scholarly journals Experimental recalibration of the Cr-in-clinopyroxene geobarometer: improved precision and reliability above 4.5 GPa

2021 ◽  
Vol 176 (2) ◽  
Author(s):  
Z. J. Sudholz ◽  
G. M. Yaxley ◽  
A. L. Jaques ◽  
G. P. Brey

AbstractThe pressure dependence of the exchange of Cr between clinopyroxene and garnet in peridotite is applicable as a geobarometer for mantle-derived Cr-diopside xenocrysts and xenoliths. The most widely used calibration (Nimis and Taylor Contrib Miner Petrol 139: 541–554, 2000; herein NT00) performs well at pressures below 4.5 GPa, but has been shown to consistently underestimate pressures above 4.5 GPa. We have experimentally re-examined this exchange reaction over an extended pressure, temperature, and compositional range using multi-anvil, belt, and piston cylinder apparatuses. Twenty-nine experiments were completed between 3–7 GPa, and 1100–1400 °C in a variety of compositionally complex lherzolitic systems. These experiments are used in conjunction with several published experimental datasets to present a modified calibration of the widely-used NT00 Cr-in-clinopyroxene (Cr-in-cpx) single crystal geobarometer. Our updated calibration calculates P (GPa) as a function of T (K), CaCr Tschermak activity in clinopyroxene $$\left( {a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}} } \right)$$ a CaCrTs cpx , and Cr/(Cr + Al) (Cr#) in clinopyroxene. Rearranging experimental results into a 2n polynomial using multiple linear regression found the following expression for pressure:$$P\left( {{\text{GPa}}} \right) = 11.03 + \left( { - T{ }\left( {\text{K}} \right){\text{ ln}}(a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}} ) \times 0.001088{ }} \right) + \left( {1.526 \times {\text{ln}}\left( {\frac{{{\text{Cr}}\#^{{{\text{cpx}}}} }}{{T{ }\left( {\text{K}} \right)}}} \right)} \right){ }$$ P GPa = 11.03 + - T K ln ( a CaCrTs cpx ) × 0.001088 + 1.526 × ln Cr # cpx T K where $${\text{Cr}}\#^{{{\text{cpx}}}} = \left( {\frac{{{\text{Cr}}}}{{{\text{Cr}} + {\text{Al}}}}} \right)$$ Cr # cpx = Cr Cr + Al , $$a_{{{\text{CaCrTs}}}}^{{{\text{cpx}}}} = {\text{Cr}} - 0.81 \cdot {\text{Cr}}\#^{{{\text{cpx}}}} \cdot \left( {{\text{Na}} + {\text{K}}} \right),$$ a CaCrTs cpx = Cr - 0.81 · Cr # cpx · Na + K , with all mineral components calculated assuming six oxygen anions per formula unit in clinopyroxene.Temperature (K) may be calculated through a variety of geothermometers, however, we recommend the NT00 single crystal, enstatite-in-clinopyroxene (en-in-cpx) geothermometer. The pressure uncertainty of our updated calibration has been propagated by incorporating all analytical and experimental uncertainties. We have found that pressure estimates below 4 GPa, between 4–6 GPa and above 6 GPa have associated uncertainties of 0.31, 0.35, and 0.41 GPa, respectively. Pressures calculated using our calibration of the Cr-in-cpx geobarometer are in good agreement between 2–7 GPa, and 900–1400 °C with those estimated from widely-used two-phase geobarometers based on the solubility of alumina in orthopyroxene coexisting with garnet. Application of our updated calibration to suites of well-equilibrated garnet lherzolite and garnet pyroxenite xenoliths and xenocrysts from the Diavik-Ekati kimberlite and the Argyle lamproite pipes confirm the accuracy and precision of our modified geobarometer, and show that PT estimates using our revised geobarometer result in systematically steeper paleogeotherms and higher estimates of the lithosphere‒asthenosphere boundary compared with the original NT00 calibration.

2006 ◽  
Vol 4 ◽  
pp. 224-236
Author(s):  
A.S. Topolnikov

The paper is devoted to numerical modeling of Navier–Stokes equations for incompressible media in the case, when there exist gas and liquid inside the rectangular calculation region, which are separated by interphase boundary. The set of equations for incompressible liquid accounting for viscous, gravitational and surface (capillary) forces is solved by finite-difference scheme on the spaced grid, for description of interphase boundary the ideology of Level Set Method is used. By developed numerical code the set of hydrodynamic problems is solved, which describe the motion of two-phase incompressible media with interphase boundary. As a result of numerical simulation the solutions are obtained, which are in good agreement with existing analytical and experimental solutions.


1985 ◽  
Vol 50 (3) ◽  
pp. 745-757 ◽  
Author(s):  
Andreas Zahn ◽  
Lothar Ebner ◽  
Kurt Winkler ◽  
Jan Kratochvíl ◽  
Jindřich Zahradník

The effect of two-phase flow regime on decisive hydrodynamic and mass transfer characteristics of horizontal-tube gas-liquid reactors (pressure drop, liquid holdup, kLaL) was determined in a cocurrent-flow experimental unit of the length 4.15 m and diameter 0.05 m with air-water system. An adjustable-height weir was installed in the separation chamber at the reactor outlet to simulate the effect of internal baffles on reactor hydrodynamics. Flow regime maps were developed in the whole range of experimental gas and liquid flow rates both for the weirless arrangement and for the weir height 0.05 m, the former being in good agreement with flow-pattern boundaries presented by Mandhane. In the whole range of experi-mental conditions pressure drop data could be well correlated as a function of gas and liquid flow rates by an empirical exponential-type relation with specific sets of coefficients obtained for individual flow regimes from experimental data. Good agreement was observed between values of pressure drop obtained for weirless arrangement and data calculated from the Lockhart-Martinelli correlation while the contribution of weir to the overall pressure drop was well described by a relation proposed for the pressure loss in closed-end tubes. In the region of negligible weir influence values of liquid holdup were again succesfully correlated by the Lockhart-Martinelli relation while the dependence of liquid holdup data on gas and liquid flow rates obtained under conditions of significant weir effect (i.e. at low flow rates of both phases) could be well described by an empirical exponential-type relation. Results of preliminary kLaL measurements confirmed the decisive effect of the rate of energy dissipation on the intensity of interfacial mass transfer in gas-liquid dispersions.


1989 ◽  
Vol 54 (11) ◽  
pp. 2951-2961 ◽  
Author(s):  
Miloslav Karel ◽  
Jaroslav Nývlt

Measured growth and dissolution rates of single crystals and tablets were used to calculate the overall linear rates of growth and dissolution of CuSO4.5 H2O crystals. The growth rate for the tablet is by 20% higher than that calculated for the single crystal. It has been concluded that this difference is due to a preferred orientation of crystal faces on the tablet surface. Calculated diffusion coefficients and thicknesses of the diffusion and hydrodynamic layers in the vicinity of the growing or dissolving crystal are in good agreement with published values.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Richard J. Smith ◽  
Fernando Pérez-Cota ◽  
Leonel Marques ◽  
Matt Clark

AbstractBrillouin light scattering (BLS) is an emerging method for cell imaging and characterisation. It allows elasticity-related contrast, optical resolution and label-free operation. Phonon microscopy detects BLS from laser generated coherent phonon fields to offer an attractive route for imaging since, at GHz frequencies, the phonon wavelength is sub-optical. Using phonon fields to image single cells is challenging as the signal to noise ratio and acquisition time are often poor. However, recent advances in the instrumentation have enabled imaging of fixed and living cells. This work presents the first experimental characterisation of phonon-based axial resolution provided by the response to a sharp edge. The obtained axial resolution is up to 10 times higher than that of the optical system used to take the measurements. Validation of the results are obtained with various polymer objects, which are in good agreement with those obtained using atomic force microscopy. Edge localisation, and hence profilometry, of a phantom boundary is measured with accuracy and precision of approximately 60 nm and 100 nm respectively. Finally, 3D imaging of fixed cells in culture medium is demonstrated.


1992 ◽  
Vol 114 (1) ◽  
pp. 14-30 ◽  
Author(s):  
E. F. Caetano ◽  
O. Shoham ◽  
J. P. Brill

Mechanistic models have been developed for each of the existing two-phase flow patterns in an annulus, namely bubble flow, dispersed bubble flow, slug flow, and annular flow. These models are based on two-phase flow physical phenomena and incorporate annulus characteristics such as casing and tubing diameters and degree of eccentricity. The models also apply the new predictive means for friction factor and Taylor bubble rise velocity presented in Part I. Given a set of flow conditions, the existing flow pattern in the system can be predicted. The developed models are applied next for predicting the flow behavior, including the average volumetric liquid holdup and the average total pressure gradient for the existing flow pattern. In general, good agreement was observed between the experimental data and model predictions.


Molecules ◽  
2021 ◽  
Vol 26 (12) ◽  
pp. 3627
Author(s):  
Nikola Sakač ◽  
Dubravka Madunić-Čačić ◽  
Dean Marković ◽  
Lucija Hok ◽  
Robert Vianello ◽  
...  

A 1,3-dihexadecyl-1H-benzo[d]imidazol-3-ium-tetraphenylborate (DHBI-TPB) ion-pair implemented in DHBI-TPB surfactant sensor was used for the potentiometric quantification of anionic surfactants in detergents and commercial household care products. The DHBI-TPB ion-pair was characterized by FTIR spectroscopy and computational analysis which revealed a crucial contribution of the C–H∙∙∙π contacts for the optimal complex formation. The DHBI-TPB sensor potentiometric response showed excellent analytical properties and Nernstian slope for SDS (60.1 mV/decade) with LOD 3.2 × 10−7 M; and DBS (58.4 mV/decade) with LOD 6.1 × 10−7 M was obtained. The sensor possesses exceptional resistance to different organic and inorganic interferences in broad pH (2–10) range. DMIC used as a titrant demonstrated superior analytical performances for potentiometric titrations of SDS, compared to other tested cationic surfactants (DMIC > CTAB > CPC > Hyamine 1622). The combination of DHBI-TPB sensor and DMIC was successfully employed to perform titrations of the highly soluble alkane sulfonate homologues. Nonionic surfactants (increased concentration and number of EO groups) had a negative impact on anionic surfactant titration curves and a signal change. The DHBI-TPB sensor was effectively employed for the determination of technical grade anionic surfactants presenting the recoveries from 99.5 to 101.3%. The sensor was applied on twelve powered samples as well as liquid-gel and handwashing home care detergents containing anionic surfactants. The obtained results showed good agreement compared to the outcomes measured by ISE surfactant sensor and a two-phase titration method. The developed DHBI-TPB surfactant sensor could be used for quality control in industry and has great potential in environmental monitoring.


Author(s):  
Sadao Kurosawa ◽  
Kiyoshi Matsumoto

In this paper, numerical method for predicting critical cavitation performance in a hydraulic turbine is presented. The prediction method is based on unsteady cavitation flow analysis to use bubble two-phase flow model. The prediction of the critical cavitation performance was carried out for the aixal hydraulic turbine and the francis turbine as a typical examples. Results compared to the experiment showed a good agreement for the volume of cavity and the performance drop off and it was recognized that this method could be used as an engineering tool of a hydraulic turbine development.


1970 ◽  
Vol 48 (7) ◽  
pp. 827-833 ◽  
Author(s):  
S. T. Lam ◽  
A. E. Litherland ◽  
J. J. Simpson

The 1459-keV level of 19F was populated by the 19F(p,p′γ)19F reaction at a proton energy of 2.78 MeV. The E2/M1 mixing ratio for the 1459 → 110 keV transition was determined to be [Formula: see text] from a combination of the γ-ray angular distribution and linear polarization and the nuclear lifetime. The γ-ray angular distribution was measured with a coaxial Ge(Li) detector and the γ-ray linear polarization with a planar Ge(Li) detector. The corresponding E2 and M1 transition strengths for a lifetime of 0.084 ± 0.020 ps are found to be [Formula: see text] and 0.10 ± 0.03 W.u. respectively. They are in good agreement with the particle–hole calculations of Benson and Flowers. The branching ratios of the 1459-keV level agree well with those of Poletti et al. The γ-ray transitions from the 1459-keV level provide a good example for demonstrating the usefulness of a single crystal Ge(Li) polarimeter.


1982 ◽  
Vol 104 (4) ◽  
pp. 750-757 ◽  
Author(s):  
C. T. Avedisian

A study of high-pressure bubble growth within liquid droplets heated to their limits of superheat is reported. Droplets of an organic liquid (n-octane) were heated in an immiscible nonvolatile field liquid (glycerine) until they began to boil. High-speed cine photography was used for recording the qualitative aspects of boiling intensity and for obtaining some basic bubble growth data which have not been previously reported. The intensity of droplet boiling was found to be strongly dependent on ambient pressure. At atmospheric pressure the droplets boiled in a comparatively violent manner. At higher pressures photographic evidence revealed a two-phase droplet configuration consisting of an expanding vapor bubble beneath which was suspended a pool of the vaporizing liquid. A qualitative theory for growth of the two-phase droplet was based on assuming that heat for vaporizing the volatile liquid was transferred across a thin thermal boundary layer surrounding the vapor bubble. Measured droplet radii were found to be in relatively good agreement with predicted radii.


Earlier work on condensation phenomena is briefly reviewed, and existing measurements of condensation energies are summarized. Measurements of condensation energies have been made for aluminium, silver and cadmium on glass and for aluminium and silver on single-crystal cleavage surfaces of sodium chloride and potassium bromide. Adhesive energies or binding energies between film and substrate have been calculated in each case. Association energies for nucleation are obtained by difference and shown to be consistent. Results for cadmium show good agreement with earlier work, but results for aluminium do not agree with the earlier results of Rhodin who measured the condensation energies for aluminium on various substrates, obtaining values which suggest chemisorption. These results appear to be too high and a possible explanation is given. It is concluded that the adhesive energy is due to physical adsorption and can be explained in terms of van der Waals forces only.


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