Liquid-phase Diffusion Coefficients Research Articles

Determination of effective liquid-phase diffusion coefficients by tracer method in continuous packed columns

Many industrially relevant chemical processes are affected by the liquid-phase diffusion resistance in porous materials, for example in heterogeneous catalysts. Therefore, reliable experimental methods for the determination of effective diffusion coefficients in porous structures are highly desirable. In this work, a method was developed to study the internal diffusion effects in porous media by step response experiments with tracers injected to fixed beds filled with porous particles and inert material. The tracer responses were recorded at the outlet of the bed by UV–vis spectrometry. Ethanol was used as the tracer and water as the solvent. Porous aluminum oxide particles were selected as the model material. The step responses were described with a dynamic axial dispersion model, i.e. partial differential equations for the inert and catalyst sections of the bed. The partial differential equations describing the model were discretized with finite differences and the resulting ordinary differential equations were solved numerically with a solver for stiff ordinary differential equations. From the experimental data, the dispersion coefficients of the bed and the effective diffusion coefficient in the porous aluminum oxide particles were successfully determined by non-linear regression analysis. The values of the effective diffusion coefficents had a good agreement with the liquid-phase diffusion coefficients estimated from correlations. The method is applicable for any porous material.

The Preparation, Microstructure, and Wet Wear Properties of an Fe55-Based Welding Layer with the Co-Addition of 0.01 wt% CeO2 and 1.5 wt% SiC Particles Using the Plasma Beam Spraying Method

Severe erosion wear is found on valve spools, which threatens the safety and reliability of these units. The use of the plasma beam spraying surfacing method can significantly improve the corrosion resistance and sealing performance of hydraulic valve spools, reduce material waste, and reduce maintenance costs. The effects of the co-addition of CeO2 and SiC particles on the morphology, surface cracks, microstructure, precipitated phases, and wear property of plasma-beam-sprayed Fe55-based coatings on 1025 steel were investigated using OM, EDS, ultra-deep field microscopy, and a wet sand rubber wheel friction tester, respectively. The dendrite exhibited a directional growth pattern perpendicular to the substrate and the transitional states of the microstructure with the co-addition of CeO2 and SiC particles. CeO2 or SiC reduced the liquid phase diffusion coefficient DL of Cr and C and resulted in a decrease in the G/R ratio. The dendrites changed into equiaxed grains. The main phase composition of the Fe55 welding layer was Cr7C3, γ-Fe. The martensite in the surfacing layer and the carbides formed Cr7C3, which can improve the hardness of the surfacing layer. The grain boundaries consisted mainly of a reticular eutectic structure. The uniform distribution of the Cr7C3 hard phase in the Fe55+1.5 wt% SiC+0.01 wt% CeO2 resulted in a uniformly worn surface. The sub-wear mechanisms during the friction process were micro-ploughing and micro-cutting. The hardness and toughness of Fe55+1.5 wt% SiC+0.01 wt% CeO2 were well-matched, avoiding excessive micro-cutting and microplastic deformation. A low content of CeO2 could lead to the formation of equiaxed grain and effectively improve the uniformity of the microstructure. The wear-resistant layer of Fe55+1.5 wt% SiC+0.01 wt% CeO2 can effectively improve the service life and long-term sealing performance of the valve spools.

The strategy of solid-liquid phase separation diffusion with DyH3 to approach a trade-off between properties and cost for sintered Nd-Fe-B magnets

Approach a trade-off between properties and cost for sintered Nd-Fe-B magnets in grain boundary diffusion (GBD) helps widen their application. In this study, we fabricated GBD Nd-Fe-B magnets via solid-liquid phase separation diffusion (SepD) with DyH3 nanopowder as the diffusion source. Investigations and comparisons with the traditional solid-liquid phase simultaneous diffusion (SimD) magnets were made regarding the liquid phase diffusion (LPD) temperature, magnetic characteristics, microstructures, diffusion coefficient, and domain morphology of SepD magnets. In addition, the cost was calculated and compared with TbH3 SepD magnets. It is determined that the optimal LPD temperature of DyH3 was 625 °C. Compared to the SimD magnet, Dy had a faster LPD rate in the SepD magnet, which leads to a deeper diffusion depth of 1200 µm. Consequently, the SepD magnet develops more core-shell structures. Additionally, SepD could prevent the development of anti-core-shell formations in the magnet's surface region. As a result, the SepD magnet had higher comprehensive magnetic properties and coercivity temperature stability. Impressively, compared to TbH3 SepD magnets, the cost of per kOe coercivity enhancement for per kilogram magnets of DyH3 SepD magnets can be reduced by more than 50 %.

Experimental study and modified modeling on effect of SO2 on CO2 absorption using amine solution

Understanding the competitive mechanism in absorption process between SO2 and CO2 is essential for simultaneous absorption of SO2 and CO2. In this study, the effect of SO2 on CO2 absorption using amine solution was studied experimentally and theoretically. The CO2 absorption rates in MEA/MMEA/MDEA solutions were determined using wetted wall column. Results showed that the reduction of flue gas temperature was beneficial for CO2 absorption at the typical coal-fired flue gas CO2 concentration. On this basis, the effect of SO2 on CO2 absorption performance was studied. Firstly, the overall CO2 mass transfer coefficient decreased under exposure to SO2. Secondly, in the presence of SO2, pH variation of amine solution increased. In addition, the saturated CO2 capacity largely decreased when SO2 was continuously bubbled into the solution. Furthermore, the quantum chemical calculation showed that CO2 had little effect on the absorption performance of SO2 whereas SO2 greatly weakened the interaction between CO2 and amines. The overall CO2 mass transfer coefficient was modified considering the effect of SO2. The competitive absorption factor, χ, was introduced to modify the CO2 liquid phase diffusion coefficients. The average deviation of overall CO2 mass transfer coefficient narrowed to 1.76 % (0.5 mol/L MEA), 1.13 % (1.0 mol/L MEA), 1.88 % (1.0 mol/L MMEA) and 1.43 % (1.0 mol/L MDEA) respectively, which agreed well with the experimental results.

Database for liquid phase diffusion coefficients at infinite dilution at 298 K and matrix completion methods for their prediction

We present new matrix completion methods for the prediction of binary liquid phase diffusion coefficients at infinite dilution, which are trained to a newly consolidated database in this work and outperform the established semiempirical correlations.

Estimation of Battery Separator Area, Cell Thickness and Diffusion Coefficient Based on Non-Ideal Liquid-Phase Diffusion Modeling

The aim of this work is to present a fast and in situ diffusion modeling technique to extract essential electrochemical parameters from liquid-phase diffusion which can be used to implement a realistic battery in a pseudo-2D finite element modeling environment. A generalized Warburg element was used within an extended Randles equivalent circuit to obtain an appropriate fit on non-ideal diffusion impedance. Based on the calculation method presented in this paper, the values of diffusion-related parameters such as the cross-sectional area of the separator Asep, cell thickness Lcell as well as liquid-phase and solid-phase diffusion coefficients Dl and Ds were derived, successfully. A characteristic cell which allowed the exchange current density i0 and reaction rate constant k0 to be calculated was also established. The experimental data was measured by electrochemical impedance spectroscopy (EIS), resistivity measurement and the galvanostatic intermittent titration technique (GITT). The results show that our hypothesis to extract essential electrochemical parameters from the tail part of diffusion impedance is correct. The applicability of our concept is confirmed by the prosperous validation results produced by computed tomography (CT) and battery dynamics simulation in finite-element environment. Due to the inherent limitations of the pseudo-2D Doyle-Fuller-Newman (DFN) model, our technique is accordingly valid within the current range of 0–1 C.

Neural Network-Based Prediction of Liquid-Phase Diffusion Coefficient to Model Fuel-Oil Dilution on Engine Cylinder Walls

Neural Network-Based Prediction of Liquid-Phase Diffusion Coefficient to Model Fuel-Oil Dilution on Engine Cylinder Walls

A Bayesian neural network methodology to predict the liquid phase diffusion coefficient

This paper deals with the development of an Artificial Neural Network methodology for the prediction of the liquid phase diffusion coefficient between species at infinite dilution in binary mixtures. The proposed methodology was implemented to estimate the diffusion coefficients with improved accuracy with respect to empirical correlations, which are widely used despite their significant errors, especially on organic mixtures. The final aim of the work is to propose a novel methodology to apply in industrial fields where the mass transport by diffusion between organic liquids plays a key role, e.g. the lubricant degradation and scraping due to the dilution with the liquid fuel in the engine combustion chamber and the dilution of heavy oils and bitumens with organic solvents. In spite of the classical use of Artificial Neural Networks, this work is based on the mutual support between a reference empirical correlation and the Neural Network model, where the former is used to directly calculate the diffusion coefficient while the latter is trained to correct the correlation's result depending on the bonds strength in the solvent and the solute. Moreover, since the prediction of the diffusion coefficient for new mixtures (i.e. where no experimental measures are available) with Artificial Neural Network models should not be taken blindly, a Bayesian Neural Network is implemented, since it is capable to provide the degree of uncertainty of its prediction. This Bayesian Neural Network, given a selection of fluid properties as input features, was trained on 263 experimental data collected from literature findings. The proposed methodology achieved the prediction of the 80% of the available data with absolute relative errors lower than 10%, while the most recognized empirical correlations predicted the same data with absolute relative errors from 30 to 45%. A proof of the reliability of this methodology is the fact that the experimental data corresponding to the points predicted with the higher errors however fall in the predicted uncertainty, whose average width is below the ±20% of the predicted mean.

Determination of the liquid diffusion coefficient of the Sn-Ni peritectic alloy through temperature gradient zone melting

In the present work, a new method determining the liquid phase diffusion coefficients DL in a binary peritectic alloy is presented. This method is based on the evolution in both the microstructure and melt concentrations which can be linked through liquid droplet migration in the mushy zone during thermal stabilization. The thermal stabilization experiments of different time (2 to 8 h) are performed on Sn–Ni peritectic alloy (L+Ni3Sn2→Ni3Sn4) in a Bridgman-type directional solidification furnace. Two different mushy zones are formed during thermal stabilization of samples which are kept still in the furnace. The diffusion-controlled liquid droplet migration is caused by remelting/resolidification by temperature gradient zone melting (TGZM). It leads to not only the variation of volume fractions of solid(fS)/liquid(fL) phases in the mushy zone but also the increase of the melt concentration in the complete-liquid zone C. Thus, based on the conservation of mass during thermal stabilization, fS and fL can be correlated to not only the liquid droplet migration velocity vm but also the melt concentration in the complete-liquid zone C during thermal stabilization. Since fS and fL can be easily obtained through microstructure analysis, the experimental value of vm at specific location/temperature is given. Then, the expression of vm which is function of DL is provided by an analytical model describing the remelting/resolidification process during the liquid migration. Finally, DL and the activation energy of the Sn-Ni peritectic alloy are obtained by equating the experimental values of vm with the expression of vm by this analytical model.

Effect of Source on the Properties and Behavior of Cellulose Nanocrystal Suspensions

Sulfuric acid hydrolysis of native cellulose fibers results in colloidally stable suspensions of cellulose nanocrystals (CNCs). We have investigated the effect of the cellulose source on the suspension properties of CNCs extracted from cotton and wood sources using a comparable preparation strategy. The structural properties were revealed to be similar within the given standard deviation and prevalent polydispersity, whereas other properties such as liquid crystalline phase behavior, viscosity, diffusion coefficients, and surface tension were found to differ significantly. This study shows that ostensibly similar suspensions may exhibit rather differing behaviors and attempts to interpret this phenomenon. This finding shows that full characterization and a detailed description of the preparation of the nanocrystals used in publications are extremely important and should be reported in detail in all instances.

用双液芯柱透镜测量蔗糖水溶液的液相扩散系数

Based on the consideration of the high resolution of the spatial resolution of the refractive index of the double liquid-core cylindrical lens(DLCL), the liquid-phase diffusion coefficients of different concentrations of aqueous sucrose solution are measured at room temperature(25℃) using two methods. Method 1:equivalent RI(refractive index) method is used to calculate the liquid phase diffusion coefficient by recording the time-dependent change of a specific refractive index layer during diffusion. Method 2:instantaneous diffusion analytical method is used to determine the liquid diffusion coefficient by reading the relationship between image width and diffusion position in an instantaneous diffusion image. The front liquid core of the DLCL serves as a diffusion cell and a main imaging element, and the rear liquid core serves as an aplanatic auxiliary system. The spherical aberration at a particular thin liquid layer can be reduced as needed with a DLCL, and the spherical aberration advantage within a certain range of refractive index can also be reduced. Both methods have the characteristics of high measurement accuracy. The relative errors between the measured results and the literature values of the two methods are less than 1.3% and 3.9%, respectively, indicating that the measurement system is stable and reliable and the measurement results are accurate when the liquid-phase diffusion coefficient is measured with a DLCL.

Effect of immobilization methods and the pore structure on CO2 separation performance in silica-supported ionic liquids

The CO2 separation performance in ionic liquids modified porous silica gels prepared by the impregnation and grafting methods were investigated. The effects of impregnation amount and pore size distribution of adsorbents with different types of ionic liquids on the CO2/N2 selectivity and water vapour adsorption and diffusion coefficient were analyzed in detail. The porous structures were characterized by CO2 adsorption isotherms at 0 °C. Adsorption behavior of CO2 (at 25, 40 and 60 °C) and N2 (at 40 °C) was measured using a gravimetric method. Compared with the impregnated samples, the grafting of ILs on the support surface only causes a weak loss of microporosity, leading to a slight decrease in CO2 adsorption capacity, and has much better recycling. CO2/N2 selectivity and water resistance are however enhanced, especially samples with the longer chain on imidazolium cation. A conventional homogeneous surface diffusion model for ILs grafted silica was used to estimate the diffusivities and good agreement between experimental values and fitting curves were obtained. For ILs modified silica prepared with impregnation method, the CO2 diffusivity constants include diffusion coefficients in ionic liquid phase and silica phase simultaneously. The diffusion coefficients are at a level of 10−7-10−9 m2 s−1 and about two or three orders of magnitude higher than that of neat ILs. The grafted silica exhibits diffusivities faster than those of the impregnated silica, indicating that more ionic liquids accessed into inner pore is unfavorable for CO2 diffusion.

Fast Diffusion of O2 on Nitrogen-Doped Graphene to Enhance Oxygen Reduction and Its Application for High-Rate Zn-Air Batteries.

N-doped graphene (NDG) was investigated for oxygen reduction reaction (ORR) and used as air-electrode catalyst for Zn-air batteries. Electrochemical results revealed a slightly lower kinetic activity but a much larger rate capability for the NDG than commercial 20% Pt/C catalyst. The maximum power density for a Zn-air cell with NDG air cathode reached up to 218 mW cm-2, which is nearly 1.5 times that of its counterpart with the Pt/C (155 mW cm-2). The equivalent diffusion coefficient (DE) of oxygen from electrolyte solution to the reactive sites of NDG was evaluated as about 1.5 times the liquid-phase diffusion coefficient (DL) of oxygen within bulk electrolyte solution. Combined with experiments and ab initio calculations, this seems counterintuitive reverse ORR of NDG versus Pt/C can be rationalized by a spontaneous adsorption and fast solid-state diffusion of O2 on ultralarge graphene surface of NDG to enhance effective ORR on N-doped-catalytic-centers and to achieve high-rate performance for Zn-air batteries.

Extensive database of liquid phase diffusion coefficients of some frequently used test molecules in reversed-phase liquid chromatography and hydrophilic interaction liquid chromatography

Diffusion plays an important role in all aspects of band broadening in chromatography. An accurate knowledge of molecular diffusion coefficients in different mobile phases is therefore crucial in fundamental column performance studies. Correlations available in literature, such as the Wilke-Chang equation, can provide good approximations of molecular diffusion under reversed-phase conditions. However, these correlations have been demonstrated to be less accurate for mobile phases containing a large percentage of acetonitrile, as is the case in hydrophilic interaction liquid chromatography.A database of experimentally measured molecular diffusion coefficients of some 45 polar and apolar compounds that are frequently used as test molecules under hydrophilic interaction liquid chromatography and reversed-phase conditions is therefore presented. Special attention is given to diffusion coefficients of polar compounds obtained in large percentages of acetonitrile (>90%). The effect of the buffer concentration (5–10mM ammonium acetate) on the obtained diffusion coefficients is investigated and is demonstrated to mainly influence the molecular diffusion of charged molecules.Diffusion coefficients are measured using the Taylor-Aris method and hence deduced from the peak broadening of a solute when flowing through a long open tube. The validity of the set-up employed for the measurement of the diffusion coefficients is demonstrated by ruling out the occurrence of longitudinal diffusion, secondary flow interactions and extra-column effects, while it is also shown that radial equilibration in the 15m long capillary is effective.

Effect of liquid diffusion coefficients on microstructure evolution during solidification of Al356.1 alloy

The effect of liquid diffusion coefficients on the microstructure evolution during solidification of primary (Al) phase in Al356.1 alloy was investigated by means of the phase-field simulation using two sets of diffusion coefficients in liquid phase, while fixing other thermophysical and numerical parameters. The first set is only with impurity coefficients of liquid phase in Arrhenius formula representing only the temperature dependence. While the second set is with the well-established atomic mobility database representing both temperature and concentration dependence. For the second set of liquid diffusion coefficients, the effect of non-diagonal diffusion coefficients on the microstructure evolution in Al356.1 alloy during solidification was also analyzed. The differences were observed in the morphology, tip velocity and composition profile ahead of the tip of the dendrite due to the three cases of liquid diffusivities. The simulation results indicate that accurate databases of mobilities in the liquid phase are highly needed for the quantitative simulation of microstructural evolution during solidification.

Multicomponent NAPL Source Dissolution: Evaluation of Mass-Transfer Coefficients

Mass transfer rate coefficients were quantified by employing an inverse modeling technique to high-resolution aqueous phase concentration data observed following an experimental release of a multicomponent nonaqueous phase liquid (NAPL) at a field site. A solute transport model (SEAM3D) was employed to simulate advective-dispersive transport over time coupled to NAPL dissolution. Model calibration was demonstrated by accurately reproducing the observed breakthrough times and peak concentrations at multiple observation points, observed mass discharge at pumping wells, and the reported mass depletions for three soluble NAPL constituents. Vertically variable NAPL mass transfer coefficients were derived for each constituent using an optimized numerical solute transport model, ranging from 0.082 to 2.0 day(-1) across all constituents. Constituent-specific coefficients showed a positive correlation with liquid-phase diffusion coefficients. Application of a time-varying mass transfer coefficient as NAPL mass depleted showed limited sensitivity during which over 80% of the most soluble NAPL constituent dissolved from the source. Long-term simulation results, calibrated to the experimental data and rendered in terms of mass discharge versus source mass depletion, exhibited multistage behavior.

The convective drying of liquid films on slender wires

We solve numerically the balance equations of mass and thermal energy for drying liquid films of binary solutions on cylindrical substrates to simulate the drying process of liquid coatings on round metal wires, which are used for electrical insulation in magnet wire technology. The liquid phase diffusion coefficient and the solvent activity are treated as concentration and temperature dependent. The evaporation rate of the solvent across the shrinking liquid–gas interface is determined using the film theory, accounting for the thermodynamic state of the ambient medium and the convective flow situation. The quality of the coatings is assessed by the temporal evolution of radial profiles of the solute mass fraction and by detecting boiling, which leads to the formation of vapour bubbles in the liquid films and is undesired. A guideline for uniform drying at various drying conditions is presented. The simulation model is applied to the test system PVA-water.

Short Time Scale Dynamics and a Second Correlation between Liquid and Gas Phase Chemical Rates: Diffusion Processes in Noble Gas Fluids

A theoretical formula for single-atom diffusion rates that predicts an isothermal correlation relation between the liquid (l) and gas (g) phase diffusion coefficients, D(T, ρl) and D(T, ρg) is developed. This formula is based on a molecular level expression for the atom’s diffusion coefficient, D(T, ρ), and on numerical results for 1715 thermodynamic states of 25 rare gas fluids. These numerical results show that at fixed temperature, T, the decay time, τDIF, which governs the shortest time decay of an appropriate force autocorrelation function, F(t) F0, is density (ρ)-independent. This independence holds since τDIF arises from the ρ-independent shortest time inertial motions of the solvent. The ρ independence implies the following l−g diffusion coefficient correlation equation: D−1(T, ρl) = (ρl/ρg) D−1(T, ρg) [ρl−1F0,l2/ρg−1F0,g2]. This relation is identical in form to the familiar (isolated binary-collision-like) empirical correlation formula for vibrational energy relaxation rate constants. This is because both correlation relations arise from inertial dynamics. Inertial dynamics always determines short-time fluid motions, so it is likely that similar correlation relations occur for all liquid phase chemical processes. These correlation relations will be most valuable for phenomena dominated by short time scale dynamics.

Sugar Hydrogenation Over Supported Ru/C—Kinetics and Physical Properties

The hydrogenation kinetics of some natural sugars to corresponding sugar alcohols in aqueous solutions was investigated on Ru/C catalysts in a pressurized slurry reactor. The kinetic data were well described by a Langmuir-Hinshelwood model assuming that the hydrogenation step on the catalyst surface is rate determining. The density, viscosity and hydrogen solubility of the reacting liquid were measured. This information was used to estimate the liquid-phase diffusion coefficients, which were utilized in a reaction-diffusion-catalyst deactivation model for porous catalyst layers. The model indicated that diffusional resistance becomes severe for rather small catalyst particles and the model described the movement of the reactive front inside the particle during the reaction. The simulation results indicate that structured reactors would provide a better approach than the conventional fixed bed technology, if continuous operation is desired.

Concentration profiles in drying cylindrical filaments

We analyze theoretically the drying of cylindrical filaments. For modelling the mass transfer on the gas side of the liquid-gas interface of the shrinking circular cylindrical filament, we apply the model of Abramzon and Sirignano, which was originally developed for spherical geometry. As a consequence of mass transfer at constant Sherwood number, we obtain a d2-law for the shrinkage of the cylinder as in the case of the spherical geometry, which expresses that the cross-sectional area of the cylinder shrinks at a constant rate with time. For this situation, the diffusion equation for the liquid phase mixture components becomes separable upon transformation into similarity coordinates and is solved analytically to obtain the concentration profiles inside the filament as functions of time. The dependency of the profiles on the radial coordinate is determined by a series of Kummer’s functions. Applying this result, we study the evolution of the concentration profiles in the liquid phase with time as dependent on a parameter given as the ratio of rate of shrinkage of the cross-sectional area of the cylinder to liquid-phase diffusion coefficient, which was identified as relevant for the shape of the concentration profiles formed in the liquid during the drying process. As an example, we present computed results for the constant evaporation rate regime in the dry-spinning process of a polyvinyl-alcohol (PVA)-water system. Comparison of our analytical results with full numerical solutions of the diffusion equation from the literature, achieved with concentration-dependent diffusion coefficient, reveals very good agreement.