Interfacial Transport Phenomena Research Articles

Investigation and Characterization of Interfacial Transport Phenomena in the Catalyst Layer Using Rheo-Impedance Measurement

Electrodes or catalyst layers (CLs) are the heart of fuel cell and electrolyzer cell devices. They are mainly heterogeneous porous electrodes composed of catalyst particles, ion-conducting polymer material, and void spaces that make up the triple-phase boundary (TPB). It is important to tailor the CL’s microstructure such that there are abundant TPBs where reactions take place to maximize catalyst utilization and improve cell performance. However, this is a critical challenge due to lack of fundamental understanding of the interfacial transport within the CL. Understanding how catalyst ink parameters affect ink properties and how ink components interact, and ultimately, their relationship with CL microstructure formation and cell performance, are essential to designing electrodes. Electrode morphology is important and is controlled by the ionomer/catalyst interactions formed in precursor inks that evolve during mixing and electrode fabrication.In this study, we probe interactions in catalyst inks with different formulations (ionomer-to-carbon ratio and IPA/water) using a new experimental method to unravel the complexities of ionomer/catalyst particle interactions. The new experimental method is a combination of rheological and electrical impedance spectroscopy measurements (rheo-EIS) that takes advantage of the dynamic nature of catalyst ink and the fact that the rheological and electrical behaviors of the ink are coupled to the microstructure of the material. Using rheo-EIS tool, in combination with zeta (ζ) potential and dynamic light scattering (DLS) measurements, we were able to systematically study how the level of agglomeration of the inks and microstructures evolve with respect to different I/C ratios, solvent formulation, and external shear forces. Results from the three-phase rebuilt test designed to simulate the ink coating condition with single-frequency EIS measurement give information on how the ionomer/catalyst particle interactions form and recover during the coating process. In addition, the full frequency range EIS measurements provide complementary data of the ionic and electrical resistance of the ink before and after high shear applications. Furthermore, the observations of the effect of I/C and IPA/water ratios from this study provide insights on how to better engineer suitable catalyst inks and how to control specific CL microstructure without the need for time-consuming optimization and empirical studies.

3D Printed Drug Delivery Systems in Action-Magnetic Resonance Imaging and Relaxometry for Monitoring Mass Transport Phenomena.

The hypothesis of the study was that (1) 3D printed drug delivery systems (DDS) could be characterized in situ during drug release using NMR/MRI techniques in terms of mass transport phenomena description (interfacial phenomena), particularly for systems dealing with two mobile phases (e.g., water and low molecular weight liquid polymer); (2) consequently, it could be possible to deduce how these interfacial mass transport phenomena influence functional properties of 3D printed DDS. Matrix drug delivery systems, prepared using masked stereolithography (MSLA), containing poly(ethylene glycol) diacrylate (PEGDA) and low molecular weight polyethylene glycol (PEG) with ropinirole hydrochloride (RH) were studied as example formulations. The PEGDA to PEG (mobile phase) concentration ratio influenced drug release. It was reflected in spatiotemporal changes in parametric T2 relaxation time (T2) and amplitude (A) images obtained using magnetic resonance imaging (MRI) and T1-T2 relaxation time correlations obtained using low-field time-domain nuclear magnetic resonance (LF TD NMR) relaxometry during incubation in water. For most of the tested formulations, two signal components related to PEG and water were assessed in the hydrated matrices by MRI relaxometry (parametric T2/A images). The PEG component faded out due to outward PEG diffusion and was gradually replaced by the water component. Both components spatially and temporally changed their parameters, reflecting evolving water-polymer interactions. The study shows that dynamic phenomena related to bidirectional mass transport can be quantified in situ using NMR and MRI techniques to gain insight into drug release mechanisms from 3D printed DDS systems.

An approach for topology optimization of heat sinks for two-phase flow boiling: Part 1 – Model formulation and numerical implementation

Two-phase flow boiling in heat sinks and cold plates is attractive for various thermal management applications due to high effective heat capacity rates and high heat transfer coefficients compared to single-phase operation. In addition, multi-physics topology optimization is sought for generation of high performance thermal management components. Yet, the design of heat sinks using topology optimization has been restricted to single-phase flow physics, due to incompatibility between available two-phase flow models and traditional single-phase topology optimization approaches. Interface-capturing two-phase flow models are too computationally expensive for optimization; mixture and two-fluid models that treat the liquid and vapor phases as an interpenetrating continuum with interfacial transport phenomena captured through empirical correlations are computationally tractable for heat-sink-scale optimization. However, the penalization approaches commonly used to define the structures formed during topology optimization results in arbitrary fin and channel geometries for which a universal two-phase flow correlation is not available. To enable coupling with two-phase mixture models, this work leverages a homogenization approach to topology optimization wherein heat sink designs are represented using spatially varying microstructures with optimized dimensions. A predefined microstructure geometry is chosen for which two-phase flow correlations exist and therefore topology optimization can be performed. This work is the first to develop a topology optimization algorithm using a mixture model for simulating two-phase flow boiling to design heat sinks and cold plates. Part 1 of this study develops and implements the algorithm to investigate topology optimized heat sinks at various heat inputs, topology optimization grid sizes, and maximum vapor quality constraints. Topology optimized heat sinks designed for single-phase versus two-phase flow are compared. There are significant differences in hydraulic and thermal responses of the single-phase and two-phase designs due to high effective heat capacity rates and high heat transfer coefficients of flow boiling. A companion paper (Part 2) focuses on manufacturing, model calibration, and experimental validation of the topology optimized heat sinks under two-phase flow boiling. The algorithm demonstrated in this work extends the capabilities of topology optimization to two-phase flow physics, and thereby enables the design of various two-phase flow components such as evaporators, condensers, heat sinks, and cold plates.

Elucidating Interfacial Hole Extraction and Recombination Kinetics in Perovskite Thin Films

Hybrid organic–inorganic perovskite solar cells (PSCs) are receiving huge attention owing to their marvelous advantages, such as low cost, high efficiency, and superior optoelectronics characteristics. Despite their promising potential, charge-carrier dynamics at the interfaces are still ambiguous, causing carrier recombination and hindering carrier transport, thus lowering the open-circuit voltages (Voc) of PSCs. To unveil this ambiguous phenomenon, we intensively performed various optoelectronic measurements to investigate the impact of interfacial charge-carrier dynamics of PSCs under various light intensities. This is because the charge density can exhibit different mobility and charge transport properties depending on the characteristics of the charge transport layers. We explored the influence of the hole transport layer (HTL) by investigating charge transport properties using photoluminescence (PL) and time-resolved (TRPL) to unveil interfacial recombination phenomena and optoelectronic characteristics. We specifically investigated the impact of various thicknesses of HTLs, such as 2,2′,7,7′-tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9′-spirobifluorene (spiro-OMeTAD), and poly(triaryl)amine (PTAA), on FA0.83MA0.17Pb(Br0.05I0.95)3 perovskite films. The HTLs are coated on perovskite film by altering the HTL’s concentration and using F4-TCNQ and 4-tert-butylpyridine (tBP) and lithium bis(trifluoromethanesulfonyl)imide (LiTFSi) as dopants both for spiro-OMeTAD and PTAA. These HTLs diversified the charge concentration gradients in the absorption layer, thus leading to different recombination rates based on the employed laser intensities. At the same time, the generated charge carriers are rapidly transferred to the interface of the HTL/absorption layer and accumulate holes at the interface because of inefficient capacitance and mobility differences caused by differently doped HTL thicknesses. Notably, the charge concentration gradient is low at lower light intensities and did not accumulate holes at the HTL/absorption layer interface, even though they have high charge mobility. Therefore, this study highlights the importance of interfacial charge recombination and charge transport phenomena to achieve highly efficient and stable PSCs.

Liquid crystal-based label-free low-cost sensing platform: Engineering design based on interfacial interaction and transport phenomena

Typically, the detection methods of chemical species in sensing platform involves the use of labelling agents. Even though it is selective, the process is complex and time consuming. Liquid crystals (LC) are sensitive and rapidly responsive to the presence of any foreign species. When a LC layer interacts with aqueous (ionic surfactant) solution, there is homeotropic alignment of the director orientation due to the anisotropic interactions at the interface. This leads to the dark birefringence patterns observed in polarised microscope under cross polarisation. In the presence of H+ in the aqueous layer, the LC orientation is distorted resulting in a change of the birefringence patterns in the polarised micrographs. We have prepared an optical cell where the aqueous solution can interact with the LC layer confined within micrometre sized grids. The flow arrangement and the associated mass transfer process is optimised for enhanced interaction. The elastic interactions of the LC layer with H+ at the interface distorts the director orientation, and the birefringence pattern is captured with polarised microscope (cross-polarisation). There is a correlation between the polarised micrographs and the concentration of the H+, which forms the basis of detection principle. The detection of H+ has no interference with salts. The present method can be used for recognition of (bio-) chemical reactions releasing H+. The developed optical flow cell is inexpensive, less than $1. The outcome of the present work may be useful for technological adaption and prospective use in point-of-care devices and field test kits.

Reducing interfacial thermal resistance between polyethylene oxide-based solid-state polymer electrolyte and lithium anode by using IVA group two-dimensional materials: A molecular dynamics study

Solid-state lithium-ion batteries, as a new generation of high energy density electrochemical energy storage devices, need to meet more stringent thermal management standards. In this work, the interfacial thermal transport phenomena between a polyethylene oxide based solid electrolyte and a lithium anode in solid-state lithium-ion batteries was investigated by using a non-equilibrium molecular dynamics simulation method. To reveal the internal heat transport mechanism of the batteries at the microscopic level and to enhance the heat dissipation in them, IVA group two-dimensional monolayer materials such as graphene, silicene, and germanene were inserted at the interface and the interfacial thermal resistances were calculated to compared with the pristine interface. It was found that interfacial interactions were enhanced and the lattice vibrations were coupled by inserting the monolayer materials. Also, compared to the pristine interface, the interfacial thermal resistance was reduced by 83.89 %, 76.05 % and 55.99 %, respectively. Thus, this work provides valuable insights into the thermal transport between electrodes and electrolytes in solid-state lithium-ion batteries, and provides methodological references for improving the heat dissipation and thermal management efficiency inside the batteries.

A systematic non-equilibrium thermodynamics approach for assessing transport mechanisms in membrane distillation

Membrane distillation (MD) is a promising technique for purifying volatile liquids at temperatures below their boiling points. This study presents a systematic non-equilibrium thermodynamics (NET) approach for analysis of transport mechanisms in direct-contact membrane distillation (DCMD). By incorporating the transport properties of the membrane, membrane interfaces, and temperature polarization layers, a unified framework is established to assess mass and heat transfer, including coupling effects in the composite membrane system. Explicit expressions for the transport properties are derived, and a numerical solution procedure is used to obtain temperature and partial pressure profiles through the system. The NET approach reveals that the temperature difference across the membrane is the true driving force of mass transfer, which after suitable approximations is equivalent to the saturation pressure difference. The commonly employed formula for distillate flux in MD literature was found to agree with the comprehensive NET approach within 3% when predicting the water flux through a DuraPore GVHP membrane. Incorporating a correction factor that accounts for kinetic heat-mass coupling effects improves the agreement to 0.5%. The simplified model disregards interfacial transport phenomena and mass-heat coupling. These effects are shown to be insignificant for the DuraPore GVHP membrane. However, it is crucial to account for temperature polarization to obtain agreement with experimental results. The resistance of the vapor-liquid interface is shown to be more important if the membrane has a Cassie-Baxter wetting state than a Wenzel wetting state, and this can enhance the water flux. When the pore-sizes approach the nanometer scale, we show that direct interactions between the molecules and the pore walls must be accounted for due to sorption effects. In applications where nanometer scale pores are important, such as in systems where the membrane must maintain a large pressure difference, it may be important to take such corrections into consideration. The presented NET approach provides a comprehensive toolkit for assessing and analyzing transport properties in membrane systems, which can be used to better understand how the properties of MD systems can be tailored to enhance performance.

Performance of Rhodamine-Sensitized Solar Cells Fabricated with Silver Nanoparticles

A plasmonic effect of silver nanoparticles (AgNPs) in dye-sensitized solar cells (DSSCs) is studied. In this investigation, the efficiency of dye-sensitized solar cells has been remarkably increased by infusion of synthesized silver nanoparticles into the TiO2 photoanode. Rhodaminederivative RdS1 was synthesized by microwave-assisted condensation of hydrazide and 3-for-mylchromone. The synthesized silver nanoparticles were characterized with UV/Vis absorption spectroscopy and transmission electron microscopy. The interfacial charge transport phenomena of the dye-sensitized solar cell (DSSCs) are determined by electrochemical impedance spectroscopy and the corresponding efficiencies are calculated using current-voltage (I-V) curve. The solar cell photoanode with silver nanoparticles infused with RdS1 in titanium dioxide had the highest solar-to-electric power efficiency at 0.17%.

Characteristics of one-dimensional bubbly flow interfacial area transport in horizontal narrow rectangular channel

The experiments of horizontal adiabatic air-water flow in narrow rectangular channel with a cross-sectional area of 68 mm × 1.9 mm were conducted under an atmosphere pressure condition in order to study bubbly flow interfacial area transport phenomenon. The liquid film thickness was obtained by PCB liquid film sensor. The results show that the liquid film thickness can be correlated with the product of Capillary number Ca and jg/jl, so a correlation for liquid film thickness was proposed. The effect of liquid film thickness on IAC and void fraction was also evaluated. The results show that the average error caused by ignoring liquid film thickness is about 6.1% and 10.1%, respectively. The lateral profiles and axial direction development of the void fraction, interfacial area concentration, bubble Sauter mean diameter were obtained by high-speed camera at three axial locations of Z/D = 63, 241 and 510. The simplified one-dimensional, steady-state, one-group interfacial area transport equation for an adiabatic bubbly flow with six sets of IAC source and sink models was evaluated by the current experimental data. The evaluation results showed that the models of Yao and Morel (2004) and Shen and Hibiki (2013) performed better with mean prediction errors of 12.13% and 18.92%, respectively.

Imaging Vibrational Excitations in the Electron Microscope

Vibrational spectroscopy is a powerful tool for probing atomic motions in molecules and extended solids. Recent advances in aberration-corrected, monochromated-scanning transmission electron microscopy (STEM) now allow imaging of individual phonon modes at the nanoscale, overcoming the spatial limit imposed by diffraction-limited optical spectroscopy techniques. In this Perspective, we summarize the recent progress in high-resolution electron energy-loss spectroscopy (EELS), which now enables vibrational spectroscopy to be performed in the electron microscope. The high spatial and energy resolution of low-loss EELS can be used to directly image phonons inside or near inorganic and organic materials without considerable sample damage. Monochromated EELS can furthermore resolve isotope specific vibrational signatures and phonon modes arising from single-atom dopants. In parallel with these advances, we highlight the ability of spatial- and momentum-resolved EELS to measure the phonon dispersions at material interfaces, obtaining valuable knowledge about interfacial thermal and electrical transport phenomena. Before concluding, we illustrate how imaging infrared (IR) plasmons at high spatial resolution deepens our understanding of how plasmons interact with molecular vibrations. Taken together, these diverse studies illustrate the capability of monochromated STEM-EELS to image low-energy phonon and plasmon excitations at the nanoscale and the new insights from these studies can be leveraged to engineer the specific material properties needed for next-generation devices.

Mesoscopic approach for nanoscale liquid-vapor interfacial statics and dynamics

Nanoscale liquid-vapor interfacial transport phenomena are of great significance to a variety of applications including evaporation, condescension, boiling and micro/nano-fluidics. In this work, we propose a mesoscopic approach to describe the nanoscale liquid-vapor interfacial statics and dynamics by combining the pseudopotential multiphase lattice Boltzmann method, the theorem of corresponding states and the principle of dynamic similarity. We demonstrate that our mesoscopic predictions of density profile, interfacial thicknesses and surface tensions for planar liquid-vapor interfaces of various real fluids agree very well with the NIST recommended data and molecular theories of capillarity in a very wide temperature range. We quantify the size effects of nano-bubbles and nano-droplets on the surface tension of water under a saturation temperature of 100°C. We show that the surface tensions of nano-bubbles decrease while the surface tensions of nano-droplets increase with increasing size, and the predictions from static cases and dynamic cases are consistent. The mesoscopic approach proposed in this paper could well resolve nanoscale liquid-vapor interfacial phenomena for various real fluids with high resolution, high accuracy and affordable computation cost in a very wide temperature range, which paves the way for quantitative investigations of nanoscale liquid-vapor interfacial transport for real fluids in practical applications.

Nonequilibrium statistical thermodynamics of multicomponent interfaces

Nonequilibrium interfacial thermodynamics has important implications for crucial biological, physical, and industrial-scale transport processes. Here, we discuss a theory of local equilibrium for multiphase multicomponent interfaces that builds upon the "sharp" interface concept first introduced by Gibbs, allowing for a description of nonequilibrium interfacial processes such as those arising in evaporation, condensation, adsorption, etc. By requiring that the thermodynamics be insensitive to the precise location of the dividing surface, one can identify conditions for local equilibrium and develop methods for measuring the values of intensive variables at the interface. We then use extensive, high-precision nonequilibrium molecular dynamics (NEMD) simulations to verify the theory and establish the validity of the local equilibrium hypothesis. In particular, we demonstrate that equilibrium equations of state are also valid out of equilibrium, and can be used to determine interfacial temperature and chemical potential(s) that are consistent with nonequilibrium generalizations of the Clapeyron and Gibbs adsorption equations. We also show, for example, that, far from equilibrium, temperature or chemical potential differences need not be uniform across an interface and may instead exhibit pronounced discontinuities. However, even in these circumstances, we demonstrate that the local equilibrium hypothesis and its implications remain valid. These results provide a thermodynamic foundation and computational tools for studying or revisiting a wide variety of interfacial transport phenomena.

Increasing the Performance of Anion Exchange Membrane Water Electrolyzer Operating in Neutral pH

Anion exchange membrane water electrolysis (AEMWE) for generation of hydrogen from water is an emerging technology with high potential to surpass peer electrolyzers. However, current AEMWEs exhibit significant overpotential loss. Almost all the reported improvements in AEMWE performance have been confined to development and optimization of the conductive membranes and active electrodes to address issues regarding the ohmic and activation loss in AEMWE. However, coming from a different perspective, the strong effect of other cell components, which directly influence interfacial contact and transport phenomenon, is an important aspect to further improve the AEMWE performance and should not be neglected . Here, for the first time we report a solution to solve this missing piece of the puzzle with a highly conductive novel multifunctional liquid/gas diffusion layers (LGDLs), which consisted of well-tuned pores to asynchronously transport electrons, heat and liquid/gas while minimizing ohmic, mass transport and interfacial losses. The ohmic and mass transfer losses were reduced by 48% and 58%, respectively, thanks to the developed multifunctional LGDL and as a result the performance increased by 13 % at 0.5 A cm-2 in water, which places AEMWE close in effectiveness to more mainstream alkaline electrolyzers but without the need of using corrosive alkaline solutions as electrolyte. This multifunctional LGDL, called NiMPL-PTL, was developed by introducing nickel based micro porous layers (MPLs) using atmospheric plasma spray (APS) technique on the top of a porous transport layer (PTL) substrate. The low tortuosity of this novel porous NiMPL-PTL can reduce capillary pressure and bubble point, which can efficiently remove the unavoidable gas bubbles formed at electrode surface. Moreover, this NiMPL-PTL can decrease the contact resistance, since it increases the contact area between PTL and membrane electrode assembly (MEA) by reducing the aperture size of the PTL. Therefore, a significant mitigation of mass transport issues at high current densities and an improvement in interfacial contact resistance (ICR) were achieved by implementing NiMPL-PTL in the AEMWE operated in water. Electrochemical results showed that for AEMWE cell with well-tuned NiMPL-PTLs, the operating voltage required at the current density of 0.5 A cm-2 is as low as 1.90 V with an operating efficiency of 76%HHV, which was 290 mV lower than that of cell with the uncoated PTLs , which could only reach to efficiency of 65%HHV. To the best of our knowledge, there has been no such a genuine design of multifunctional coated backing layer PTL to improve the AEMWE performance in water.

(Invited) Epitaxial Thin Films of Solid-State Battery Material

Solid-state batteries are regarded as next-generation batteries, which will play important roles in the coming low-carbon society; however, they have been suffering from their low power densities. Although low ionic conductivities of solid electrolytes had been the reason for the low power densities, intense studies have given solid electrolytes with high ionic conductivities: The highest conductivity exceeded 10−3 S cm−1 in 1990s and has reached 10−2 S cm−1 recently among sulfides. These conductivities are comparable to, or higher than, those of organic-solvent liquid electrolytes; however, even such high conductivities do not lead to high power densities without fast ionic conduction at the interfaces between the battery materials. In spite of the importance, studies on interfacial transport phenomena are still pioneering stage. For example, although high interfacial resistances between high-voltage cathodes and sulfide solid electrolytes have successfully reduced [1], mechanism of the high interfacial resistance is still in an argument; and although oxide systems have been suffering from high grain boundary resistance [2], origin of the grain boundary resistance is still unclear.Thin-film systems are ideal for such fundamental studies on the interfaces owing to their simple geometry, in which the interface can be a plane, and the ionic conduction can be regarded as one-dimensional. The thin films should be single crystal with controlled crystal orientation in order to construct interfaces formed between defined crystal planes and free from any defects including grain and domain boundaries.We have been focusing our attention on making such thin films by epitaxial growth. We have successfully formed some battery materials into single-crystal-like thin films with controlled crystal orientation [3–5]. An epitaxial film of perovskite-type solid electrolyte shows the influence of domain boundaries on ionic conduction, while anisotropic ionic conduction expected in LiCoO2 is clearly observed in a high-quality epitaxial film for the first time.

Numerical investigation of interfacial transport phenomena in a superhydrophobic microcontactor used for water oxygenation

Numerical investigation of interfacial transport phenomena in a superhydrophobic microcontactor used for water oxygenation

A mesoscale method for effective simulation of Rayleigh convection in CO2 storage process

Rayleigh convection is an interfacial transport phenomenon in the CO2 capture and storage processes. In the present paper, we proposed a mesoscale model to capture the convection structure caused by Rayleigh convection in a 20mm×10mm CO2 absorption cell with low mesh density. To close this mesoscale model, we analyzed the relationship between entropy generation caused by mass transfer and viscous dissipation, and raised a criterion. This criterion was also verified by a PIV/LIF quantitative experiment in CO2 absorption cell with Ra=1.15∼2.3×107. The proposed mesoscale method can prediction the concentration and velocity distributions of Rayleigh convection effectively. The relative error of total mass transfer flux can be decreased from 43% to 6.3%. The idea of this mesoscale method is promising for solving complicated transport problem that is difficult to find the conservation model.

Numerical investigation of interfacial transport phenomena in a superhydrophobic microcontactor used for water oxygenation

Numerical investigation of interfacial transport phenomena in a superhydrophobic microcontactor used for water oxygenation

Local and global force balance for diffusiophoretic transport.

Electro- and diffusio- phoresis of particles correspond respectively to the transport of particles under electric field and solute concentration gradients. Such interfacial transport phenomena take their origin in a diffuse layer close to the particle surface, and the motion of the particle is force-free. In the case of electrophoresis, it is further expected that the stress acting on the moving particle vanishes locally as a consequence of local electroneutrality. But the argument does not apply to diffusiophoresis, which takes its origin in solute concentration gradients. In this paper we investigate further the local and global force balance on a particle undergoing diffusiophoresis. We calculate the local tension applied on the particle surface and show that, counter-intuitively, the local force on the particle does not vanish for diffusiophoresis, in spite of the global force being zero as expected. Incidentally, our description allows to clarify the osmotic balance in diffusiophoresis, which has been a source of debates in the recent years. We explore various cases, including hard and soft interactions, as well as porous particles, and provide analytic predictions for the local force balance in these various systems. The existence of local stresses may induce deformation of soft particles undergoing diffusiophoresis, hence suggesting applications in terms of particle separation based on capillary diffusiophoresis.

Mass transfer modeling and simulation of a transient homogeneous bubbly flow in a bubble column

Bubble columns have wide applicability in the industry as contactors such as absorbers, strippers, and multiphase reactors. Despite their simple construction and operation, the success in the design of bubble columns requires deep knowledge of transport phenomena applied to multiphase flow. Modeling and simulating the fluid dynamics through numerical methods may circumvent the high cost of empirical methods when analyzing key parameters for the design and scale-up of bubble columns. The main objective of this work is to model and simulate the interfacial mass transfer in a bubble column, for both steady-state and transient analysis. The equations of mass, momentum, and species conservation are described in a Euler-Euler framework using a one-dimensional Two-Fluid Model (TFM), taking adequate closure relations for modeling interfacial transport phenomena. The equations are integrated by the Finite Volume Method (FVM) in an algorithm developed by the authors and the numerical results obtained are compared with experimental data found in the literature. The simulations are predictive and run with no need for matching experimental data, which is the main contribution of this work. The results obtained showed good agreement when compared with experimental data. Additionally, a high-order in space (TVD) and time (Crank-Nicolson) is developed to capture the gradients of gas fraction and composition, providing a remarkable tool for transient analysis.

A continuum model of heterogeneous catalysis: Thermodynamic framework for multicomponent bulk and surface phenomena coupled by sorption

We derive a thermodynamically consistent model of heterogeneous catalysis for chemically reacting fluid mixtures formulated in the framework of continuum thermodynamics. The model takes into account standard transport phenomena in the bulk domain and involves mass transfer of the species between the bulk and the catalytic (active) part of the boundary where the surface counterparts to the bulk transport processes take place.Concerning the balance laws on the catalytic surface, the model benefits from description of the active part of the boundary as an interface between the bulk domain and its exterior which allows to employ the framework of continuum mechanics with interfacial transport phenomena. The constitutive relations involving vectorial and tensorial quantities such as the Cauchy stress, energy and entropy fluxes and diffusive fluxes relevant to individual constituents are constructed in a systematic manner ensuring compatibility with the second law of thermodynamics. The constitutive procedure follows from the specification of constitutive equations for suitable thermodynamic potentials (free energies) of the mixture in the bulk and on the active part of the boundary and from the identification of the bulk and surface entropy productions. The active part of the boundary is described by means of statistical physics and this description then serves as a building block for the derivation of surface continuum thermodynamic potentials.The derived model is suitable for further mathematical, numerical and computational analysis of relevant initial and boundary value problems. While the model employs a relatively simple description of the active part of the boundary as a monolayer lattice with single-site Langmuir-type adsorption, its detailed derivation presented here provides clear guidelines for the incorporation of other sorption models.