Rapid estimation of corrected cut point in hydrocyclone classification units

In dressing plants, the rapid determination of the corrected cut point in hydrocyclone classification is desirable, useful, and important. In this work, classification tests have been carried out on white sand using a 10-cm diameter hydrocyclone to examine closely the relation between the recovery to underflow and the corrected separation size, $\text{d}{}_{50}$. The study was carried out at wide ranges of: apex diameter, vortex-finder diameter, solid content of feed, and length of vortex finder.A simple, yet reliable, equation relating the solid recovery of underflow to $\text{d}{}_{50}$, is developed using all the obtained results. The predicted data show good agreement with the experimental.     

Changes in the content and composition of pedogenic iron oxyhydroxides in a chronosequence of soils in southern California

Studies of the pedogenic iron oxyhydroxides in suites of latest Holocene to middle Pleistocene soils formed on fluvial deposits of the transverse ranges, southern California, indicate that the content and composition of iron oxyhydroxide change in a systematic manner. Analysis of total secondary free iron oxides (dithionite extractable, Fe₂O₃d) and ferrihydrite (oxalate extractable, Fe₂O₃o) shows that (1) a single-logarithmic model (Y = a + b log X) or double logarithmic model (log Y = a + b log X), where Y is the total mass of pedogenic Fe oxides (g/cm²-soil column) and X is soil age, describes the rate of increase in Fe₂O₃d with time; (2) the Fe₂O₃d content correlates linearly with soil reddening and clay content; (3) the $\text{Fe}{}_2\text{O}{}_3\text{o}\text{Fe}{}_2\text{O}{}_3\text{d}$ ratio, which indicates the degree of Fe oxide crystallinity, is moderately high to very high (0.22–0.58) in middle Holocene to latest Pleistocene soils and progressively decreases to less than 0.10 in older soils; (4) the value of the $\text{Fe}{}_2\text{O}{}_3\text{o}\text{Fe}{}_2\text{O}{}_3\text{d}$ ratio also appears to be infuenced by climate; and (5) temporal changes in Fe oxide content and mineralogy are accompanied by related, systematic changes in clay mineralogy and organic matter content. These relationships are attributed to a soil environment that must initially favor ferrihydrite precipitation and/or organic matter-Fe complexation. Subsequent transformation to hematite causes increasingly intense reddening and a concomitant decrease in the $\text{Fe}{}_2\text{O}{}_3\text{o}\text{Fe}{}_2\text{O}{}_3\text{d}$ ratio. The results demonstrate that iron oxide analysis is useful for numerical age studies of noncalcic soils and shows potential as an indicator of paleoclimates.     

The partial molal volume of silicic acid in 0.725 m NaCl

The partial molal volume ($\text{V}\text{?}$) of silicic acid in 0.725 m NaCl at 20°C has been calculated from (1) direct volume changes due to the dissolution of anhydrous sodium silicate and (2) some literature values for the partial molal volumes of NaOH and water. , unconnected for electrostriction effects, was found to be 53 ± 2 ml mole^?1. , corrected for volume changes due to solvent electrostriction by charged Si species, was estimated to be in the range 58–62 ml mole^?1; this range is 7–11 ml mole^?1 greater than the calculated from Willey's (Mar. Chem. 2, 239–250, 1974) solubility data obtained from the dissolution, in seawater, of amorphous silica subjected to hydrostatic pressure. Our does, however, agree within experimental error with the calculated from Jones and Pytkowicz's (Bull. Soc. Roy. Sci. Liege 42, 118–120, 1973) data for the solubility of amorphous silica in seawater at high pressure and is nearly in agreement with Willey's (Ph.D. thesis, Dalhousie University, 1975) solubility data for amorphous silica in 0.6 m NaCl.     

Total individual ion activity coefficients of calcium and carbonate in seawater at 25°C and 35%. salinity,and implications to the agreement between apparent and thermodynamic constants of calcite and aragonite

We have calculated the total individual ion activity coefficients of carbonate and calcium, and , in seawater. Using the ratios of stoichiometric and thermodynamic constants of carbonic acid dissociation and total mean activity coefficient data measured in seawater, we have obtained values which differ significantly from those widely accepted in the literature. In seawater at 25°C and 35%. salinity the (molal) values of and are $\text{0.038 ± 0.002}$ and $\text{0.173 ± 0.010}$, respectively. These values of and are independent of liquid junction errors and internally consistent with the value . By defining and on a common scale (), the product is independent of the assigned value of and may be determined directly from thermodynamic measurements in seawater. Using the value and new thermodynamic equilibrium constants for calcite and aragonite, we show that the apparent constants of calcite and aragonite are consistent with the thermodynamic equilibrium constants at 25°C and 35%. salinity. The demonstrated consistency between thermodynamic and apparent constants of calcite and aragonite does not support a hypothesis of stable Mg-calcite coatings on calcite or aragonite surfaces in seawater, and suggests that the calcite critical carbonate ion curve of Broecker and Takahashi (1978, Deep-Sea Research25, 65–95) defines the calcite equilibrium boundary in the oceans, within the uncertainty of the data.     

The partial molal volume of silicic acid in 0.725 M NaCl at 1°C determined by the neutralization of Na2SiO3

The partial molal volume of silicic acid ($\text{V}\text{?}\text{(Si(OH)}{}_4\text{)}$) in 0.725 M NaCl at 1°C was calculated from the measured volume change (Δ$\text{V}\text{?}{}_{\mathrm{n}}$) due to the neutralization of anhydrous sodium metasilicate with HCl and the $\text{V}\text{?}\text{(HCl)}$ and $\text{V}\text{?}\text{(NaCl)}$ obtained from the literature. $\text{V}\text{?}\text{(Si(OH)}{}_4\text{) = 59.0 cm}{}^3\text{mol}\text{? 1}$, determined under experimental conditions of pH = 2.2, compares favorably with $\text{V}\text{?}\text{(Si(OH)}{}_4\text{) = 58.9 cm}{}^3\text{mol}{}^{\mathrm{?1}}$ calculated from the measured volume change due to the hydrolysis of the meta-silicate salt at pH = 11 and from the partial molal volume due to electrostriction ($\text{V}\text{?}{}_{\mathrm{elect}}$) of water by charged Si species present in the solution at the high pH. This agreement lends support to a semiempirical model for calculating $\text{V}\text{?}{}_{\mathrm{elect}}$ in developed by Millero (1969). $\text{V}\text{?}\text{(NaOH) = ? 5.45 cm}{}^3\text{mol}{}^{\mathrm{?1}}$ in 0.725 M NaCl needed for this calculation was also determined in this work. The rate of polymerization of Si(OH)₄ at 1°C was monitored to insure that the monomer Si(OH)₄ was the main Si species present during the determination of $\text{V}\text{?}\text{(Si(OH)}{}_4\text{)}$ by neutralization of the alkali silicate. $\text{V}\text{?}\text{(Si(OH)}{}_4\text{)}$ determined in this study compares favorably with the value calculated from high pressure solubility measurements.     

Selective flotation of inherently hydrophobic minerals by controlling the air/solution interfacial tension

Selective wettability and floatability of several inherently hydrophobic minerals have been investigated using aqueous methanol solutions of various surface tensions. The relationship between the critical surface tension of wetting, $\text{γ}{}_{\mathrm{<mtext>c</mtext>}}$, and of floatability, $\text{γ}{}_{\mathrm{<mtext>cf</mtext>}}$, of the samples is examined. Experimental evidence is provided to show that a flotation feed cannot be represented by an uniquely defined $\text{γ}{}_{\mathrm{<mtext>cf</mtext>}}$ value. It is appropriate to specify for an inherently hydrophobic solid a critical surface tension range of floatability with upper and lower limits, $\text{γ}{}_{\mathrm{<mtext>cmf</mtext>}}$ and $\text{γ}{}_{\mathrm{<mtext>clf</mtext>}}$ respectively. The particles which are predominated by cleavage or crystal faces determine the lower limit, while those with some threshold degree of ionic character determine the upper limit. Examples of separation tests presented demonstrate that in the case of equality between $\text{γ}{}_{\mathrm{<mtext>c</mtext>}}$ values of two inherently floatable solids (or their $\text{γ}{}_{\mathrm{<mtext>clf</mtext>}}$ values), a difference in $\text{γ}{}_{\mathrm{<mtext>cmf</mtext>}}$ values determines the efficiency of their separation. It is also shown that the interfacial tension of maximum separation efficiency may be predicted from the individual surface tension of floatability curves which may be represented by second-order functions.     

The role of CO2 in the chemical modification of deep continental crust

Compositional differences between granulite facies rocks and equivalent amphibolite facies rocks and the observation of CO₂-rich fluid inclusions in granulites, have led to the suggestion that CO₂ must play a role in modifying the composition of deep continental crust. How CO₂ effects this change has remained unclear. Using the thermodynamic properties of aqueous ions in a fluid of evolving $\text{CO}{}_2\text{H}{}_2\text{O}$ ratio, it is possible to model the incongruent dissolution of feldspars under conditions appropriate for granulite facies metamorphism. The results demonstrate that dissolution will be strongly enhanced at high $\text{CO}{}_2\text{H}{}_2\text{O}$ ratios, with ion solubilities being Na⁺ >K⁺ ? Ca⁺⁺. This enhancement is compatible with the reported compositional contrasts between granulite and amphibolite facies rock, but requires large fluid volumes.To test the dissolution model, a detailed field and petrologic study was conducted in a well exposed granulite facies terrane in West Greenland. Strong correlation between fluid composition and bulk rock chemistry can be documented; CO₂-rich regions contain rocks which consistently have low ratios, while H₂O-rich regions consistently have high ratios. Magnetite rims on sulfide grains are ubiquitous in high regions and are absent in high regions, and they provide evidence that CO₂ was introduced into the region. These correlations and observations are predictable from the properties of the dissolution process. These considerations, along with observations regarding graphite petrogenesis, provide strong arguments that the total fluid volume interacting with the rock during metamorphism was very large, in some cases equaling or exceeding total rock volume. Such large fluid volumes can lead to significant compositional modification of the crust, and will mask the original protolith chemistry. Such processes should lead to Ca- and Al-enriched, Na-, K-, S- and Si-depleted residues in the deep crust.     

Use of Pitzer's equations to determine the media effect on the formation of lead chloro complexes

The spectrophotometric measurements of chloro complexes of lead in aqueous HCl, NaCl, MgCl₂ and CaCl₂ solutions at 25°C have been analyzed using Pitzer's specific interaction equations. Parameters for activity coefficients of the complexes PbCl⁺, PbCl₂⁰ and PbCl₃^? have been determined for the various media. Values of $\text{K}{}_1\text{= 30.0 ± 0.6}$, $\text{K}{}_2\text{= 106.7 ± 2.1}$ and $\text{K}{}_3\text{= 73.0 ± 1.5}$ were obtained for the cumulative formation constants. [$\text{Pb}{}^{\mathrm{2+}}\text{+ nCl}{}^{\mathrm{?}}\text{→ PbCl}{}_{\mathrm{n}}{}^{\mathrm{2?n}}\text{)}$]. These values are in reasonable agreement with literature data. The Pitzer parameters for the PbCl ion pairs in various media were used to calculate the speciation of Pb²⁺ in an artificial seawater solution.     

Solubility product of galena at 298°K: A possible explanation for apparent supersaturation in nature

The synthetic chelating agent ethylenediaminetetraacetic acid (EDTA) has been used to evaluate the stoichiometric solubility product of galena (PbS) at 298°K: $\text{K}{}_{\mathrm{s2}}\text{=}{}^{\mathrm{a}}\text{Pb}{}^{\mathrm{2+}}{}^{\mathrm{a}}\text{HS}{}^{\mathrm{?}}{}^{\mathrm{a}}\text{H}{}^{\mathrm{+}}$ This method circumvents the possible uncertainties in the stoichiometry and stability of lead sulfide complexes. At infinite dilution, $\text{Log K}{}_{\mathrm{s2}}\text{= ?12.25 ±0.17}$, and at an ionic strength corresponding to seawater ($\text{I = 0.7 M}$), $\text{Log K}{}_{\mathrm{s2}}\text{= ?11.73 ± 0.05}$. Using the value of $\text{K}{}_{\mathrm{s2}}$ at infinite dilution, and the free energies of formation of HS^? and Pb²⁺ at 298°K (literature values), the free energy of formation of PbS at 298°K is computed to be $\text{?79.1 ± 0.8 KJ/mol (?18.9 Kcal/mol)}$. Galena is shown to be more than two orders of magnitude more soluble than indicated by calculations based on previous thermodynamic data.     

A valid Margules formulation for an asymmetric ternary solution: revision of the olivine-ilmenite thermometer,with applications

The olivine-ilmenite thermometer of Andersen and Lindsley (1979) was based on an incorrect formulation for the excess free energy of an asymmetric ternary solution. A valid formulation is derived and used to revise the parameters of the olivine-ilmenite thermometer. For olivine and ilmenite that have equilibrated above 700°C, temperature can be calculated from: $\text{T(°C) = ?273 +¦-12549 + P[0.03X}{}_{\mathrm{fa}}\text{+ 0.01099(X}{}_{\mathrm{gk}}\text{?X}{}_{\mathrm{il}}\text{)?0.062] + 10496 X}{}_{\mathrm{fa}}\text{+ 5767(X}{}_{\mathrm{gk}}\text{?X}{}_{\mathrm{il}}\text{) + X}{}_{\mathrm{hem}}\text{(38602?141550X}{}_{\mathrm{il}}\text{?47183X}{}_{\mathrm{gk}}\text{)|/[5.67?R ln K}{}_{\mathrm{D}}\text{+ 6.52X}{}_{\mathrm{fa}}\text{+ 3.09(X}{}_{\mathrm{gk}}\text{?X}{}_{\mathrm{il}}\text{) + X}{}_{\mathrm{hem}}\text{(16.49?109.46 X}{}_{\mathrm{il}}\text{?36.49X}{}_{\mathrm{gk}}\text{)]}$ with $\text{K}{}_{\mathrm{d}}\text{=}\text{(X}{}_{\mathrm{il}}\text{X}{}_{\mathrm{fo}}\text{)}\text{(X}{}_{\mathrm{gk}}\text{X}{}_{\mathrm{fa}}\text{)}$. The revised model gives W^il·gk_G = 5767?3.09T + 0.011P and ΔG_exch = 7301 ? 8.9T ? 0.047P (T in K, P in bars). Applications include Apollo 17 breccias and kimberlites.     

Titanium in some Carboniferous sediments from Great Britain

In shale, mudstone and siltstone samples (154) a positive relationship exists between the $\text{TiO}{}_2\text{Al}{}_2\text{O}{}_3$ ratio and the quartz content. As the grain size of the sediment increases, so titanium oxides (rutile and anatase are present) increase in importance relative to the silicates, due to sorting. In sandstones the ratio reflects the maturity, but the degree of sorting must be taken into account. The ratio of TiO₂ substituting in the clay minerals to the Al₂O₃ content is not greater than 0.025 based on the whole rock analyses. This is borne out by values close to 0.010 obtained following the method of Raman and Jackson (Amer. Mineral. 50, 1086–1094, 1965). The addition of volcanic material to the normal sediment may either increase or decrease the whole rock $\text{TiO}{}_2\text{Al}{}_2\text{O}{}_3$ ratio depending on the ash composition. Volcanic contributions may thus be recognized and several examples are given from the British Carboniferous.     

Fission track studies of xenolithic chondrites: implications regarding brecciation and metamorphism

We have studied fission tracks in phosphates from one gas-poor chondrite and three gas-rich chondrites to determine their thermal history and brecciation time scales. More than 70 percent of the tracks in whitlockites in these meteorites are due to the decay of extinct Pu²⁴⁴.Whitlockites separated from Bhola, a gas-poor chondrite, have $\text{ρ}{}_{\mathrm{Pu}}\text{ρ}{}_{\mathrm{U}}\text{= 2.6–5.2}$ and a model fission track age of 4.0 Gyr for a $\text{(}\text{Pu}\text{U}\text{)}{}_{\mathrm{4.55Gyr}}\text{= 0.045}$. Brecciation of the Bhola meteorite must have occurred at ?4.3 Gyr to account for the metal data (Scott and Rajan, 1981). A minimum cooling rate of $\text{0.9}{}_{\mathrm{–0.2}}{}^{0.3}\text{K}\text{Myr}$ in the temperature interval 800 to 300 K obtained from the track data is a factor of seven higher than the metallographic cooling rate ($\text{0.1}\text{K}\text{Myr}$).For the gas-rich chondrites, the $\text{ρ}{}_{\mathrm{Pu}}\text{ρ}{}_{\mathrm{U}}$ in whitlockites are: Weston, 32–148; Fayetteville, 21–227; and St. Mesmin, 26–137. Whitlockites from all these meteorites give model fission track ages of 4.4 Gyr assuming a $\text{(}\text{Pu}\text{U}\text{)}{}_{\mathrm{4.55\; Gyr}}\text{= 0.045}$. The final brecciation event definitely did not reset the track clock in phosphates of St. Mesmin. Our data suggest that it is also true for Weston and Fayetteville. We conclude that our observed fission track ages date the end of metamorphic cooling in the meteorite parent bodies and support the planetesimal model for the formation of xenolithic chondrites.     

Methane-producing bacteria: natural fractionations of the stable carbon isotopes

The ${}^{13}\text{C}{}^{12}\text{C}$ fractionation factors ($\text{CO}{}_2\text{CH}{}_4$) for the reduction of CO₂ to CH₄ by pure cultures of methane-producing bacteria are, for Methanosarcina barkeri at 40°C, 1.045 ± 0.002; for Methanobacterium strain M.o.H. at 40°C, 1.061 ± 0.002; and, for Methanobacterium thermoautotrophicum at 65°C, 1.025 ± 0.002. These observations suggest that the acetic acid used by acetate dissimilating bacteria, if they play an important role in natural methane production, must have an intramolecular isotopic fractionation ($\text{CO}{}_2\text{H}\text{CH}{}_3$) approximating the observed $\text{CO}{}_2\text{CH}{}_4$ fractionation.     

Steady diffusion model for olivine-plagioclase corona growth

This paper describes an application of a steady diffusion model (Joesten, 1977) to an olivineplagioclase corona and some new results about a theoretical background on the steady diffusion equations.The olivine-plagioclase corona in a metanorite from Mt. Ikoma. Japan, has a layer sequence of olivinecummingtonite-hornblende + spinel-plagioclase. An analysis of a set of steady diffusion equations for the corona in the four-component system, MgO-AlO_{$\text{3}\text{2}$}-SiO₂-Na_0.1Ca_0.9O_0.95 (NC) with excess H₂O. successfully gives the exchange cycle (Fisher, 1973) in the layer sequence with specific values of the phenomenological coefficients' ratios; $\text{L}{}_{\mathrm{<mtext>MgMg</mtext>}}\text{L}{}_{\mathrm{<mtext>SiSi</mtext>}}$, $\text{L}{}_{\mathrm{<mtext>MgMg</mtext>}}\text{L}{}_{\mathrm{<mtext>AlAl</mtext>}}$ and $\text{L}{}_{\mathrm{<mtext>MgMg</mtext>}}\text{L}{}_{\mathrm{<mtext>NCNC</mtext>}}$. The factor which controls most strictly the stability of the layer sequence under isobaric-isothermal conditions is $\text{L}{}_{\mathrm{<mtext>MgMg</mtext>}}\text{L}{}_{\mathrm{<mtext>AlAl</mtext>}}$.Theoretical considerations on the steady diffusion equations show that the L-ratios does not depend on concentrations even if the phenomenological coefficients themselves are functions of concentrations. Equivalence of the steady state condition and the minimum rate of entropy production law (Prigogine, 1967) is also proved for the system with fixed chemical potential gradients under isobaric-isothermal conditions, such as reaction bands. These results give a strong background for the model.     

Density calculations for silicate liquids. I. Revised method for aluminosilicate compositions

Equations are developed for calculating the density of aluminosilicate liquids as a function of composition and temperature. The mean molar volume at reference temperature T_r, is given by $\text{V}{}_{\mathrm{r}}\text{= ∑X}{}_{\mathrm{i}}\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{i}}\text{+ X}{}_{\mathrm{A}}\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$, where the summation is taken over all oxide components except A1₂O₃, X stands for mole fraction, terms are constants derived independently from an analysis of volume-composition relations in alumina-free silicate liquids, and $\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is the composition-dependent apparent partial molar volume of Al₂O₃. The thermal expansion coefficient of aluminosilicate liquids is given by $\text{α = ∑X}{}_{\mathrm{i}}\text{}\text{?}\text{ga}{}_{\mathrm{i}}{}^{\mathrm{o}}\text{+ X}{}_{\mathrm{A}}\text{}\text{?}\text{ga}{}_{\mathrm{A}}{}^{\mathrm{o}}$, where $\text{}\text{?}\text{ga}{}_{\mathrm{i}}{}^{\mathrm{o}}$ terms are constants independent of temperature and composition, and $\text{}\text{?}\text{ga}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is a composition-dependent term representing the effect of Al₂O₃ on the thermal expansion. Parameters necessary to calculate the volume of silicate liquids at any temperature T according to V(T) = V_rexp[α(T-T_r)], where T_r = 1400°C have been evaluated by least-square analysis of selected density measurements in aluminosilicate melts. Mean molar volumes of aluminosilicate liquids calculated according to the model equation conform to experimentally measured volumes with a root mean square difference of 0.28 $\text{cc}\text{mole}$ and an average absolute difference of 0.90% for 248 experimental observations. The compositional dependence of $\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is discussed in terms of several possible interpretations of the structural role of Al³⁺ in aluminosilicate melts.     

Partial molal volume calculations for the dissolution of aged amorphous silica in salt water and seawater at 0–2°C

Measurement of solubility as a function of pressure allows calculation of $\text{3}\text{V}\text{?}{}_1$. Using this experimental approach, the best estimate of $\text{3}\text{V}\text{?}{}_1$ for the dissolution of aged amorphous silica in salt water or seawater at 0–2°C is ?9.9 cm³ mol^?1 (standard error = 0.4 cm³ mol^?1). This gives , which compares well with other published values of .     

Correction of ground-water chemistry and carbon isotopic composition for effects of CO2 outgassing

Direct measurements on water samples from several CO₂-charged warm springs are significantly higher than values calculated from field pH and alkalinity (and other constituents). In addition, calcite saturation indices calculated from field pH and solution composition indicated supersaturation in samples which, on the basis of hydrogeologic concepts, should be near saturation or undersaturated. We attribute these discrepancies to uncertainties in field pH, resulting from CO₂ outgassing during pH measurement. Because samples for direct measurement can be taken with minimal disturbance to the water chemistry, we have used the measured to back calculate an estimate of the field pH and the carbon isotopic composition of the water before outgassing. By reconstructing water chemistry in this way, we find generally consistent grouping of $\text{δ}{}^{13}\text{C}$, pH, and degree of calcite saturation in samples taken from the same source at different times, an observation which we expect based on our understanding of the hydrogeology and geochemistry of the ground-water systems. This suggests that for very careful geochemical work, particularly on ground-waters much above ambient temperature, measurements may provide more information on the system and a better estimate of its state of saturation with respect to carbonate minerals than can field measurements of pH.     

Light hydrocarbons in Red Sea brines and sediments

Light hydrocarbon (C₁-C₃) concentrations in the water from four Red Sea brine basins (Atlantis II, Suakin, Nereus and Valdivia Deeps) and in sediment pore waters from two of these areas (Atlantis II and Suakin Deeps) are reported. The hydrocarbon gases in the Suakin Deep brine (T = ~ 25°C, $\text{Cl}{}^{\mathrm{?}}\text{= ~ 85‰}$, $\text{CH}{}_4\text{=}\text{~ 71}\text{1}$) are apparently of biogenic origin as evidenced by $\text{C}{}_1\text{(C}{}_2\text{+ C}{}_3$) ratios of ~ 1000. Methane concentrations (6–8 μl/l) in Suakin Deep sediments are nearly equal to those in the brine, suggesting sedimentary interstitial waters may be the source of the brine and associated methane.The Atlantis II Deep has two brine layers with significantly different light hydrocarbon concentrations indicating separate sources. The upper brine (T = ~ 50°C, $\text{Cl}{}^{\mathrm{?}}\text{= ~ 73‰}$, CH₄ = ~ 155 μl/l) gas seems to be of biogenic origin [$\text{C}{}_1\text{(C}{}_2\text{+ C}{}_3\text{) = ~1100}$], whereas the lower brine (T = ~ 61°C, $\text{Cl}{}^{\mathrm{?}}\text{= ~ 155‰}$, CH₄ = ~ 120μl/l) gas is apparently of thermogenic origin [$\text{C}{}_1\text{(C}{}_2\text{+ C}{}_3\text{) = ~ 50}$]. The thermogenic gas resulting from thermal cracking of organic matter in the sedimentary column apparently migrates into the basin with the brine, whereas the biogenic gas is produced in situ or at the seawater-brine interface. Methane concentrations in Atlantis II interstitial waters underlying the lower brine are about one half brine concentrations; this difference possibly reflects the known temporal variations of hydrothermal activity in the basin.     

A recycle flow flotation machine model

Residence time measurements were made on a Denver laboratory flotation machine with and without the DR ring assembly. Soluble and insoluble tracers were used (a dye and fine quartz, respectively), and the variables studied were tank liquid volume, $\text{V}$, water and air volumetric flow rates, Q and Q_A respectively, and some geometric and design variables.By analogy with nominal residence time, $\text{t}{}_{\mathrm{<mtext>N</mtext>}}\text{(=}\text{V}\text{Q}\text{)}$, a term “effective residence time” $\text{t}{}_{\mathrm{<mtext>E</mtext>}}$ is defined by:

$\text{f}\text{(t)=}\text{exp}\text{[?}\text{t}\text{t}{}_{\mathrm{E}}$

where f(t) is the fraction of tracer remaining in the tank at time t. Perfect mixing is indicated if and only if: (i) data satisfies the exponential relationship; and (ii) $\text{t}{}_{\mathrm{<mtext>E</mtext>}}\text{t}{}_{\mathrm{<mtext>N</mtext>}}\text{= 1}$.Using the soluble tracer the machine behaved substantially as a perfect mixer under all operating conditions, except with the DR ring at values of Q_A nearly double the natural aeration capacity of the machine; condition (i) above was satisfied, but $\text{t}{}_{\mathrm{<mtext>E</mtext>}}\text{t}{}_{\mathrm{<mtext>N</mtext>}}\text{～ 1.1}$.With the insoluble tracer the machine behaved as a perfect mixer only without air. As Q_A increased, $\text{t}{}_{\mathrm{<mtext>E</mtext>}}\text{t}{}_{\mathrm{<mtext>N</mtext>}}$ increased from unity to about 1.2, and the effect was emphasized by the DR ring. In all cases condition (i) above was satisfied.A model in which the flow pattern in the tank includes a large component of pulp recirculation through the impeller region is developed. This model can account for the experimental findings but the details remain to be elucidated.