Account Mass Transport Research Articles

Experimental study and numerical simulation on porosity dependent direct reducibility of high-grade iron oxide pellets in hydrogen

The transition to more environmentally friendly steel production methods has intensified research into hydrogen-based direct reduction (HyDR) of iron oxide pellets. The aim of this study is to systematically investigate the kinetics of the reduction process, the evolution of porosity and the resulting microstructural changes on the reduction behavior of high-quality pellets during HyDR of iron ore at different temperatures. A modified mathematical model is developed based on the shrinkage kernel model, taking into account both mass and heat transport in a hydrogen atmosphere. The effects of temperature, particle size and time on the reduction behavior of the pellets are investigated. The simulated results are validated and discussed by the results of a batch of iron oxide pellets consisting of ten almost spherical pellets subjected to the direct reduction process with pure hydrogen. The results show that the total energy input to the HyDR process is a complex balance of factors, including chemical reaction rates, diffusion dynamics and entropy generation. The increase in free volume and simultaneous decrease in pore diameter reflect the dynamic nature of the microstructure, which includes additional free volume and defects due to the volume discrepancies and associated stresses between the reactant and product phases. Furthermore, the data show that higher temperatures accelerate the reduction reactions, especially the transformation of wustite into metallic iron. This phase transition is characterized by a significant volume change that cannot be accommodated by elastic deformation alone, leading to the development of lattice defects such as cracks, creep pores and dislocations that serve as stress relief mechanisms. The trends for porosity change at 950 °C and 1000 °C observed in the experimental results are correct and in good agreement with the numerical and simulated results.

Classifying Electrolyte Solutions by Comparing Charge and Mass Transport

The conventional classification of electrolyte solutions as “strong” or “weak” accounts for their charge transport properties, but neglects their mass transport properties, and is not readily applicable to highly concentrated solutions. Here, we use the Onsager transport formalism in combination with linear response theory to attain a more general classification taking into account both charge and mass transport properties. To this end, we define a molar mass transport coefficient , which is related to equilibrium center‐of‐mass fluctuations of the mobile ions and which is the mass‐transport analogue of the molar ionic conductivity . Three classes of electrolyte solution are then distinguished: (i) “Strong electrolytes” with ; (ii) “weak charge transport electrolytes” with ; and (iii) “weak mass transport electrolytes” with . While classes (i) and (ii) encompass the classical “strong” and “weak” electrolytes, respectively, many highly concentrated electrolytes fall into class (iii) and thus exhibit transport properties clearly distinct from classical strong and weak electrolytes.

Effect of elastocapillarity on the swelling kinetics of hydrogels

The swelling behavior of hydrogels, involving coupled diffusion and large deformations, makes them ideal for biomedical applications such as micro- and nano-scale drug delivery systems. Understanding the transient swelling or drying behavior of hydrogels at relevant length-scales will provide insight for the development of specialized and controlled drug release. At sub-millimeter length-scales, surface stresses have been shown to significantly influence material behavior for soft polymers and hydrogels, but very little is known about the influence of surface stresses on the swelling kinetics of hydrogels. In this paper, we present a non-linear theory and mixed finite element formulation that takes into account mass transport, large deformations, and elastocapillary effects for hydrogels. Focusing on hydrogel micro-spheres, we provide a comparison of swelling kinetics between the presented non-linear theory and an analytical solution using linear poroelasticity that incorporates surface stresses. Our results demonstrate that when the surface free energy is constant per unit current area (fluid-like) and the elastocapillary length-scale is on the order of the size of the hydrogel micro-sphere, the transient response equilibrates approximately an order of magnitude faster in time compared to the case without surface effects irrespective of swelling or drying. This difference in equilibration time suggests the interplay between competing processes of solvent diffusion, large deformations, and surface effects. Furthermore, we demonstrate that a Neo-Hookean type surface free energy can result in an even faster equilibration as compared to a fluid-like surface free energy. Lastly, our finite element implementation predicts the transient response of complex shapes and constrained structures.

A numerical analysis of unsteady transport phenomena in a Direct Internal Reforming Solid Oxide Fuel Cell

In this paper, a transient microstructure-oriented numerical simulation of a planar Direct Internal Reforming Solid Oxide Fuel Cell (DIR-SOFC) is delivered. The performance criteria in a direct steam reforming for a fuel starvation scenario are analyzed in order to optimize the underlying process. The proposed two-dimensional multiscale model takes into account mass and heat transport, electrochemistry, as well as the intrinsic steam-reforming kinetics. In the paper, the methane/steam reforming process over the Ni/YSZ catalyst is experimentally investigated to verify the used chemical reaction model. A three-dimensional digital microstructure representation of the commercial anode is analyzed using a Focused Ion Beam-Scanning Electron Microscope (FIB-SEM) and the nickel-pore contact surface is calculated to relate the reforming reaction rate to the catalyst’s active area. Based on the complete DIR-SOFC model, a parametric study is carried out, to simulate the dynamic response of a fuel cell for different design and operating conditions. The results prove the dominant impact of inlet fluid temperature and methane content on the calculated distribution of hydrogen across the channel, while the collected current density was found to be a less important factor. The simulations indicate, that in the case of the direct reforming, fuel starvation is likely to occur in the upstream of the anode channel, where the reforming reaction does not keep up with producing hydrogen. The obtained results provide a significant insight into safe and efficient control strategies for Solid Oxide Fuel Cells.

Optimizing the flocculation of powdered activated carbon in wastewater treatment by dosing iron salt in single- and two-stage processes

For the removal of anthropogenic micropollutants from wastewater, adsorption onto powdered activated carbon (PAC) is increasingly applied in wastewater treatment. To prevent desorption of adsorbed micropollutants into natural water bodies, the PAC is mostly separated from treated water by combined flocculation and filtration. While the adsorption efficiency of PAC has been thoroughly investigated in the past, no studies on its flocculation behavior and recommendations for operating large-scale PAC flocculation processes are available up to now.In this study, flocculation experiments were performed using secondary treated wastewater samples, a commercially available PAC product and an iron-based coagulant. Single- and two-stage flocculation processes were simulated in laboratory scale under variation of coagulant dosage, stirring rates and retention times in each process stage. In order to obtain real-time quantitative results, the flocculation process was continuously monitored by Focused Beam Reflectance Measurement and evaluated with regard to the reduction of a fine particle fraction sized <10μm. The flocculation kinetics were modelled by exponential curves, taking into account mass transport limitations in the first phase of the process as well as equilibria between floc growth and break-up at longer retention times. On this basis, optimum operating parameters for PAC flocculation were determined and strategies to meet fluctuating process conditions were deduced. By operating a fast mixing stage at velocity gradients of 50–90/s for 10min and, subsequently, a slow mixing stage at 20/s for 10min, the concentration of particles sized <10μm could be reduced by around 99%.

Water loss and crust formation during bread baking, Part I: Interpretation aided by mathematical models with highlights on the role of local porosity

ABSTRACTThis study aimed to achieve greater understanding of the contributions of different mechanisms of water transport to the overall amount of water lost by bread loaves during baking. The analysis was based on simulations from a previously published baking model which takes into account heat and mass transport as well as the expansion of the gaseous phase leading to oven rise. Liquid and gaseous diffusion, convective transport through the gaseous phase (Darcy’s law), and the diffusive transport of vapor (evaporation–condensation–diffusion) were considered. When only permeation (Darcy’s law) prevailed, the greater the porosity of the top dough surface, the lower and slower the water loss (WL): in fact, the greater the porosity, the thicker the top area. This in turn limited the rate at which heat penetrated the top layers down to the vaporization front and slowed WL. At earlier baking times, when the ebullition temperature was not reached uniformly through the crumb, the evaporation–condensation–diffusion was involved at the same time as permeation. The water flux by evaporation–condensation–diffusion was orientated toward the dough core; it accelerated the crust thickening and slowed WL. It appeared that the higher the porosity in the crumb beneath the crust, the higher the flux by evaporation–condensation–diffusion, and the lower the WL. Local porosity variations in the crust (top surface) and the crumb beneath the crust could be reproduced experimentally by constraining the total expansion of the loaf with a permeable fabric cover. Experimental and simulated trends in WL were consistent, supporting the understanding of WL proposed.

Reliable estimation of the kinetic parameters of redox enzymes by taking into account mass transport towards rotating electrodes in protein film voltammetry experiments

In Protein Film Voltammetry, a redox enzyme is immobilized on a rotating electrode in a configuration allowing fast, direct electron transfer. This technique is used to probe the mechanism of enzymes by quantitatively interpreting the response in current as a function of the experimental parameters. Limitation by mass transport of the substrate towards the electrode may obscure important features and complicate the analysis of the enzymatic response, all the more that the enzyme has high activity. In this work, we derive equations taking into account mass transport of substrate, for the steady-state current generated by an enzyme following Michaelis-Menten kinetics and immobilized onto a hydrodynamic (e.g. rotating) electrode. We use these equations to model the current response of films of CO-dehydrogenase, a metalloenzyme that catalyzes the oxidation of CO, to transient exposures to its gaseous substrate. We show that neglecting transport yields poor fits and overestimated, unreliable, values of Km (even when using the Koutecky-Levich approximation), whereas taking into account transport yields much better fits and more reliable parameters. We interpret new and previously published data by taking into account transport limitations. We propose a simple method using QSoas (http://qsoas.org) to analyze data.

Three-dimensional reconstruction of bioactive membranes and pore-scale simulation of enzymatic reactions: The case of lactose hydrolysis

Two-layered hollow-fiber membrane bioreactors containing immobilized enzymes are investigated in this work at mesoscopic and macroscopic scales. Layer-by-layer reconstruction of the membrane in three dimensions is achieved using two different stochastic techniques that draw data only from electron microscopy images of the structure. The reconstructed layers are subsequently used for the prediction of effective transport properties through the numerical solution of the relevant transport equations. The methodology is used for the investigation of hydrolysis of lactose, employing a convective diffusion and reaction macroscopic model. Direct comparison of model predictions with experimental data from the literature reveals a good agreement, provided that one uses the effective transport coefficients that are calculated from the reconstruction process. A parametric investigation of the hydrolysis process and its efficiency was conducted. The three-dimensional reconstructions are also used for the modeling of the hydrolysis of lactose at the pore scale, taking into account mass transport limitations and applying the same hydrolysis kinetics as in the macroscopic model. The agreement was quite satisfactory. Among the advantages of the pore scale approach that is formulated here is its ability to correlate pore structure details with the performance of the lactose hydrolysis process at the inevitable expense of computational resources.

Cathodic reduction of iron(III) and copper(II) on various sulfide minerals in chloride solutions

A comparative study of the electrochemical reduction of iron(III) and copper(II) ions on selected sulfide minerals in concentrated chloride solutions has been carried out as part of a broader study of the kinetics of the leaching of chalcopyrite, covellite, enargite and pyrite under chloride heap leaching conditions. Mixed potential, cyclic voltammetric and potentiostatic measurements have been made using rotating disk electrodes of massive mineral samples. For comparative purposes, arsenopyrite, platinum and gold electrodes have also been used under the same conditions. The mixed potentials of the various minerals in solutions containing 4.2mol/L sodium chloride, 0.1mol/L hydrochloric acid and 0.054mol/L iron(III) and/or 0.047mol/L copper(II) ions at 25°C vary with time depending on the mineral reactivity. The difference between the mixed potentials and the solution potentials provide qualitative indications of mineral reactivity to dissolution with iron(III) or copper(II) as oxidants.Cyclic voltammetry conducted at potentials negative to the mixed potentials at slow sweep rates after the mixed potential measurements has shown variable reactivity of the minerals for reduction of iron(III) and copper(II) ions. The data has been analysed in terms of electrochemical kinetics using a modified Butler-Volmer approach that takes into account mass transport of the oxidized and reduced species and anodic oxidation of the minerals. The electrochemical rate constant derived from a fit of the data to the rate equation shows that all the minerals have greater reactivity for the reduction of copper(II) than iron(III) ions.The rate constant varies by about an order of magnitude within the mineral group for both iron(III) and copper(II) reduction and the rate of reduction on platinum and gold electrodes are higher for both couples than for the mineral electrodes. The ratio of the rate of copper(II) reduction to iron(III) reduction is significantly greater for the minerals containing copper than for those without copper.The observed influence of mass transport on the cathodic currents close to the mixed potentials for the reduction of copper(II) on platinum, pyrite and enargite has been quantitatively explained in terms of the effect of mass transport on the surface concentration of copper(I).An attempt has been made to correlate the kinetic data with published data on the semi-conducting properties of the metal sulfides. With the exception of covellite (which is not considered a semiconductor), the formal potentials of the copper(II)/copper(I) and iron(III)/iron(II) couples fall within the bandgaps of the metal sulfides and there does not appear to be any correlation between the energy levels of the couples in solution relative to the conduction bands of the sulfides and the reactivity for electron transfer to the metal ion couples. The effect of illumination with light of wavelength 405nm on the cathodic currents has been demonstrated to be due to thermal and not photocurrent effects.

A one-dimensional stochastic approach to the study of cyclic voltammetry with adsorption effects

In this study, a one-dimensional stochastic model based on the random walk approach is used to simulate cyclic voltammetry. The model takes into account mass transport, kinetics of the redox reactions, adsorption effects and changes in the morphology of the electrode. The model is shown to display the expected behavior. Furthermore, the model shows consistent qualitative agreement with a finite difference solution. This approach allows for an understanding of phenomena on a microscopic level and may be useful for analyzing qualitative features observed in experimentally recorded signals.

Modeling of contaminant migration through porous media after underground coal gasification in shallow coal seam

The migration rates of representative underground coal gasification (UCG) related products and contaminants through porous surroundings of a georeactor in a shallow coal seam in gaseous and liquid phases were studied in this work. The proposed comprehensive model, taking into account mass transport phenomena both in gaseous and liquid phase, was based on the real data obtained during the UCG field-scale study carried out at the Experimental Mine “Barbara” in Poland in the framework of the RFCS Project HUGE (2007–2010). The mass transport from the reaction zone was modeled by means of constitutive equations, in gas phase permeation, in liquid phase advection, axial dispersion, diffusion, and adsorption. The applied input values of parameters were based on results from previous pilot experiments. The effects of pore size, porosity, tortuosity, and reaction conditions on the migration rate were individually evaluated and taken into account. The contamination risk for aquifers and potential leakage of poisonous gases and their environmental impact were assessed and thoroughly discussed. It was found that porosity, pore diameter and tortuosity, which belong to the key transport parameters, play a major role in overall permeation transport of gaseous contaminants compared with physical characteristics—pressure and temperature. Migration rates of UCG-related contaminants in the liquid phase are significantly slower compared with the gaseous phase.

Effects of cathode and electrolyte properties on lithium–air battery performance: Computational study

Li/O2 batteries draw much attention due to its outstanding theoretical specific energy, but the value of practically achievable specific energy is still under the question. In this paper we employ a numerical model of Li/O2 cell, which takes into account mass transport processes, to simulate non-uniform product precipitation at different discharge current densities in acetonitrile, dimethyl sulfoxide and 1,2-dimethoxyethane-based electrolytes. Even for 1,2-dimethoxyethane, which has the highest oxygen mobility and solubility, oxygen transport restrictions at 1 mA/cm2 lead to cell-level specific energy of about 650 Wh/kg if a pure oxygen is supplied to the cell. Finally, in order to assist the ongoing search for new cathode materials, which can be alternative to carbon, we also investigate the effect of electrode material density on cell-level specific energy and show that materials with densities up to 10 g/cm3 can be used without serious penalty to the specific energy.

Buoyancy-thermocapillary convection of volatile fluids under their vapors

Convection in a layer of fluid with a free surface due to a combination of thermocapillary stresses and buoyancy has been studied extensively under atmospheric conditions. However, recent experimental results have shown that removing most of the air from a sealed cavity significantly alters the flow structure and, in particular, suppresses transitions between different convection patterns found at atmospheric conditions. On the other hand, removing air has a very small effect on the flow speed, while a simple analytical estimate predicts that complete removal of noncondensable gases such as air should reduce the flow speed by an order of magnitude. To understand these unexpected results, we have formulated and numerically implemented a detailed transport model that takes into account mass and heat transport in both phases in the absence of noncondensables. The model was used to investigate how the flow is affected by the magnitude of the (poorly defined) accommodation coefficient and by the temperature jump across the liquid–vapor interface predicted by some phase change models. Our results eliminate both effects as possible explanations for the unexpected experimental observations, suggesting that the small amount of air left in the cavity in the experiments is the most likely, albeit somewhat unexpected, explanation for the observations.

A Time Dependent Model of Electroless Deposition of Co-Mn Alloy

A time dependent model of electroless cobalt-manganese deposition will be presented. The results are obtained from the development of a time-dependent mathematical model for the electroless deposition of cobalt based on fundamental principles. The experimental conditions used to develop this model include, temperature of 80oC and pH of 8.5. The governing equations take into account mass transport by migration and diffusion and Butler Volmer kinetics. The model can be used to predict the concentration profile of each species in the solution and the thickness of composite deposit. The simplifying assumptions made in model equations derivation have significant influence on the accuracy of the model predictions.

A three-dimensional model for transient performance of a solid oxide fuel cell

This paper presents an analysis of transient behavior of an anode-supported solid oxide fuel cell (SOFC) using a model, which has recently been built for steady state operation. The model is three dimensional (3D), which takes into account heat and mass transport, chemical and electrochemical reactions taking place simultaneously in the cell. The electrochemical processes are assumed to take place in a layer of finite thickness at electrode–electrolyte interfaces. A repeating unit of a planar anode-supported SOFC with co-flow configuration is investigated. Step changes of working voltage and fuel composition are applied to the cell. Results for the dynamic profiles of the temperature, the current density and the activation overpotential distributions in the cell are presented and discussed.

Modeling of CO2 absorption in a membrane contactor considering solvent evaporation

A comprehensive mathematical model that takes into account momentum, energy, and mass transport was developed. The model is taking into consideration the amount of water evaporated from the liquid solvent at various inlet absorbent temperatures and the accompanied latent heat of vaporization. The model considers the transport of the gas mixture of carbon dioxide and methane through a hollow fiber membrane (HFM) contactor module. The model was based on the non-wetted mode, in which the gas mixture fills the membrane pores in a countercurrent gas–liquid contact. Axial and radial diffusion inside the hollow fiber membrane, through the membrane skin, and within the shell side of the contactor were incorporated to the model. The model was validated for changes in liquid absorbent temperature with the experimental results obtained for carbon dioxide removal from a CO2/CH4 gas mixture using lab-made polyvinylidene fluoride (PVDF) hollow fiber membranes fabricated via thermally induced phase separation. The effect of the inlet liquid absorbent temperature on the membrane performance was validated with the experimental data. The amount of water evaporated during the change in absorbent inlet temperature was measured and compared with model predictions. The COMSOL software package was used for solving the model equations. The amount of water vapor increased with increased absorbent inlet temperatures. The CO2 flux increased with inlet absorbent temperature. The model predictions were in good agreement with experimental data.

Modeling bimetallic corrosion under thin electrolyte films

A finite element model (FEM) was developed to calculate the potential distribution in the electrolyte in the case of bimetallic corrosion between iron and zinc electrodes, taking into account mass transport of oxygen in the solution. This model was first compared with experimental results obtained by scanning vibrating electrode technique (SVET) on a galvanized steel cut-edge in immersion conditions in a 0.03 M NaCl electrolyte. A good agreement was obtained between the calculated and experimental current densities. The model predicted the evolution of the galvanic coupling as function of the electrolyte thickness and for various iron–zinc surface area ratios. Different coupling regimes were highlighted when the electrolyte thickness was decreased: from a kinetic (cathodic) control in full immersion conditions, to an ohmic control for very thin electrolyte films, leading to a decrease of the protection efficiency. The evolution of the critical electrolyte thickness limiting these different regimes as function of the conductivity and geometrical conditions was also studied.

A Dynamic Circuit Model of a Small Direct Methanol Fuel Cell for Portable Electronic Devices

Direct methanol fuel cells (DMFCs) constitute nowadays a promising alternative to lithium ion batteries for powering portable devices. The effective design of power-management units for interfacing DMFCs requires accurate models able to account for variable-load conditions and fuel consumption. A dynamic nonlinear circuit model for passive methanol fuel cells is presented in this paper. The model takes into account mass transport, current generation, electronic and protonic conduction, methanol adsorption, and electrochemical kinetics. Adsorption and oxidation rates, which mostly affect the cell dynamics, are modeled by a detailed two-step reaction mechanism. The fully coupled multiphysics equivalent circuit is solved by assembling first-order differential equations into a nonlinear state-variable system in order to simulate the electrical evolution of the fuel cell from its initial conditions. The fuel-cell discharge and methanol consumption are computed by combining mass-transport and conservation equations. As a result, the runtime of a DMFC can be predicted from the current load and the initial methanol concentration.

Electrochemical ion transfer across liquid/liquid interfaces confined within solid-state micropore arrays – simulations and experiments

Miniaturised liquid/liquid interfaces provide benefits for bioanalytical detection with electrochemical methods. In this work, microporous silicon membranes which can be used for interface miniaturisation were characterized by simulations and experiments. The microporous membranes possessed hexagonal arrays of pores with radii between 10 and 25 microm, a pore depth of 100 microm and pore centre-to-centre separations between 99 and 986 microm. Cyclic voltammetry was used to monitor ion transfer across arrays of micro-interfaces between two immiscible electrolyte solutions (microITIES) formed at these membranes, with the organic phase present as an organogel. The results were compared to computational simulations taking into account mass transport by diffusion and encompassing diffusion to recessed interfaces and overlapped diffusion zones. The simulation and experimental data were both consistent with the situation where the location of the liquid/liquid (l/l) interface was on the aqueous side of the silicon membrane and the pores were filled with the organic phase. While the current for the forward potential scan (transfer of the ion from the aqueous phase to the organic phase) was strongly dependent on the location of the l/l interface, the current peak during the reverse scan (transfer of the ion from the organic phase to the aqueous phase) was influenced by the ratio of the transferring ion's diffusion coefficients in both phases. The diffusion coefficient of the transferring ion in the gelified organic phase was ca. nine times smaller than in the aqueous phase. Asymmetric cyclic voltammogram shapes were caused by the combined effect of non-symmetrical diffusion (spherical and linear) and by the inequality of the diffusion coefficient in both phases. Overlapping diffusion zones were responsible for the observation of current peaks instead of steady-state currents during the forward scan. The characterisation of the diffusion behaviour is an important requirement for application of these silicon membranes in electroanalytical chemistry.

Polymer Electrolyte Membrane Fuel Cell Modelling: d.c. and a.c. Solutions

A model of a polymer electrolyte membrane fuel cell (PEMFC) is proposed to predict the polarization curves and corresponding impedance diagrams for a small membrane electrode assembly sandwiched between bipolar plates. This theoretical approach takes into account mass transport for the following species: reactants and products along the flow channel, and water across the membrane. A global mass transport coefficient allows characterization of the mass transport flux through the gas-backing layer of the GDE, and the flooded agglomerate model is used to describe the active layer within the gas diffusion electrode. Applying this model to usual PEMFC shows that diffusion plays a crucial role at cathode for high current densities when using air as reactant. Finally, the influence of working conditions and PEMFC structure is investigated.