error of representation is considerably small should be adopted.ii) When the parameter s defining the sharpness of classification is not infinity, errors of estimation of P/F and cp(x) due to the error of representation of classification matrices can reach a fairly high level according to the combination of s value with other operating factors. Consequently, a smaller size ratio of intervals in matrices should be chosen in the neighbourhood of cut-size of classifier.

ChemInform Abstract: THE THERMAL DECOMPOSITION AND REDUCTION OF SILVER(I) OXIDE

AbstractUnter isotherrnen Bedingungen werden die Kurven fraktionierte Zersetzung gegen Zeit aufgenommen.

The Thermal Decomposition and Reduction of Silver(I) Oxide

Abstract The thermal decomposition of silver(I) oxide and its reduction with reductive gases, such as ethylene, hydrogen, and carbon monoxide, have been studied by using a fixed-bed flow reactor. Under isothermal conditions, each reaction gave a sigmoidal shape to the fractional decomposition vs. time curves, and these curves were in good agreement with Avrami’s equation. The temperature at which the reaction commenced corresponded well to the chemical affinity of the reaction, and a linear free-energy relationship holds between the apparent activation energy and the standard enthalpy change of the reaction. In the thermal decomposition, an enlargement in particle size resulting from the melting and sintering of the product silver was recognized, but in the reduction the particle size scarcely varied during the reaction. On the basis of these results, the mechanism of each reaction was discussed.

The prediction of overall collection efficiency of air pollution control devices from fractional efficiency curves.

The application of air pollution control devices requires the prediction of overall collection efficiency from the particle size distribution of the dust and the fractional efficiency of the air pollution control device. The cumulative particle size distribution of dust resulting from industrial processes can usually be represented by a straight line on logarithmic probability paper or a log normal function. The fractional efficiency curves of many air pollution control devices such as cyclones or wet scrubbers can also be adequately represented by a log normal function. Only two parameters are required to define a log normal function, a median diameter and a geometric standard deviation. Both of these can easily be obtained from a plot on logarithmic probability paper. The overall collection efficiency has been found to be Very simply related to the four parameters required to define the log normal functions representing the particle size distribution and the collector fractional efficiency. These four parameters are: the mass median diameter and the geometric standard deviation of the dust size distribution, the cut diameter (50% efficiency diameter), and geometric standard deviation of collector fractional efficiency curve. Using this relationship the prediction of overall collection efficiency is greatly simplified with no loss of accuracy.

The c.hfl-value of the NO δ(0, 0) band by the line absorption method

The resonance-line absorption method has been applied to the isolated but unresolved (0, 0) band of the NO δ system, C 2Π - X 2Π. The light source was the N + O radiative recombination afterglow in a discharge flow system. This is an optically-thin source of δ(0, 0) emission, with known rotational temperature and Doppler width, uncontaminated with overlapping ε bands. Corrections for effects of accidental line overlap within the band and perturbation between the C and B states have been applied in comparing observed and computed band fractional absorption curves. For the δ(0, 0) band, this comparison gives c.hfl = (2·2 ± 0·3) × 10 -3. Our result is compared with previous measurements obtained by four other independent methods.

Decomposition reactions of nickel formate, nickel malonate, nickel maleate and nickel fumarate in oxygen

Decomposition of nickel formate, nickel malonate, nickel maleate and nickel fumarate in oxygen yields nickel oxide and carbon dioxide only. The shape of each fractional reaction-time curve is comparable with that for the vacuum pyrolysis of the salt, there is no evidence that the product oxide provided a progressively increasing barrier to the progress of the oxidation process. The values of the activation energies for the decomposition reactions of all four salts are 150 ± 10 kJ mol–1 and different from those for reactions in vacuum. From the observations we conclude that the geometry of advance of the reactant/product interface, during nucleation and subsequent growth of the product phase, for reactions in oxygen and in vacuum are closely comparable, if not identical. The chemical processes occurring at the metal carboxylate/nickel oxide interface during the reaction in oxygen are discussed. It is suggested that the rate controlling process is largely determined by the surface and defect properties of the nickel oxide product phase.

AN ANALYSIS OF THE FRACTIONAL RECOVERY CURVES OF STURTEVANT-TYPE AIR CLASSIFIERS IN HIGH SOLID CONCENTRATION CONDITIONS

The partition phenomenon in the classification characteristics of Sturtevant-type air classifiers, usually observed in high solid concentration conditions, are studied and analyzed under the assumption of a collision-interference model. Based on the above analysis, the stochastic model by Molerus on classification is modified and a comparison is made between the theoretical fractional recovery curves and those observed for a classifier in operation. Based on all the above investigations, some suggestions on optimization of operating conditions and in the design of closed-circuit grinding systems are made.

Determination of depths and frequency factors of traps by UV amplitude modulated excitation

A study is made of the photoluminescence of ZnS-type phosphors submitted to a UV excitation modulated at various frequencies. The resulting emission shows a modulation rate and a phase shift which are functions of the occupancy of the various groups of traps, and therefore depend on temperature. Starting from the phase shift, the activation energy as well as the frequency factor of various trapping levels in ZnS/Cu and CdS, ZnS/Mn, Au samples have been computed. These results are compared with those deduced from ordinary or fractional glow curves. The advantage of the present modulated excitation method is to yield simultaneously both the activation energy and the frequency factor.

Radial Diffusion of Free Energy In Stem Phloem: An Experimental Study1

AbstractThe rehydration of a water‐stressed cotton (Gossypium hirsutum L.) stem was studied experimentally. The main objective of the experiments was to ascertain if a proposed diffusion theory can describe the dynamics of the rehydration process. Stem shrinkage was induced by allowing the soil‐root system of potted cotton plants to dry by evapotranspiration. Tension in the xylem was then released suddenly by severing the stem under distilled, degassed water, with the subsequent increase in stem diameter monitored with an LVDT. From the basic data of stem diameter vs time, fractional uptake curves for free energy were computed and compared with predictions derived from theory. The comparisons indicate that the theory is applicable at least to first order. The overall study illustrates the intimate involvement of the xylem and phloem as far as radial water exchange is concerned.

A controlled apparatus for the automatic measurement of fractional glow curves

A complete automatically controlled apparatus for the measurement and the registration of fractional glow curves is described. Specifications are given.

Studies on the pathogenesis of Babesia argentina and Babesia bigemina infections in splenectomised calves.

The sequence of pathological changes in both B. argentina and B. bigemina infections of splenectomised calves are described. Renal damage preceded hepatic damage by one to two days. BUN levels increased 2-4 times; SGOT increased 4 times. Unconjugated bilirubin levels increased from {reversed tilde equals} 0.30 mg% to a peak 4.12 mg%±1.90 mg% in one group and up to 8-10 times in others. Conjugated bilirubin levels fell terminally. BSP fractional clearance levels fell in severe B. argentina cases but remained relatively unaltered in B. bigemina infections. A biphasic BSP fractional clearance curve was present in both normal and infected calves. Serum and urine sodium concentrations remained static. Serum potassium concentrations fell in some B. bigemina and B. argentina infected calves. Urine potassium levels rose in all groups. Tubulonephrosis and degeneration of the convoluted and collecting tubules was present in severe infections. Vascular congestion was frequently observed, but vascular stasis only occurred in severe B. argentina cases. Glomerular shrinkage was usual in moderate and severe cases. Severe hepatic centrilobular and midzonal degeneration and necrosis was common in all severe cases. Vascular congestion accompanied this, but stasis was present only in some B. argentina infections.

Measurement of Fractional Efficiency Curve of Air Filter Mat

Measurement of Fractional Efficiency Curve of Air Filter Mat

An Improved Numerical Technique for Solving Multidimensional Miscible Displacement Equations

Abstract Difference analog equations of high-order accuracy describing stable miscible displacement are presented. The high-order-difference scheme eliminates almost all the numerical smearing, which is the result of the normally used approximations, and leaves only the effect of the physical dispersion in the solution. In a one-dimensional system, the technique involves an addition of a negative dispersion term to the continuity equation. The negative dispersion term, which is called the numerical dispersion coefficient, depends upon the flow velocity, the time-step size and the block size. The procedure is extended to multidimensional systems. As a check, comparisons of the computed results with analytical solutions in one- and two-dimensional systems are made. The error-function solution in a one-dimensional miscible system and a five-spot fractional flow curve computed from the potentiometric model are considered as the analytical potentiometric model are considered as the analytical solutions in the two cases. Based on the computed results, it has been concluded that the effect of the term with the negative numerical dispersion coefficient accounts for almost all the truncation error within the practical limits of oilfield problems. Introduction Miscible flooding is one of the most efficient hydrocarbon recovery processes known at the present time. Its application in the field, however, present time. Its application in the field, however, remains limited because of economic requirements. Recently, the development of vertical miscible floods has made the process economically attractive. The result is that many oil companies have proposed and started such floods in suitable reservoirs. The amount of solvent required to flood an entire reservoir miscibly can be roughly calculated by analytical methods. Since these methods are derived for a one-dimensional system, some important questions remain unanswered. Some of these questions are:How will the solvent bank develop under the proposed injection scheme?What will be the condition of the solvent bank at breakthrough? These questions can only be answered by two- or three-dimensional studies. Known numerical techniques simulating miscible displacement give considerable smearing of concentration in the liquid-liquid transition zone when applied to a Held case. The effect of numerical smearing in this case is significantly larger than the effect of physical dispersion. Therefore, in the past, immiscible simulators with controlled numerical past, immiscible simulators with controlled numerical smearing were used to simulate miscible floods. For example, in one case the two-phase saturation profile was displaced as near piston-like as possible, profile was displaced as near piston-like as possible, neglecting mixing due to molecular diffusion and convective dispersion. In another case, capillary pressure and relative permeability functions were pressure and relative permeability functions were modified to simulate the dispersion effect. It was stated that the second method is applicable to a system where numerical smearing is considerably less than the effect of physical dispersion. This limits the use of the second method to a system such as gas-gas displacement. In this article a high-order difference scheme for miscible equations is given. This scheme eliminates most of the numerical smearing, leaving only the effect of physical dispersion in the transition zone. The procedure is developed for one- and two-dimensional systems. Calculated results are compared with analytical solutions. It is shown that the procedure can be extended to a three-dimensional system. FORMULATION OF THE PROBLEM The differential equations governing a miscible displacement process for an incompressible system are the continuity equations and the flow equations. Numerical solutions of this set of equations have been described by Peaceman and Rachford and Warren et al. Their methods are adequate to simulate miscible displacement in laboratory systems. If one applies them to a field-size system, significant truncation errors are introduced in the results. Usually these errors are large compared with the effect of physical dispersion on the results. SPEJ P. 277

Air Classification in High Solid Concentration (I)

As the sharpness of air classification generally decreases with the increase of the solid concentration, or mixing ratio namely, the ratio of solid feed rate to air flow rate, the mixing ratio has been limited to not higher than 0.3 in real industrial operations. Accordingly, besides improving the sharpness, the classification with much higher concentration flow has been required for increasing the throughput of classifiers.In this report, the fractional recovery curve was investigated by using a vertical type and two kinds of zig-zag type classifiers in fairly wide range of mixing ratio from 0.06 to 10. The cut size of classification was 270μ.The results obtained were as follows:(1) When the mixing ratio is less than 0.1, there is no difference of classification between the vertical type and the zig-zag type, but when the ratio is more than 0.1, the classification with latter type is more sharper than that of the former one.(2) Comparing the zig-zag types having the inclination of 30 degrees and that of 45 degrees, the former shows the sharper classification than the latter in the case of mixing ratio less than 1.0. However, this trend reverses at the ratio more than 1.0.

Analysis of the Cyclone Operating Data in the Primary Grinding Circuit.

At Hitachi Mill, two stage grinding circuit has been adopted since 1963, and a hydrocyclone is used for classifying the rod mill discharge.The influences of some variables on the cyclone performance at high pulp densities in the feed pulp (5065% solids) were investigated based on the operating data.The results obtained are summarized as follows.(1) The separating size and the sharpness of separation were largely influenced by the feed pulp density.(2) There was a half logarithmic relationship between the separating size and the solid recovery in the underflow.(3) The sharpness of separation increased linearly with the solid recovery in the underflow.(4) The sharpness of separation decreased with increased separating size and a half logarithmic relationship was obtained between them.(5) It was pointed out that the fractional recovery curves should be drawn separately for the gangue minerals with low specific gravity and the sulphide minerals with high specific gravity, and so some more valuable informations could be obtained.

Thermal Decomposition Kinetics of Boehmite

The decomposition of boehmite, or alpha alumina monohydrate, was studied in water vapor and nitrogen atmospheres between 430° and 500°C. Powder samples used consisted of agglomerates of very small boehmite crystallites. The rate of decomposition was determined with a transducer which measured the loss of sample weight due to the liberation of gaseous water. A linear rate law is obeyed by the decomposition of boehmite and, because of the characteristics of the fractional weight loss-time curve, an interface model was suggested as the mechanism of decomposition. The activation energy was 70 kcal/mole. The effect of water vapor on the rate of decomposition was investigated. A simple forward-back reaction mechanism did not satisfactorily explain the data. Two models, either of which could be valid, were proposed to describe the relation between decomposition rate and water vapor pressure: (1) An adsorption-desorption process of water on the boehmite was assumed, and (2) an intermediate species of Al2O3 entering into the decomposition reaction was assumed.

Proposal of a New Index for Expressing the Performance of Screens

Using Gaudin's probability of particle passage through an opening (a) in the screen cloth (Eq. 1), and introducing the idea of the number of trials of passages (i) covered by a particle before it is screened, the author derived a theoretical formula for the fractional recovery curve (Eq. 4).For practical use, however, Eq. 4 may be rewritten as follows:where, On the assumption that the number of trials of passages made by a particle per unit length of screening (ξ) is constant over the whole screening surface, i will be equal to ξ·l, and the relationship between the separating size x0.5 (the size of a particle corresponding to ri=0.5) and the length of screening (l) will be given by the following equation:The values of a and ξ, therefore, will be determined by plotting x0.5 relative to.The question of whether the above expression is valid or not may be answered by determining a series of corresponding values of l and x0.5. Some of the experimental results are shown in Figs. 4, 6 and 8. The index ξ may be used for expressing the performance of screens as compared with the corresponding ideal screening process based on the Gaudin's probability, and thus we have succeeded in obtaining a practical meassure of screening result.Furthermore, by using the index ξ and the table of normal distribution, we may construct the fractional recovery curves as given in Figs. 5, 7 and 9.The value of a serves as a measure of an effective opening of the screen.

FRACTIONAL DISSOLUTION CURVES OF NITRATED PULPS WITH ETHYL ACETATE-ETHANOL MIXTURES

In the previous paper, the effects of fiber structure and the average degree of polymerization of cellulose chains on the shape of the fractional dissolution curve were studied. And it was found that the effect of the fiber structure on the shape of the curve is dominant.The swelling or solubility of the linear polymer is principally the function of both the length of molecules and the state of cohesion of the molecules. In this paper, the effects of the distribution of the cellulose chain length on the shape of the curve have been studied to confirm the results obtained in the previous paper. And the distributions of cellulose chain length of original pulps and the degree of polymerization of each fractional dissolved were determined.The results obtained showed the fractional dissolution curve does not represent the distribution of cellulose chain length of the pulp, and supported the results obtained in the previous paper. Furthermore, the results obtained in this paper and previous paper are discussed based on the fiber structure model.

FRACTIONAL DISSOLUTION CURVES OF NITRATED PULTS WITH ETHYL ACETATE-ETHANOL MIXTUTES

Ranby et al. had extracted nitrated pulp fibers with ethyl acetate-ethanol mixtures of increased ethyl acetate concentration, and found that the solubility curve thus obtained shows a level (Fig. 1). This fact means the carbohydrates are deposited in the plant fibers as two fractions differing markedly in solubility after nitration. In their investigation, two fractions were denitrated, hydrolyzed to monosaccharides and then analyzed by paper chromatography. This solvent-nonsolvent system gives a swelling of the fibers without destroying the fiber structure, until the concentration of ethyl acetate in mixture becomes about 60% (in volume). Therefore, the shape of this solubility curve can be effected not only by the amounts of easily soluble carbohydrates, but also the fiber structures, mainly outer layer of the cell wall and fine structure.The purpose of this investigation has been to establish what effect the fiber structurs and average degree of polymerization of pulp could have on the shape of the fractional dissolution curve. The following samples were prepared for determining the solubility curve:1. F-pulp fibers, which had been immersed in water, frozen and thawed, were prepared. This can be seen as destroyed of outer layer of cell wall or loosen fiber framework without the degradation of cellulose chain and the change of crystalline region.2. Acid hydrolyzed pulp fibers were prepared under the mild conditions. This can be seen as degradated of cellulose chain and as destroyed of outer layer of cell wall without any change in crystalline region.Two kinds of acid were used for hydrolysis of pulp fibers, namely sulfuric acid and lignosulfonic acid. According to the investigation by Samuelson, the latter had “screen effect”, then the outer layer of cell wall can be attacked more severely with lignosulfonic acid than with sulfuric acid.3. Mercerized pulp fibers were prepared. This can be seen as disordered of the crystalline region without degradation of cellulose chain. A part of easily soluble carbohydrates goes into solution during mercerization treatment.4. Linters pulp (Li. P), dissolving sulfite pulp (DSP), dissolving sulfate pulp (DKP), bleached paper sulfite pulp (BSP) and bleached paper sulfate pulp (BKP) were also used as original pulps.Mitchell's mixture was used for nitration of pulp fibers and the fractional dissolution was performed in the way Ranby did. The shape of solubility curve has been expressed by l, h, α and s (Fig. 1).As a result, it was found that l and α are effected by fiber structure, namely outer layer of cell wall and fine structure. When the outer layer of cell wall was destroyed or lateral order of cellulose was lowered, I decreased. In the case of DKP, the recrystallization had occured during freezing or acid hydrolysis and l increased. h shows the amounts of easily soluble carbohydrates in the fiber, and the shape s depends on the corelation between h and character of outer layer of cell wall. And the effect of average degree of polymerization of cellulose chain on the shape of fractional dissolution curve can be seen as subordinated to the fiber structure.