Tracer diffusion of aromatic hydrocarbons in n-hexane up to the supercritical region

Tracer diffusion coefficients are determined with the Taylor-Aris dispersion method for benzene, toluene, p-xylene, mesitylene, naphthalene and phenanthrene in liquid n-hexane along the vapour-liquid coexistence curve from 333.2 to 485.4 K and in supercritical n-hexane at 507.4, 522.0, 533.3, 543.2K and several pressures. A rough-hard-sphere model is found to represent quite well (to within ± 6%) the observed tracer diffusivities in the density region where computer simulation results for D₁₂^SHS/D₁₂^E are available, i.e. 1.5 V/V₀ 3. Furthermore, Hildebrand's free volume model together with the excluded-volume effect provides the basis for a general linear relationship between D₁₂V_C12 and V for tracer diffusion in liquid n-hexane up to its critical temperature. For diffusion in the supercritical region two definitions of reduced tracer diffusivity, one based on the rough-hard-sphere theory of tracer diffusion and the other on the extension of Helfand-Rice corresponding state principle for self-diffusion, permit generalized correlations that are capable of representing the experimental results in both supercritical n-hexane and carbon dioxide to within ±4% on average.     

Correlation between equation of state and temperature and pressure dependence of self-diffusion coefficient of polymers and simple liquids

Correlation between the equation of state and the temperature dependence of the self-diffusion coefficient D for polymers such as polystyrene (PS) and polydimethyl siloxane (PDMS) and simple liquids such as argon, methane and benzene and the pressure dependence of D for oligomers such as dimethyl siloxane (DMS) and simple liquids such as cyclohexane and methanol has been examined based on the equation of state derived previously. The experimental data used were published by Antonietti et al. and McCall et al. for polymers, by McCall for linear dimethylsiloxanes and by Jonas et al. and Woolf et al. for simple liquids. The expression for D in this work is given by

where A₁(M) is a function of molecular weight M_w, C₁(T) and P₁(T) are functions of temperature and B₁, n₁ and m₁ are constants determined experimentally. For simple liquids, the values of n₁ obtained range from 0.3 to 1.2, with an average , and m₁ is in the range 0.5–1.2, with . For polymers, values of n₁ are in the range 2.5–7.0 for PS and 0.5–1.3 for PDMS and m₁ for DMS is in the range 0.8–1.0. The relation Dη/T = f(M) is found to be useful for simple liquids over a wide range of temperature including the critical region and for pressures up to ≈5 kbar

1 kbar = 100 MPa There is a close correlation between ln(D/T) and _p and β_T through ln(D/T)ln D_c−⁻¹_p−β⁻¹_T, where D_c is D at the critical temperature and _p and β_T are the thermal expansion coefficient and compressibility, respectively. The molecular weight dependence of D for polymers and simple liquids is discussed based on the experimental data and recent theory of Doi and Edwards. A new model for the mechanism of self-diffusion in the liquid state is proposed.     

Diffusional deposition from a fluid flowing radially between concentric, parallel, circular plates

We have made a theoretical study of the diffusional losses of particles from a fluid flowing radially inward between concentric, parallel, circular plates of radius, R_o. The relative number of particles remaining in the fluid at a distance, r, from the axis of the plates is

where γ = 4πD (Ro² − r²)/3Qh, D is the diffusion coefficient of the particles, Q is the volumetric flow rate, and 2h is the separation between the plates. The practical application of the system is discussed.

The same equation applies to parallel flow through a duct of rectangular cross-section if γ = 4DBl/3Qh, where B and l are respectively the duct width and length. It is more accurate than equations now in use to describe this process.     

空气在二甲基硅油和液压油中扩散系数的测量

A piston-cylinder apparatus was established to measure the solubility and diffusivity of air in dimethyl silicone oils and in hydraulic oils based on the PVT state equation of air and the solution of unsteady one-dimensional diffusion equation. The measured diffusivity-temperature relation can be well fitted by the Arrhenius equation for engineering applications. The correlation between the solute diffusivity D and solvent viscosity  is examined. In terms of Eyring’s activation theory, the activation in the air-silicone-oil diffusion process is quite different from that in the momentum transport of the silicone oil: the activation entropy of the former is positive while that of latter is negative. However, the activation enthalpies of the two processes are in the same order of magnitude, which leads to the observation that D/T is roughly constant.     

Gas-liquid-liquid extraction in a novel rotating microchannel extractor

In this work, a novel rotating microchannel extractor (RME) is designed and further used for the extraction of chromium (III) from water. Unexpectedly, the micro-extraction had the same effect as carrying out 2.9-stage cross-flow extractions. Various factors, including the gas intake methods, gas intake quantity (Q_g), distance between inner rotor and outer wall (D), rotational inner rotor speed (R) and volumetric flow rate (Q_a, Q_o), were selected to investigate their effect on the extraction efficiency (η) thoroughly. The relation map of η with Wea and We_o-g for RME provides a comprehension for the gas-liquid-liquid extraction process in this RME system.     

LAG TIME AND STEADY-STATE PERMEABILITY FOR A DIFFUSION SYSTEM WITH SERIAL AND/OR PARALLEL PATHS

A diffusion system is considered in which transport occurs along two parallel paths which, in turn, are in series with another path. Relations for the steady-state permeability and lag time are obtained in terms of the cross-sectional areas and lengths of diffusion, diffusivities and interfacial partition coefficients. The relations are derived from the slope and intercept (on the time axis) of the linear asymptote for the total amount of diffusant released into the receiver. The asymptote is calculated by repeated integration rather than a complete solution to the coupled diffusion equations. Equivalence relations are given for the transformation of the parallel paths into a single path, thus allowing for a treatment of the whole system in the form of two homogeneous paths in series. These equivalence relations include an effective partition coefficient as an average of its component's partition coefficient weighted by the corresponding fraction of cross-sectional area, and an effective diffusivity as an average of individual diffusivities weighted by the corresponding fraction of the product of cross-sectional area and partition coefficient.     

ANALYSIS OF MECHANICALLY AGITATED FLUID-PARTICLE CONTACT DRYERS

Incorporation of agitation to spouted and fluidized bed dryer result in significant increases in the drying capacity (Q_s), although product retention persist, which is reduced by increasing the air flow. The physical phenomena occurring in these dryers with several liquid substrates was analyzed and the residence time distributions (RTD) were obtained by the use of dye tracers. The residence time (τ) was found to be a function of the rate of agitation (n) and reaches a minimum at n = n_opt, which was characteristic for each type of substrate, and where maxima also appeared for the drying capacity (Q_s = Q_{s max}) and the heat transfer coefficient (Nu_p = Nu_{p max}). The RTD can be modeled by series of consecutive dryers and a modified Vanderschuren and Delvosalle model can be employed to calculated moisture of the dry product.     

RECIPROCITY OF LAG TIME FOR REACTIVE DIFFUSION THROUGH HETEROGENEOUS MEMBRANES: A GREEN'S FUNCTION APPROACH

Forward and reverse diffusion through heterogeneous membranes with position-dependent diffusivity, partition coefficient and reaction rate constant are considered. The reciprocity of the lag time is proved, utilizing the symmetry of the corresponding Green' function with respect to the exchange of the coordinate arguments. Simple relations between the permeabilities, reactive diffusion fluxes and total released amounts for forward and reverse diffusion direction are derived.     

THE EFFECT OF MACROMIXING ON OSCILLATORY BEHAVIOR IN RECOMBINANT FERMENTATION IN A CONTINUOUS STIRRED TANK REACTOR

A general model is presented for recombinant fermentation in a chemostat in which micromixing may be imperfect. Using the production of tryptophan synthetase as an example and the dilution rate, D, as the bifurcation parameter, conditions are first derived for Hopf bifurcation in a perfectly mixed chemostat. The bifurcation surfaces in three-dimensional space are such that oscillatory solutions exist above the surfaces and washout conditions below. A similar analysis is done for imperfect mixing. The bifurcation region is a concave hyperboloid in the [D,f, n]-space, where f and n ; are model parameters. It is argued that poor macromixing reduces the range of D over which bifurcation to periodic solutions is possible.     

Capacity intermittent titration technique (CITT): A novel technique for determination of Li solid diffusion coefficient of LiMn2O4

The capacity intermittent titration technique (CITT) has been developed on basis of the ratio of the potentio-charge capacity to the galvano-charge capacity (RPG) method to determine continuously the solid diffusion coefficient D of the intercalary species within insertion-host materials. In experiment, CITT is based on the capacity response of galvano–potentio-charge in a small voltage region. In theory, CITT is based on the linear equations of D versus q (value of RPG) in different range of q. By the CITT, the Li⁺ solid diffusion coefficients within LiMn₂O₄ have been determined at different voltages and different galvano-charge currents. Results shows that the order of magnitude of D varies non-linearly with the “W” shape from 10⁻⁹ to 10⁻¹¹ cm² s⁻¹ in the voltage range from 3.3 to 4.3 V. The galvano-charge current also leads to the error due to the semi-conductive character of LiMn₂O₄, and the maximal error may reach as much as one order of magnitude. In addition, the main approximations that lead to errors of CITT are qualitatively analyzed.     

Diffusion of linear paraffins in NaCaA studied by the ZLC method

The zero length column (ZLC) technique has been applied to investigate the kinetics of linear alkanes (n-hexane to n-tetradecane) in a sample of zeolite NaCaA. The diffusivity values are found to be monotonically decreasing with chain length from n-hexane to n-undecane, slightly increasing between n-undecane and n-tridecane, and eventually levelling-off at n-tetradecane. The initial monotonic decreasing trend is similar to previous ZLC studies, although the values are somewhat higher for the heavier alkanes. The values found are reasonably close to PFG-NMR results and have similar qualitative trends, but do not show a marked maximum in comparison to recent neutron spin echo (NSE) results. The difference between the infinite dilution ZLC data and the microscopic techniques can not be ascribed to the intrusion of surface resistances since partial loading experiments provide clear evidence that the measurements are controlled by internal diffusion. The activation energy of linear alkanes in NaCaA lies between 20 and 26 kJ/mol.     

Asymmetry of Peak Shapes in Linear Gas—Liquid Chromatography

Abstract

A mathematical model describing axial dispersion, interparticle mass transfer, intraparticle gas diffusion, and diffusion in a uniform thickness liquid film is used systematically to investigate the influence of intraparticle diffusivity, diffusivity in a stationary liquid phase (SLP), partition coefficient, and thickness of liquid film on the shape of the peaks in linear gas—liquid chromatography by converting Laplace transformed equations into time domain. The low diffusivities of intraparticle and/or SLP can cause the asymmetry and long tail in chromatographic peaks. A higher partition coefficient and the film thickness at low diffusivities also give skewed peaks. At a higher mass transfer rate, the peak becomes sharper. From these results a guide can be suggested to avoid the asymmetric condition of long-tailing peaks.     

Kinetics and equilibrium swelling of gelatine gels

The swelling features of gelatine gels in water (good solvent) were studied as a function of thermodynamic conditions of sol—gel transition and ripening. It is shown that the degree of equilibrium swelling Q_e varies with the volume fraction of the polymer in a casting solution φ_o in accordance with the prediction of the classic theory: Q_e φ_o^−0.4. Q_c, as a function of the gelation temperature T_g, the ripening time t_r and φ_o, can be rescaled and described by the single empirical equation: Q_e T_g^−x t_r^−yφ_o^−0.4, where x = 0.1, y = 0.15 for wet gels and X = −0.5, y = 0.04 for dried gels. The kinetics of macroscopic swelling is described by the equation of Peters and Candau, with values of collective diffusion coefficients being in good agreement with values obtained by other workers via photon correlation spectroscopy.     

Diffusion of adhesion promoting and crosslinking additives in an uncured silicone sealant

A method has been devised for measuring the diffusion coefficient D of additives that act as adhesion promoters and crosslinking agents in uncured silicone sealants. This has been used to measure D for tetra-t-butyltitanate (TBT) and isobutyltrimethoxysilane (BTMS) in a sealant at 25°C. The value of D for TBT was found to be constant but that for BTMS decreased with the duration of the experiment, possibly due to the interaction of the silane with the silica particles.     

Surface dynamics during latex film formation

Surface dynamics during latex film formation has been investigated theoretically and experimentally by atomic force microscopy. The peak-to-valley distance, y(t), of the latex particles in the surface plane of the latex film decayed exponentially with time during film formation. A theoretical relationship between y(t) and time, t, is given by y(t)=y(0) exp[−t/τ], where y(0) is the value of y(t) when t is zero. τ is a characteristic constant related to the nature of polymer, the particle radius, the surface diffusion coefficient and the temperature. The relationship between the surface diffusion coefficient, D_s, y(0), the radius of the latex particles, R, temperature, T, and τ is given approximately by D_s=1.2×10⁻²⁰y(0)²[2R−y(0)]²T/τ (cm²/s), where the units are manometers for y(0) and R, kelvin for temperature, and seconds for τ. By measuring the decay of y(t) with time, the surface diffusion coefficient can be obtained. The surface diffusion coefficient for a poly(methyl methacrylate-co-butylacrylate) (50:50) copolymer latex film was found to be A×10⁻¹³ cm²/s, A is temperature-dependent.     

TAYLOR DISPERSION OF MULTICOMPONENT SOLUTES

Coupled transport of multicomponent solutes in globally continuous systems is considered in the framework of the Generalized Taylor dispersion theory. Coupling between transports of n different species at the local (or micro-) scale, is considered to result from first-order irreversible surface reactions occurring on the local space boundaries, or from the off-diagonal terms of the solute diffusivity matrices.

General expressions are obtained for the global effective (long-time) solute dispersion matrix cofficients: mean global scalar reactivity, velocity vector and dispersivity dyadic.

The effect of surface chemical reactions is to partition the matter between different solute constituents. This is manifested in a coupling of the global transport coefficients, which may be mathematically removed by a linear (canonic) transformation applied to the effective global transport equation. This type of coupling does not exist for inert solutes.

The second type of the global coupling is represented by the off-diagonal terms of the global velocity and dispersivity matrices. It exists for both reactive and inert solutes. This coupling stems from the convective dispersion process (dependence or the global velocity vector on the local space coordinate). Is shown to be irremovable from the global transport equation by any linear transformation via the solute partition matrix. In the canonic form of the global equation the irremovable coupling is manifested by the traceless parts of the global solute velocity matrix and the global solute dispersivity.

The solution scheme is illustrated by calculating the mean global diffusivity of a solute consisting of two components, transport of which is coupled at the microscale via the molecular diffusivity matrix. At the macroscale the coupling is shown to be represented by negative off-diagonal terms of the global diffusivity matrix,     

Effect of electro-chemical properties of sodium salts of various anions on their diffusional parameters in symmetrical cellulose acetate membranes

A relation was obtained between electro-chemical properties of sodium salts (NaCl, NaBr, and Na₂SO₄), and the thermodynamic property of permeability in symmetrical cellulose acetate membranes, the distribution coefficient K and the kinetic property, the overall diffusion coefficients D. K and D were obtained by the method we proposed using measured unsteady- and steady-state dialysis data. The K values increase with the increase of water content and are in the range of 10⁻² for sodium halides and 10⁻³ for Na₂SO₄. D is found to increase with the increase of the solute concentration, and the extrapolated values of D to zero concentration D⁽⁰⁾ are obtained as 0.015–0.03 μm²/s and increase with the increase of water content in the membrane. D can be divided into the concentration independent diffusion coefficients in the dense part of the membrane D_d and in the porous D_p, applying a two-part (perfect or dense and imperfect or porous) model of the membrane. Contrary to D_d, D_p increases with the increase of W_w and can be correlated as D_p,c = _d exp (γ × W_w). It is shown that the averaged D_d, _D increases with the increase of the quantity of the ionic mobility u of the solutes at infinite dilution divided by valence, and that the parameter γ increases with the increase of the ionic mobility u. The value of K increases slightly with the increase of water content and decreases with the increase of the Flory—Huggins parameter χ. The Flory—Huggins parameter χ is calculated from the measured values of distribution coefficients and data obtained from the literature. And it was found that the gradient of linear decrease of χ (λ_cation) depends on equivalent ionic conductivity of anion of salt, λ_an.     

污泥厚度对超声波辅助热风干燥污泥特性的影响

由于在超声波声场中污泥微粒会发生分层现象,声互作用力使得微粒于超声传播方向相垂直的平面上发生凝聚,因此污泥厚度大小对超声波辅助热风干燥污泥特性有着重要的影响。通过实验的方法,对不同厚度污泥在超声波声场中的分层凝聚现象进行观察,发现污泥内部结构的分层现象随其厚度的增加而明显。研究了超声波对不同厚度污泥干燥过程中各时期干燥时长、干燥速率的影响效果,以及分析了湿分有效扩散系数（D_eff）随污泥厚度变化的情况。从实验结果中可以发现,在超声波功率小于135 W范围内,污泥厚度越大,干燥过程中第一降速期时间越长,干燥速率提升效果越差,而对恒速干燥期内干燥速率提升效果更明显;在5、10以及15 mm厚度的污泥中,10 mm厚度的污泥在超声波功率小于90 W的条件下总干燥时长降低幅度最大,干燥速率在各阶段提速也较快;污泥厚度越小,超声波功率对污泥湿分有效扩散系数影响越小,反之影响越大。     

Effect of sludge thickness on characteristics of ultrasonic assisted hot air drying sludge

Due to the stratification of sludge particles in the ultrasonic field, the acoustic interaction forces the particles to agglomerate on a plane perpendicular to the direction of ultrasonic propagation. Therefore, the thickness of sludge can significantly influence the characteristics of ultrasound-assisted hot air convective drying municipal sewage sludge. In this paper, the stratified aggregation phenomenon of sludge with different thicknesses was observed in the ultrasonic field using the experimental method. It was found that the stratification of the internal structure of sludge became more obvious with the increase of its thickness. The effects of ultrasound on the drying time and the drying rate of sludge with various thicknesses were studied. Meanwhile, the effective moisture diffusivity (D_eff) was analyzed. The experimental results demonstrated that the larger the sludge thickness, the longer the time length of the first falling rate stage and the promotion of the drying rate was worse when the ultrasonic power was less than 135 W. The situation was opposite at the constant rate stage. Among the sludge with the thicknesses of 5, 10, and 15 mm, the total drying time and energy consumption of the sludge with a thickness of 10 mm decreased the most substantially under the condition of ultrasonic power less than 90 W. The smaller the thickness of sludge is, the less obvious the effect of ultrasound on the effective moisture diffusivity, and vice versa.     

NETWORK SIMULATION OF RELATIVE PERMEABILITY CURVES USING A BOND CORRELATED-SITE PERCOLATION MODEL OF PORE STRUCTURE

This paper deals with the conductivity and relative conductivity properties of irregular 3-D networks of pores that represent the continua of the oil phase and the aqueous phase respectively, during steady slate two phase flow in porous media. The relative conductivity properties presented, correspond to the saturation history defined by the drainage, imbibition and secondary drainage capillary pressure curves respectively. Use has been made of the pore accessibility history of a 20 × 20 × 20 network and a 10 × 10 × 10 nodes core portion of the network is used to write the flow equations. A set of 1001 linear equations is solved using the Preconditioned Conjugate Gradients Method for the conductivities of the wetting phase and the non-wetting phase respectively, as a function of network saturation and saturation history. The effects of pore throat size distribution and pore body size distribution on relative permeability behaviour has been investigated. Furthermore, the effect of conductivity function q(D) proportional to Dⁿ (n = 0, 1, 2, 3, 4) on relative permeability behaviour was investigated, where D stands for pore throat diameter and n is an exponent depending on pore geometry.

The results of this work are very significant in elucidating the following points that are not clearly stated in the literature: 1) using the bypassing as the only trapping mechanism, the primary drainage and secondary drainage relative permeability curves are in agreement with experimental findings; 2) more realistic displacement mechanisms in secondary imbibition are required to have better agreement with experimental findings; 3) the correlated network models after the site type problem of percolation theory are realistic models of pore structure; 4) the conductivity function q(D) proportional to D³ is the most appropriate pore throat conductivity function because of lamelar like pore geometries; and 5) accurate prediction of the effective permeability requires knowledge of the porosity and the detailed pore geometry in the pore network, in addition to pore size distributions used in the network simulation.