Stokes flow and deposition of aerosol nanoparticles in model filters composed of elliptic fibers

The calculation is implemented for the fiber collection efficiencies due to diffusion of nanoparticles in model filters, i.e., separate rows of fibers with an elliptic cross section located normal to the flow at different orientations of the ellipse axes with respect to the flow. The Stokes flow field in the system of the fibers is found by the method of fundamental solutions. The concentration field of Brownian particles and the efficiency of their deposition onto the fibers are determined from the numerical solution of the equation for the convective diffusion. The dependence of the capture coefficient on the Peclet number for elliptic fibers is shown to have the form η = APe^−m, where exponent m changes from 2/3 to 3/4 at the parallel and normal orientation of the major axes of the ellipses with respect to the flow, respectively. It is shown that, from the viewpoint of aerosol nanoparticle capture, the best filters are those in which the fibers have a maximum midsection at the same cross-sectional area.     

The Deposition of Aerosol Submicron Particles on Ultrafine Fiber Filters

The diffusion deposition of submicron aerosol particles of a finite size on a model filter composed of parallel ultrafine fibers with a radius comparable with the mean free path of air molecules was considered. The diffusion capture coefficient with allowance made for particle interception _DR is found by the numerical solution of the elliptic equation of steady-state convective diffusion in the wide ranges of interception parameter R, Peclet (Pe) and Knudsen (Kn) numbers at small Reynolds numbers. It was shown that, at small Kn numbers, the _DR value exceeds the sum of capture coefficients due to specific deposition mechanisms, interception and diffusion, = _R + _D , whereas, at Kn > 1, _DR . Within the range of intermediate Pe, Kn, and R numbers, the radius of the most penetrating particles is higher than the fiber radius.     

Penetration of nanoparticles through screen-type diffusion batteries

The deposition of aerosol nanoparticles from Stokes flows in screen-type diffusion batteries designed for the determination of diffusion coefficients for suspended nanoparticles is considered. Average fiber collection efficiencies η calculated for screens consisting of two perpendicularly contacting rows of parallel equidistant straight fibers agree with the experimental data obtained for woven screens within the Peclet number range Pe = 0.15−1000. It is shown that, for dense screens, the η ∼ Pe^−2/3 power dependence is valid at Pe > 10. For rarefied screens, this dependence is fulfilled down to Pe ∼ 0.1. At Pe ≪ 1, the integral flow of particles advancing on the fibers of the first row in the screen and the fiber collection efficiency, η of an isolated row tends to a geometrical limit, which is equal to the ratio of the distance between the axes of the fibers to the fiber diameter.     

Diffusional deposition of nanoparticles in a 3D model fiber filter

Diffusional particle deposition from a flow on fibers at low Reynolds number Re ≪ 1 is studied in a model filter consisting of equidistant rows of parallel fibers perpendicular to the flow and forming a three-dimensional structure where one hexagonal 2D-dimensional lattice is inserted into another at the right angle. It is shown that under equal low filter packing density fiber collection efficiencies calculated within 3D and 2D models are practically the same.     

Dielectric relaxation of sulfolane in benzene solution from microwave absorption data

The electric constant (ɛ′) and dielectric loss (ɛ″) for dilute solutions of sulfolane in benzene solution has been measured at 9.885 GHz at different temperatures (25, 30, 35, and 40°C) by using standard microwave techniques. Following the single frequency concentration variational method, the dielectric relaxation time (τ) and dipole moment (μ) have been calculated. It is found that dielectric relaxation process can be treated as the rate process, just like the viscous flow. Based on the above studies, monomer structure of sulfolane in benzene has been inferred. The presence of solute-solvent associations in benzene solution has been proposed. Energy parameters (ΔH _ɛ, ΔF _ɛ, ΔS _ɛ) for dielectric relaxation process of sulfolane in benzene at 25, 30, 35, and 40°C have been calculated and compared with the corresponding energy parameters (ΔH _η, ΔF _η, ΔS _η) for the viscous flow.     

Excess Molar Volume and Viscosity of Isobutyric Acid + Water Binary Mixtures Near and Far Away from the Critical Temperature

The excess molar volume V^E, shear viscosity deviation Δη and excess Gibbs energy of activation ΔG^∗E of viscous flow have been investigated by using density (ρ) and shear viscosity (η) measurements for isobutyric acid + water (IBA+W) mixtures over the entire range of mole fractions at five different temperatures, both near and close to the critical temperature (2.055K ≤ (T−T_c)≤ 13.055K). The results were also fitted with the Redlich–Kister equation. This system exhibited very large negative values of V^E and very large positive values of Δη due to increased hydrogen bonding interactions and correlation length between unlike molecules in the critical region and to very large differences between the molar volumes of the pure components at low temperatures. The activation parameters ΔH^∗ and ΔS^∗ have been also calculated and show that the critical region has an important effect on the volumetric properties.     

Synthesis,Characterization and Crystal Structures of New Difurylphosphido-bridged Dinuclear Ruthenium Carbonyl Complexes Derived from Ferrocenylacetylene Ligands

The difurylphosphido-bridged dinuclear complex [Ru₂(CO)₆(μ-PFu₂)(μ-η¹,η²-Fu)] (Fu = 2-furyl) 1 readily reacts with two equivalents of each of the terminal alkynes HC≡CR (R = Fc, p-C₆H₄Fc, p-C₆H₄NO₂, Fc = Fe(η⁵-C₅H₅)(η⁵-C₅H₄)) by an interesting head-to-tail ynyl coupling with a furan group to form a series of phosphido-bridged diruthenium compounds containing a novel furyl-substituted C₄ hydrocarbyl chain of stoichiometry [Ru₂(CO)₄(μ-PFu₂){μ-η¹,η¹,η²,η³-RCC(H)C(R)C(H)Fu}] (R = Fc 2, p-C₆H₄Fc 3, p-C₆H₄NO₂ 4) in moderate to good yields. Reaction of 1 with an equimolar amount of HC≡CFc and HC≡C(p-C₆H₄NO₂) afforded a pair of isomers of [Ru₂(CO)₄(μ-PFu₂){μ-η¹,η¹,η²,η³-R¹CC(H)C(R²)C(H)Fu}] (R¹ = Fc, R² = p-C₆H₄NO₂ 5a; R¹ = p-C₆H₄NO₂, R² = Fc 5b) together with a small mixture of 4. X-ray crystal structures of 2, 3, 5a and 5b are reported. All of these new alkyne-derived dinuclear complexes are electron precise with 34 cluster valence electrons in which the μ-η¹,η²-furyl ligand acts as a three-electron donor and the μ-phosphido Ru₂ framework is retained in the products upon alkyne coupling reactions. The resulting organic fragment of each complex is coordinated to the Ru atoms via a π, a π-allyl and two σ bonds, and donates seven electrons to the metal core. Dedicated to the memory of Professor F. Albert Cotton.     

η3-Propargyl complexes of molybdenum, tungsten, and rhenium

The reactions of the Me _n C₆H_6−n M(CO)₃ (M=Cr, Mo, W;n=3, 5, 6) and C₅R₅M(CO)₃ (M=Mn, Re; R=H, Me) complexes with propargyl alcohol in acidic media under UV irradiation were studied. Novel Me _n C₆H_6−n M(CO)₂(η³-C₃H₃)BF₄ (M=Mo, W;n=3, 5, 6) and C₅R₅Re(CO)₂(η³-C₃H₃)CF₃SO₃ complexes with the 3ē-propargyl ligand were synthesized, and their properties compared with those of similar η³-allyl derivatives. The structure and dynamic propeties of the compounds obtained are discussed. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1796–1803, September, 1999.     

A note on overpotential dependence of AC impedance data

Charge-transfer resistance [R _ct = (dη/di)_{η = 0}] and Tafel plots of current density (i) versus overpotential (η) data are generally known to yield values of the energy-transfer coefficient (α) and exchange current density (i _o) of an electrochemical reaction. In the present investigation, the resistance (dη/di)_η≠0 that could be calculated by differentiating a wide range of i−η curves was also shown to provide the values of α and i _o, by plotting ln(dη/di)_η≠0 against η. Since α and i _o could also be evaluated directly from the experimental DC polarization data, the procedure was not of significant importance. Nevertheless, it was considered important in evaluating α and i _o from AC impedance data, because the procedure was based on data analysis, which was much simpler than that reported in the literature. A cobalt electrode prepared from fine metal powder was used in 1 M KOH electrolyte and the hydrogen evolution reaction was studied by AC impedance at several potentials. The resistance values measured from the complex plane impedance diagram were plotted against the potential, and the values of α and i _o were evaluated. Received: 8 October 1998 / Accepted: 11 January 1999     

Synthesis of asymmetrical bis(arene) iron complexes

Visible light irradiation of the [(η-C₆H₇)Fe(η-C₆H₆)]⁺ cation (1) in CH₂Cl₂ in the presence of alkyl-substituted benzenes results in arene exchange forming the [(η⁵-C₆H₇)Fe(η-C₆R₆)]⁺ cations (2a–d: C₆R₆ is toluene, p-xylene, mesitylene, and durene). The mixed bis(arene) [(η-C₆H₆)Fe(η-C₆R₆)]²⁺ iron complexes (3a–d) were synthesized by hydride ion abstraction from 2a–d by [Ph₃C]⁺. Dedicated to Academician G. A. Abakumov on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1864–1865, September, 2007.     

Volumetric and Transport Properties of Ternary Mixtures Containing 1-Butanol or 1-Pentanol,Triethylamine and Cyclohexane at 303.15 K: Experimental Data,Correlation and Prediction by the ERAS Model

The excess molar volumes, V _m^E, viscosity deviations, Δη, and excess Gibbs energies of activation, ΔG ^*E, of viscous flow have been investigated from density and viscosity measurements for two ternary mixtures, 1-butanol + triethylamine + cyclohexane and 1-pentanol + triethylamine + cyclohexane, and corresponding binaries at 303.15 K and atmospheric pressure over the entire range of composition. The empirical equations due to Redlich-Kister, Kohler, Rastogi et al., Jacob-Fitzner, Tsao-Smith, Lark et al., Heric-Brewer, and Singh et al. have been employed to correlate V _m^E, Δη and ΔG ^*E of the ternary mixtures with their corresponding binary parameters. The results are discussed in terms of the molecular interactions between the components of the mixture. Further, the Extended Real Associated Solution, ERAS, model has been applied to V _m^E for the present binary and ternary mixtures, and the results are compared with experimental data.     

Rearrangement products of some 1R,4R-2-arylidene-p-menthan-3-ones in acidic media, their structures, and conformational analysis

1R,4R-2-(4-Phenylbenzylidene)-p-menthan-3-one in acidic media undergoes rearrangement with migration of the exocyclic double bond to the cyclohexane ring to form three 2-(4-phenylbenzyl) derivatives ofp-menthen-3-ones. The reaction products differ in the location of the endocyclic double bond (Δ¹ or Δ⁴) and in the configuration of the new chiral C(2) center in the resultingp-menth-4-en-3-ones. The configurations of the 1R,2R- and 1R,2S-2-(4-phenylbenzyl)-p-menth-4-en-3-ones were established based on analysis of their¹H NMR spectra in combination with calculations by molecular mechanics. The molecular conformations of these compounds as well as of some racemic 2-benzyl-p-menth-1-en-3-one derivatives were studied.     

Competition of Viscosity Correlation Equations in Isobutyric Acid + Water Binary Mixtures Near and Far Away from the Critical Temperature

Shear viscosity deviations Δη have been investigated by using density (ρ) and kinematic viscosity (ν) measurements for isobutyric acid + water (IBA + W) mixtures over the entire range of mole fractions at atmospheric pressure and at two temperatures (301.15 and 315.15 K). This study extends the temperature range from the five other temperatures investigated in a previous work, 1.055 K≤(T−T _c )≤14.055 K, both far from and close to the critical temperature. This system exhibits very large positive values of Δη due to increased hydrogen bonding interactions and the correlation length between unlike molecules in the critical region, and to very large differences between the molar volumes of the pure components at low temperatures. The results were also fitted with the Redlich–Kister polynomial equations and the recently proposed Herráez correlation equation. Comparisons between the two models at different temperatures and number of parameters are discussed. We note that, in this system where the shear viscosity η as a function of mole fraction (x ₁) of IBA presents a maximum, experimental data are in agreement with the two correlation models when more than three parameters are employed, especially for temperatures far from the critical temperature.     

Iron and ruthenium triple-decker complexes with a central pentaphospholyl ligand

Thirty-electron triple-decker complexes with a central pentaphospholyl ligand [(η-C₅Me₅)Fe(μ-η:η-P₅)M(η-C₅R₅)]BF₄ (M=Fe, R=Me or M=Ru, R=H, Me) were synthesized by a stacking reaction of cationic 12-electron fragments [(η-C₅R₅)M]⁺ with (η-C₅Me₅)Fe(η-P₅). Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1625–1626, August, 1998.     

Miscibility of ethyl cellulose/copolyamide6/66/1010 blends by viscometry and refractive index method

The miscibility of ethyl cellulose (EC)/copolyamide6/66/1010 (PA-130) in formic acid is studied by viscometry and refractive index techniques at 25°C. Using viscosity data, the criteria Δb, Δb′, Δ[η]_m, interaction parameter μ, β and thermodynamic parameter α are calculated. These investigations indicate that blend of EC/PA-130 is miscible when the ethyl cellulose content is more than 50 wt % in the blend. Further the result was also confirmed by refractive index measurements.     

Thermodynamic and transport properties for binary and ternary mixtures of 2-methyltetrahydrofuran?+?chlorobenzene?+?cyclopentanone at T?=?298.15?K

Abstract  

Experimental densities ρ, viscosities η, and refractive indices n _D of the ternary mixtures consisting of 2-methyltetrahydrofuran + chlorobenzene + cyclopentanone and constituted binary mixtures were measured at T = 298.15 K for the liquid region and at ambient pressure for the whole composition range. Excess molar volumes V_\textm^\textEV_{\text{m}}^{\text{E}}, deviations in the viscosity Δη, and deviations in the refractive index Δn _D from the mole fraction average for the mixtures were derived from the experimental data. The excess partial molar volumes V_\textm,i^\textEV_{{\text{m}},i}^{\text{E}} were also calculated. The binary and ternary data of V_\textm^\textEV_{\text{m}}^{\text{E}}, Δη, and Δn _D were correlated as a function of the mole fraction by using the Redlich–Kister and the Cibulka equations, respectively. McAllister’s three-body interaction model is used for correlating the kinematic viscosity of binary mixtures with the mole fraction.     

Excess molar volumes,viscosity, refractive index,and Gibbs energy of activation of binary biodiesel + benzene,and biodiesel + toluene mixtures at 298.15 and 303.15 K

Excess molar volumes (V ^E), viscosities, refractive index, and Gibbs energies were evaluated for binary biodiesel + benzene and toluene mixtures at 298.15 and 303.15 K. The excess molar volumes V ^E were determined from density, while the excess Gibbs free energy of activation G*^E was calculated from viscosity deviation Δη. The excess molar volume (V ^E), viscosity deviation (Δη), and excess Gibbs energy of activation (G*^E) were fitted to the Redlich-Kister polynomial equation to derive binary coefficients and estimate the standard deviations between the experimental data and calculation results. All mixtures showed positive V ^E values obviously caused by increased physical interactions between biodiesel and the organic solvents.     

Density and viscosity of magnesium sulphate in formamide + ethylene glycol mixed solvents

Densities (ρ) and viscosities (η) of different strengths of magnesium sulphate (MgSO₄) in varying proportions of formamide (FA) + ethylene glycol as mixed solvents were measured at room temperature. The experimental values of ρ and η were used to calculate the values of the apparent molar volume, (φ_1,), partial molar volume, (φ₁,^ℴ) at infinite dilution,A- andB-coefficients of the Jones-Dole equation and free energies of activation of viscous flow, (Δμ ₁ ^0* ) and (Δμ ₂ ^0* ), per mole of solvent and solute respectively. The behaviour of these parameters suggests strong ion-solvent interactions in these systems and also that MgSO₄ acts as structure-maker in FA + ethylene glycol mixed solvents.     

Electronic and geometrical structures of cyclopropanes, part 51. fluorocyclopropanes. linear correlation of orbital energies with C–C bond lengths. further improvement of the two-orbitals model

The electronic and geometrical structures of fluorocyclopropanes (1–12) have been analysed using DFT B3LYP calculations. A linear relationship, Δɛ_ω=−0.172 Δr−0.171 (n=12, R=0.931), between Δɛ_ω (in eV), the difference of the energies of the Walsh orbitals ω_S and ω_A, and Δr (in pm), the difference of vicinal and distal C–C bond lengths, is established. Correcting the orbital splitting by the basic value at Δr=0.00 pm, an even better linear correlation Δɛ_ω ^eff=0.0720 Δr (n=12, R=0.984) is obtained. The results confirm the general applicability of the two-orbitals model for the relationship between geometrical and electronic structures for substituted cyclopropanes. ¹For Part 4 see Ref. [17].     

Densities,Viscosities and Speeds of Sound of Binary Mixtures of Ethyl Benzoate + Hydrocarbons at (303.15, 308.15 and 313.15) K

Densities, viscosities and speeds of sound of binary mixtures of ethyl benzoate with cyclohexane, n-hexane, heptane and octane have been measured over the entire range of composition at (303.15, 308.15 and 313.15) K and at atmospheric pressure. From these experimental values, excess molar volume (V ^E), deviation in viscosity (Δη) and deviation in isentropic compressibility (ΔK _s) have been calculated. The viscosities of binary mixtures were calculated theoretically from the pure component data by using various empirical and semi-empirical relations and the results compared with the experimental findings.