External Transport Resistance Research Articles

Comparative analysis of adsorption and release properties of β-phenylethanol on two kinds of activated carbon

In order to understand the adsorption and release properties of β-phenylethanol on activated carbon produced from different carbon sources, coconut shell activated carbon (CAC) and petroleum coke activated carbon (PAC) were selected for the immobilization β-phenylethanol. The structure and morphology of CAC and PAC were characterized by SEM, BET and TGA analysis. And then the effect of carbon sources and pore structure on β-phenylethanol adsorption and release properties were investigated by kinetic model. The results showed that the microporosity ratios for CAC and PAC were 89.13% and 77.12%, respectively, and both types of activated carbon were dominated by micropore structure. The adsorption behavior of β-phenylethanol on the CAC and PAC was both controlled by the physical adsorption, and the equilibrium adsorption capacity of CAC (391.2 mg/g) was 45.50% of that of PAC (859.8mg/g). Quasi primary equation can be used to describe the adsorption of β-phenylethanol on both types of activated carbon, i.e., the external transport resistance plays a major role in the adsorption process. The results of thermogravimetric analysis showed that the thermal stability of β-phenylethanol was obviously improved after the immobilization into activated carbon, accompanied with a higher temperature intervals for the release process and a decreased release rate. And the thermal stability of CAC loaded with β-phenylethanol was higher than that of PAC. Furthermore, the sustained release of β-phenylethanol from CAC and PAC was more consistent with the Korsmeyer-Peppas model and was dominated by Fick diffusion. The release rates of β-phenylethanol were 27.34% and 57.57% for CAC and PAC, respectively, under 35 days of storage at room temperature. The higher micropore ratio and lower mean pore width of CAC were responsible for the good stability and sustained release properties of immobilized β-phenylethanol.

Ceria Boosting on In Situ Nitrogen-Doped Graphene Oxide for Efficient Bifunctional ORR/OER Activity.

In the present work, a highly efficient and excellent electrocatalyst material for bifunctional oxygen reduction/evolution reaction (ORR/OER) was synthesized using the microwave-assisted hydrothermal method. In brief, ultrafine hexagonal cerium oxide (CeO2) nanoparticles were tailored on the layered surface of in situ nitrogen-doped graphene oxide (NGO) sheets. The nanocomposites exhibited a high anodic onset potential of 0.925 V vs. RHE for ORR activity and 1.2 V for OER activity with a very high current density in 0.5 M KOH. The influence of oxygen cluster on Ce3+/Ce4+ ion decoration on outward/inward in situ nitrogen-coupled GO enhanced the physicochemical properties of composites and in turn increased electron transferability. The microwave-assisted hydrothermal coupling technique provides a higher density, active sites on CeO2@NGO composites, and oxygen deficiency structures in ultrafine Ce-O particles and boosts higher charge transferability in the composites. It is believed that the physical states of Ce-N- C, Ce-C=O, and a higher amount of oxygen participation with ceria increase the density of composites that in turn increases the efficiency. N-doped graphene oxide promotes high current conduction and rapid electron transferability while reducing the external transport resistance in oxygen electrocatalysis by sufficient mass transfer through in-built channels. This study may provide insights into the knowledge of Ce-enabled bifunctional activity to guide the design of a robust catalyst for electrochemical performance.

Non-Isothermal Effectiveness Factor for Catalytic Particles with Non-Fickian Diffusion

Abstract In this note, the effects of the non-Fickian diffusion on the prediction of effectiveness factor in non-isothermal porous catalytic slab considering external transport resistances are studied. A Green’s function formulation is used to solve the fractional diffusion-reaction model assuming non-Fickian diffusion to describe the internal mass transport in the porous catalytic particle. Evaluation of the effectiveness factor considering linear and nonlinear reaction rates was developed under isothermal and non-isothermal conditions. In both cases, numerical simulations show the relation existent between the anomalous diffusion with the performance of the catalytic slabs.

Mn and Co Co-Substituted Fe3O4 Nanoparticles on Nitrogen-Doped Reduced Graphene Oxide for Oxygen Electrocatalysis in Alkaline Solution

A dispersion of Mn and Co co-substituted Fe3O4 (MCF, Mn:Co:Fe=1:1:1) nanoparticles on nitrogen-doped reduced graphene oxide (N-rGO) nanosheets was prepared by a hydrothermal method. When tested for oxygen electrocatalysis in alkaline solution, the nanoparticles displayed 80% of the oxygen reduction reaction (ORR) activity of a typical 20 wt% Pt/C catalyst (Sigma); and 61% of the oxygen evolution reaction (OER) activity of a 20 wt% RuO2/C catalyst. Extensive material characterizations by field-emission transmission electron microscopy (TEM), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), and inductively coupled plasma mass spectrometry (ICP-MS) were carried out to provide some understanding of the good electrochemical performance. The MCF catalyst has successfully integrated the ORR activity of manganese oxide, the OER activity of cobalt oxide; and the electronic conductivity of bulk Fe3O4 into an effective bifunctional catalyst; and its good contact with the N-rGO nanosheets also reduces the external transport resistance in oxygen electrocatalysis. Hence the MCF catalyst also delivered good performance in zinc-air full cell tests where they were used in the air electrode.

Mn and Co co-substituted Fe3O4nanoparticles on nitrogen-doped reduced graphene oxide for oxygen electrocatalysis in alkaline solution

A dispersion of Mn and Co co-substituted Fe3O4 (MCF, Mn : Co : Fe = 1 : 1: 1) nanoparticles on nitrogen-doped reduced graphene oxide (N-rGO) nanosheets was prepared by a hydrothermal method. This catalyst exhibited 80% of the oxygen reduction reaction (ORR) activity of a Sigma 20 wt% Pt/C catalyst; and 61% of the oxygen evolution reaction (OER) activity of a 20 wt% RuO2/C catalyst in alkaline solution. Extensive material characterizations by field-emission transmission electron microscopy (TEM), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) analysis, and inductively coupled plasma mass spectrometry (ICP-MS) were undertaken to suggest some possible reasons for the good electrochemical performance. The catalyst also delivered good performance in full zinc–air cell tests where it was used in the air electrode. The MCF catalyst has effectively combined the ORR activity of manganese oxide, the OER activity of cobalt oxide; and the electronic conductivity of bulk Fe3O4 into an integrated bifunctional catalytic system; and its good contact with the N-rGO nanosheets also reduces the external transport resistance in oxygen electrocatalysis.

Multiplicity analysis of a non-isothermal finite hollow cylindrical catalyst pellet

The paper examined the steady-state multiplicity of the porous, non-isothermal, finite hollow cylindrical catalyst pellet in the absence of external transport resistances. A numerical multigrid continuation technique with the preconditioned conjugate gradient squared as coarse grid solver was used. The continuation parameter is the reaction parameter (Thiele modulus). The effect of the other governing parameters (especially the geometric ratios) was analyzed. The numerical results obtained show that the finite hollow cylindrical catalyst pellet exhibits similar multiplicity patterns to the finite solid cylindrical catalyst pellet.

Hierarchical multi-scale model reduction in the simulation of catalytic converters

This paper presents a methodology for multi-scale modelling using pre-computed data for the small scales. By pre-computing the required data at the micro- and meso-scales and storing them in a look-up table, these small-scale effects can be captured in a macro-scale model that executes with practicable execution times. The methodology is presented in the context of modelling a washcoated monolith reactor for the catalytic combustion of methane using a detailed multistep mechanistic model. The modelling is illustrated as a sequence of steps of increasing model simplification. In the first instance, only the reaction rates are pre-computed. Then the washcoat diffusion is included using a 2D axisymmetric model with a washcoat of uniform thickness, then with a non-symmetrical channel with a washcoat of non-uniform thickness. It is shown how a simple 1D single channel model can accurately account for the presence of a non-uniform washcoat. Finally, the external transport resistance is included in the pre-computation step, and it is shown that a simple one dimensional pseudo-homogeneous single channel model can be used provided the effective average rates are appropriately calculated. Execution times are shown to decrease by several orders of magnitude at minimal loss of solution accuracy. The use of pre-computed data allows for the inclusion of complex heat and mass transfer phenomena, as well as complex kinetics in full scale converter models at relatively small computational cost. The implementation of look-up tables into full scale CFD models is described, and optimal strategies proposed.

Shrinking-core modeling of binary chromatographic breakthrough

Most chromatographic processes involve separation of two or more species, so development of a simple, accurate multicomponent chromatographic model can be valuable for improving process efficiency and yield. We consider the case of breakthrough chromatography, which has been considered in great depth for single-component modeling but to a much more limited degree for multicomponent breakthrough. We use the shrinking core model, which provides a reasonable approximation of particle uptake for proteins under strong binding conditions. Analytical column solutions for single-component systems are extended here to predict binary breakthrough chromatographic behavior for conditions under which the external transport resistance is negligible. Analytical results for the location and profile of displacement effects and expected breakthrough curves are derived for limiting cases. More generally, straightforward numerical results have also been obtained through simultaneous solution of a set of simple ordinary differential equations. Exploration of the model parameter space yields results consistent with theoretical expectations. Additionally, both analytical and numerical predictions compare favorably with experimental column breakthrough data for lysozyme–cytochrome c mixtures on the strong cation exchanger SP Sepharose FF. Especially significant is the ability of the model to predict experimentally observed displacement profiles of the more weakly adsorbed species (in this case cytochrome c). The ability to model displacement behavior using simple analytical and numerical techniques is a significant improvement over current methods.

Mass transport and thermodynamic analysis of PAHs in partitioning systems in the presence and absence of ultrasonication

AbstractTransport of PAHs from Desmopan polymers to methanol under various mixing conditions and in the presence of ultrasound was analyzed. PAH transport was influenced by external transport resistances; however, agitation greater than 800 rpm yielded PAH transport completely limited by internal resistances. Delivery rates of phenanthrene, fluoranthene, and pyrene with ultrasonication were faster than that under any mixing condition, suggesting enhanced internal transport properties. Ultrasound also induced increased concentrations of PAHs in solution at equilibrium. The model developed described PAH delivery under sonicated/non‐sonicated conditions, while quantifying diffusive and thermodynamic properties. Diffusivities with and without ultrasound decreased with permeant molecular size agreeing with coefficients determined for similar aromatic compounds in polymers. Partitioning coefficients under sonicated and non‐sonicated conditions conclusively differed from each other and decreased as a function of PAH molecular size. Quantitative structure‐property relationship data of PAHs yielded factors predicting thermodynamic and transport behaviors, with polarizability being the best descriptor. © 2010 American Institute of Chemical Engineers AIChE J, 2010

Multiplicity analysis of a nonisothermal finite cylindrical catalyst pellet

The paper examined the steady-state multiplicity behaviour of the porous, non-isothermal, finite cylindrical catalyst pellet in the absence of external transport resistances. A numerical multigrid continuation technique with the preconditioned conjugate gradient squared as coarse grid solver was used. The numerical methods proved to be efficient and reliable so that computations with fine grids (up to 129 × 129 grid points on the unit square) are easily performed. The key parameter of the investigation is the reaction parameter. The effect of the other governing parameters (especially the aspect ratio) was also analysed. An infinite number of steady states, with a scenario different from that usually used to explain this situation, were obtained at small values of the aspect ratio (the height of the cylinder is greater than the diameter of the cylinder).

Interfacial mass transport properties which control the migration of packaging constituents into foodstuffs

Interfacial mass transport properties, such as partition coefficients ( K), mass transfer coefficients ( h) and diffusion coefficients ( D) were estimated from controlled desorption kinetics at 40 °C, which would be realistic of extreme conditions of use of the packaging materials in contact with a liquid food. The experiments were carried out on formulated pieces of low density polyethylene (LDPE) with variable thicknesses (50, 100 and 150 μm) dispersed in ethanol, in controlled conditions of stirring, with Biot mass number between 5 and 10 3. The 3 transport properties for 8 homologous molecules ( n-alkanes and n-alcohols), 2 antioxidants and 2 fluorescent tracers were estimated from a set of 78 desorption kinetics. Concentrations in ethanol samples were measured by GC-FID. The uncertainty related to analytical errors was quantified by Monte-Carlo sampling consisting in adding an arbitrary white noise to results in the range of experimental errors. The physical interpretation of the external transport resistance is finally discussed.

Heat and mass transfer in multicylinder drying: Part II. Analysis of internal and external transport resistances

The present study investigates two models—two limiting cases—for the internal heat and mass transfer in a multicylinder dryer: the first model assumes that complete redistribution of heat and moisture in the thickness direction occurs instantaneously. The second model assumes that moisture transfer occurs only by vapor diffusion and that heat transfer takes place by conduction and condensation. The two models are written in dimensionless form, and applied for the same set of standard paper machine data. For basis weights below approximately 0.05 kg d.s./m 2 the results are so close that the first, simple model is sufficient. A higher limiting basis weight—approximately 0.16 kg d.s./m 2—was previously indicated by comparison of model predictions, assuming the simple model, to extensive sets of machine data from four different paper machines.

TRANSPORT IN BRANCHED SYSTEMS I: STEADY-STATE RESPONSE

Abstract Branched or fractal-like extended surfaces are commonly found in natural systems and in engineered systems such as heterogeneous catalysts to enhance the rates of heat or mass transfer, or chemical reaction. Simple models can be derived to simulate the effectiveness and efficiency of these structures and provide some speculation concerning transport limitations affecting the evolutionary design of natural branching structures. Though the surface area of branching structures increases with each successive generation, their efficiency and effectiveness quickly approach asymptotic values. The transport limitations inherent in the structures render subsequent branching ineffective. Such limitations, characterized by environmentally driven, external transport resistances, may affect branching patterns found in plant root systems, mammalian motoneurons, and animal circulatory systems

DEPENDENCE OF THE MULTIPLICITY FEATURES OF AN ISOTHERMAL CATALYTIC REACTION ON EXTERNAL AND INTERNAL TRANSPORT RESISTANCES

A mathematical model (Robin) which accounts for both internal and external transport resistances is used to determine the multiplicity features of a porous catalytic pellet in which an isothermal Langmuir-Hinshelwood reaction occurs. At most three solutions exist for a slab, but an arbitrarily large number of solutions can be found for an infinite cylinder or a spherical pellet. The maximal number of solutions for any finite external mass transfer resistance is bounded between that existing for a model which ignores the external mass transfer resistance and one which ignores intra-particle concentration gradients. The approximate shape of the cross section of the bifurcation set and of the uniqueness boundary of the Robin model can be estimated from the knowledge of the multiplicity features of three simplified (lumped, Dirichlet and Neumann) models, each containing one less parameter.

Integral method of analysis for chemical reaction in a nonisothermal finite cylindrical catalyst pellet-I. Dirichlet problem

An integral equation method is developed to solve the problem of diffusion and reaction in a porous nonisothermal finite cylindrical pellet in the absence of external transport resistances. Green's function method is applied to transform the partial differential equation for concentration into a Fredholm integral equation. A modified Green's function method is developed to accelerate the convergence of the partial eigen series by an order of two while exploiting the symmetry properties of the classical Green's function formulation. The resulting integral equation is solved by a Newton-Kantorovich iteration scheme to obtain effectiveness factors for various nonlinear reaction rate forms.

AN ASYMPTOTIC SOLUTION OF THE NONISOTHERMAL CATALYST PELLET PROBLEM FOR LARGE REACTION RATES AND LARGE ACTIVATION ENERGIES

Abstract The problem of diffusion and chemical reaction in a non-isothermal catalyst pellet is considered for the case of essentially complete reaction (large Thiele modulus). Limiting solutions which are uniformly valid for either large activation energy or small heat of reaction are given, for both endothermic and exothermic reactions. The analytical solutions, which have a very simple form, apply to arbitrary pellet geometries, arbitrary reaction kinetics and external transport resistance. The results could also be applied to more complicated situations involving variable properties, pre-exponential temperature dependence and volume-change due to reaction. Extensive comparison with numerical solutions indicates extremely good agreement, not only for large activation energies but over the entire ranges 0 < β <.5 and 5 < γ < 40 for both first and second order kinetics. For sixty numerical comparisons of limiting effectiveness factors, the maximum error was 1.8%; in only two of these cases did the error exceed 1%. Comparison is also made with results due to Petersen which are based on a linearization of the Arrhenius expression.

Modelling of non-catalytic gas—solid reactions—I. Transient analysis of the particle—pellet model

A transient analysis of the problem of non-catalytic gas—solid reaction based on the particle—pellet model, which considers the particulate nature of the pellet and includes the external transport resistances, is presented. The method of solution of the resulting non-linear partial differential equations is based on the orthogonal collocation technique. The transient model has been compared with the pseudo-steady analysis of the problem. The effect of various parameters on the temperature profiles in the pellet and the conversion of the solid reactant has been discussed.

Sensitivity analysis for a chemical reaction in a porous catalyst with external heat and mass transfer resistance

Using variational techniques, a computationally efficient procedure is developed for determining the sensitivity of the observed reaction rate in a porous catalyst with external transport resistances. Derivatives of the observed rate with respect to bulk fluid conditions or any other parameters in the mathematical model of the catalyst may be easily calculated for slab, cylindrical, or spherical catalyst geometry.