Donald G. Miller

Ternary diffusion coefficients of the brine systems NaCl (0.5 M)-Na2SO4 (0.5 M)-H2O and NaCl (0.489 M)-MgCl2 (0.051 M)-H2O (seawater composition) at 25°C☆

Abstract Mutual diffusion coefficients have been measured by Rayleigh interferometry for two ternary brine compositions at 25°C: NaCl (0.5 M)-Na 2 SO 4 (0.5 M)-H 2 O and NaCl (0.489 M)-MgCl 2 (0.051 M)H 2 O. The latter is a ternary analog of seawater. Four diffusion coefficients are required to characterize a ternary system. The data show that the cross term diffusion coefficients are significant, and cannot be neglected in accurate geochemical modeling. Since D 21 for NaCl-Na 2 SO 4 -H 2 O is negative, a sufficient gradient of NaCl can cause Na 2 SO 4 to move “uphill” against its own gradient. One of the cross term coefficients for NaClMgCl 2 -H 2 O is nearly as large as one of the main term coefficients.

Effects of different sized concentration differences across free diffusion boundaries and comparison of Gouy and Rrayleigh diffusion measurements using NaCl−KCl−H2O

Diffusion was systematically studied in the ternary system NaCl (0.5M)−KCl (0.5M)−H2O at 25°C. There were four purposes. First, current methods to extractDij from Gouy and Rayleigh interferometry data depend on treating theDij as effectively constant. If concentration differences ΔCi across the boundary are large, this may not be true. To explore this issue, four sets of experiments were performed. Each set had four experiments with approximately the same total number of fringesJ. Each set also had the same corresponding ΔC1/ΔC2 ratios as the other three, but the ΔCi were adjusted such that the four sets hadJ≈30, 60, 90, and 120, respectively. Noclear dependence of theDij on ΔCi was found within their realistic errors. Second, the Gosting diffusiometer can yield both Rayleigh and Gouy fringe patterns during the same experiment. Therefore, theDij from both methods were compared, and agree well. Third, a new method for analyzing Gouy fringe positions (Miller; program TNY) can be compared to the classical one (Fujita-Gosting; program RFG). TheDij from both analyses agree well. Fourth, we compared results from the Gosting diffusiometer with those at the same composition from other diffusiometers: one data set by O[Donnell and Gosting from an older Gouy apparatus, and three Rayleigh sets at differentJ values from our older Model H diffusiometer. Results from older diffusiometers were more scattered, but correspondingDij agree within realistic errors. As reported previously, realistic errors are approximately four times the statistical errors obtained by least squares. Recommended Rayleigh and GouyDij are presented for this composition.

Isopiestic determination of the osmotic and activity coefficients of ZnCl2(aq) at 298.15 K

Abstract Isopiestic vapor-pressure measurements were performed at 83 molalities of ZnCl 2 (aq) from 0.31358 to 13.134 mol · kg −1 at 298.15 K. Measurements were made by using high-purity ZnCl 2 adjusted to its stoichiometric pH value. Our results are critically compared with previous isopiestic, direct vapor-pressure, and e.m.f. measurements, and recommended values are reported for osmotic coefficients, water activities, solute activity coefficients, and chemical-potential derivatives. Published isopiestic values for ZnCl 2 (aq) up to 10 mol · kg −1 and most e.m.f. values up to about 6 mol · kg −1 generally agree well with our experimental results, but some e.m.f. results and direct vapor-pressure measurements appear to have been inaccurate.

A test of the onsager reciprocal relations and a discussion of the ionic isothermal vector transport coefficientsI Ij for aqueous AgNO3 at 25°C

Values ofIij calculated from experimental data are given for AgNO3 at 25°C. Experimental values of the ratioI12/I21 are calculated to provide a sensitive direct test of the Onsager reciprocal relations,I12=I21. This ratio is found to be unity within experimental error (ca. 2%). The general physical interpretation ofIij/N as mobilities is discussed. An approximate way of estimatingIij for dissociated salts is considered. A comparison is made between AgNO3Iij data and corresponding data for NaCl and KCl. It is concluded that ion-pair formation (1) sharply increases the magnitude of the interaction mobility,I12/N; and (2) increases the “intrinsic mobility” of Ag+,I11/N, and decreases the intrinsic mobility of NO3−,I22/N.

Sphere drag at Mach numbers from 0·3 to 2·0 at Reynolds numbers approaching 10 7

Our analysis of 18th and 19th century cannon firings shows that knowledge of sphere drag can be substantially extended into the region of 0·3 ≤ M ∞ ≤ 2·0 and Re ∞d up to 10 7 . Bashforth’s chronographic measurements (1868) are of a quality comparable to modern measurements. The data of Mayevski (chronograph, 1868), Hutton (ballistic pendulum, 1787-1791), and Didion (ballistic pendulum, 1839-1840) are of lesser accuracy but in agreement with Bashforth’s. These cannon data are combined with modern data to provide the most extensive curves available of C D vs. Re ∞d in this region. Interesting features of these curves for M ∞ ≤ 1·0 are briefly described.

Mutual diffusion coefficients of aqueous ZnSO4 at 25°C

Diffusion coefficients of the system ZnSO4−H2O at 25°C have been measured using Rayleigh optics from 0.004 to 3.33m. The results appear to extrapolate with reasonable agreement to the data of Harned and Hudson at very low concentration. The diffusion coefficients decrease from 0.8486×10−5 at 0m to 0.2813×10−5 cm2-sec−1 at 3.33m. Densities were measured over the concentration range 0.10 to 3.60m and combined with the data of Geffcken and of Gibson to obtain an analytical expression for density over the concentration range 0≤m≤3.6.

Ternary mutual diffusion coefficients of ZnCl2-KCl-H2O at 25°C by Rayleigh interferometry

Mutual diffusion coefficients and densities were measured for aqueous ZnCl2−KCl mixtures at 25° by using free-diffusion Rayleigh interferometry and pycnometry, respectively. The ZnCl2 concentrations were fixed at 1.5 mol-dm−3, whereas those of KCl were 0.5, 1.25, 2.0, or 4.0 mol-dm−3. This corresponds to a half charged zinc-chlorine storage battery at various suporting electrolyte concentrations. The main-term coefficient of ZnCl2 only varies by 10% with KCl concentration, whereas that of KCl varies by about 22%. The ZnCl2 cross-term coefficient remains small and positive; in contrast the KCl cross-term coefficient goes through a maximum and is negative at high and low KCl concentrations. At KCl concentrations of 0.5 and 4.0 mol-dm−3, solutions with the KCl Δc≈0 are statically and dynamically (diffusively) unstable at the top and bottom of the boundary. Evaluation of the parameters of the non-linear least-squares solution to the diffusion equation is difficult for the 1.25 mol-dm−3 KCl case, since this system has nearly equal eigenvalues in its diffusion coefficient matrix.

Mutual diffusion coefficients, electrical conductances, osmotic coefficients, and ionic transport coefficients l/sub ij/ for aqueous CuSO/sub 4/ at 25/sup 0/C

Experimental thermodynamic and transport data are presented for aqueous CuSO4 solution at 25°C from low concentrations to near saturation. Included are diffusion coefficients (Rayleigh interferometry), electrical conductances (DC method), and osmotic coefficients (isopiestic). These data and corresponding literature data are critically compared, as are literature density data. The resulting best values, together with previously compared transference number results, provide an extensive set of critically reviewed data for aqueous CuSO4. Onsager coefficientslijhave been calculated for this salt and are compared with data for other valence types.

An extrapolation procedure to obtain the total fringe number from Gouy fringe pattern data

A rapid new procedure is described for getting the total number of fringes J from Gouy fringe pattern data. This PQ method is exact and the results excellent (within 0.01–0.03 fringe) for ideal systems (Ωj=0 for all j, Q0=0). Such systems include most binaries; for these, the diffusion coefficient is either constant or a polynomial function of concentration with small concentration differences. For multicomponent systems and some binaries, Q0 can be significantly different from 0. In these cases, the PQ method unambiguously gives the integer number of fringes. If in addition Q0/Q1 is larger than 2.0, then J obtained from a second extrapolation procedure is also good.

Series expansion methods for extracting ternary diffusion coefficients from Rayleigh interferometric data

Three series expansions are examined for use in extracting ternary diffusion coefficients from Rayleigh interferometric data for free diffusion experiments. Convergence comparisons show that, providing enough terms are used, two of the three are suitable, including one used earlier by Albright and Sherrill. A new simpler analysis, using only linear least squares, has been applied to simulated and real data with good results. Advantages and disadvantages of series methods are compared to a direct non-linear least squares analysis.