Search Results (13)

LDPE was crosslinked with novel dynamic or conventional crosslinking agents during melt processing. Both crosslinkers were synthesized by the esterification of Thiele’s acid or adipic acid with 4-hydroxy-TEMPO. ¹H-NMR showed that a temperature of 170 °C and a reaction time of 24 min are required for a successful crosslinking. The concentrations of crosslinking agents were 1.45, 2.9, and 5.8 mol%. Conventionally crosslinked LDPEs show a decrease in soluble content in hot xylene with increased crosslinker concentrations, while dynamically crosslinked LDPEs show no change after thermal treatment, indicating the scission of dynamic crosslinks. The rheology of both crosslinked LDPEs at 130 °C shows that the stress release is slower than that of neat LDPE, confirming crosslinking, while at 170 °C a shift in the stress release and also a shift in the flow properties of dynamically crosslinked LDPE towards those of neat LDPE are observed, both indicating the cleavage of dynamic crosslinks. Compared to neat LDPE, the mechanical properties of both crosslinked LDPEs show an increase in Young’s modulus and tensile strength and a decrease in elongation and creep when the concentration of both crosslinkers is increased. By increasing the processing temperature to 170 °C, the crystallinity index decreases, leading to a rather small improvement in the mechanical properties. Full article

The biology literature addresses two puzzles: (i) the increase in specific metabolic rate of organs (SOrMR, W/kg of organ) with a decrease in body mass (M_B) of biological species (BS), and (ii) how the organs recognize they are in a smaller or larger body and adjust metabolic rates of the body (${\dot{q}}_B$) accordingly. These puzzles were answered in the author’s earlier work by linking the field of oxygen-deficient combustion (ODC) of fuel particle clouds (FC) in engineering to the field of oxygen-deficient metabolism (ODM) of cell clouds (CC) in biology. The current work extends the ODM hypothesis to predict the whole-body metabolic rates of 114 BS and demonstrates Kleiber’s power law {${\dot{q}}_B = a {M_B}^b$}. The methodology is based on the postulate of Lindstedt and Schaeffer that “150 ton blue whale. and the 2 g Etruscan shrew.. share the same.. biochemical pathways” and involve the following steps: (i) extension of the effectiveness factor relation, expressed in terms of the dimensionless group number G (=Thiele Modulus²), from engineering to the organs of BS, (ii) modification of G as G_OD for the biology literature as a measure of oxygen deficiency (OD), (iii) collection of data on organ and body masses of 116 species and prediction of SOrMR_k of organ k of 114 BS (from 0.0076 kg Shrew to 6650 kg elephant) using only the SOrMR_k and organ masses of two reference species (Shrew, 0.0076 kg: RS-1; Rat Wistar, 0.390 kg: RS-2), (iv) estimation of ${\dot{q}}_B$ for 114 species versus M_B and demonstration of Kleiber’s law with a = 2.962, b = 0.747, and (v) extension of ODM to predict the allometric law for maximal metabolic rate (under exercise, {${\dot{q}}_{B,MMR} = a_{MMR} {M_B}^{b_{MMR}}$}) and validate the approach for MMR by comparing b_MMR with the literature data. A method of detecting hypoxic condition of an organ as a precursor to cancer is suggested for use by medical personnel Full article

A steady-state tubular reactor for total oxidation reaction under typical industrial conditions in the removal of volatile organic components (VOC) is described using a one-dimensional heterogeneous reactor model with intraparticle diffusion, using a fully developed Langmuir–Hinshelwood reaction rate expression. The effectiveness factor, accounting for these intraparticle diffusion limitations, is calculated with a generalized Thiele modulus. The actual inclusion of this factor shows that higher operational reactor temperatures can be possible, since this diffusion limitation restricts the heat production inside the catalyst particle. Special attention is given to the outlet concentration of propane, taken as the model VOC, and runaway criteria, reported in the literature, are evaluated. Furthermore, the well-known Barkelew criterion (to evaluate runaway for exothermic reactions) is implemented for practical and safe reactor design. This work identifies that the critical couples populating the Barkelew diagram are positioned lower (up to a 50% difference, compared to Barkelew’s original report), so that operation of the reactor under higher hydrocarbon molar inlet fractions is possible while maintaining safe performance. Full article

Approximate models are a fast and most often precise tool for determining the effectiveness factor for heterogeneous catalysis processes that are realized in the real world. They are also frequently applied as robust transient models describing the work of a single catalyst pellet or as a part of a more complex model, for example, a reactor model, where mass balances for the gas phase and solid phase are necessary. So far, approximate models for diffusion and reaction processes have been presented for processes described by a single balance equation. In the present work, approximate models without the mentioned limitation are presented and discussed. In addition, simple rules are shown for the development of other complex approximate models without tedious derivation in the complex domain. The formulas considered in this work are typical long-time approximations of the transient process. The accuracy is good, especially in the range of small and intermediate Thiele modulus values. Full article

Ion exchange resins have many industrial applications, namely as sorbents and catalysts. In solid-catalyzed reactions, intraparticle reaction-diffusion competition is generally described by effectiveness factors calculated numerically or analytically in the case of isothermal particles and simple rate laws. Although robust, numerical calculations can be time-consuming, and convergence is not always guaranteed and lacks the flexibility of user-friendly equations. In this work, analytical equations for effectiveness factors of reversible reactions derived from the general scheme $A+B\rightleftharpoons C+D$ are developed and numerically validated. These effectiveness factors are analytically expressed in terms of an irreversible $n^{\mathrm{t}\mathrm{h}}$ order Thiele modulus (specifically written for the  $n^{\mathrm{t}\mathrm{h}}$ order forward reaction), the thermodynamic equilibrium constant, the ratios of effective diffusivities, and the ratios of surface concentrations. The application of such analytical equations is illustrated for two liquid phase reactions catalyzed by Amberlyst-15, specifically the synthesis of ethyl acetate and acetaldehyde dimethyl acetal. For both reactions, the prediction of the concentration profiles in isothermal batch reactors achieved errors between 1.13% and 3.38% for six distinct experimental conditions. Finally, the impact of non-ideal behavior upon the multicomponent effective diffusivities, subsequently conveyed to the effectiveness factors, is enlightened. Full article

The modeling and simulation of the catalytic dehydrogenation process of cyclohexanol in a fixed-bed catalytic reactor is presented, leading to finding the relationship between the effectiveness factor, the Thiele modulus, and the Weisz–Prater modulus of the catalyst particles with respect to their axial and radial position, for which the external conditions of concentration and temperature around each particle were previously obtained by applying the material and energy balances in the catalyst bed considering a two-dimensional pseudo-homogeneous model with radial diffusion. Subsequently, the material balances are established in terms of the molar flux density and conversion, the energy balance in terms of the heat flux density, Fick’s law, Fourier’s law, and the differential form of the effectiveness factor non-isothermal for each particle chosen based on the proposed meshing. The Thiele modulus calculated for most of the points is between 0.8 and 0.25, with a tendency towards the lower limit, and the theoretical values established as the limit for the Thiele modulus fluctuate between $0.4<T_h<4$. Therefore, the effectiveness factor analyzed is between 1 and $1/T_h$; this indicates that both the reaction speed as well as the diffusion speed within the particle have an influence on the intraparticle process, which is confirmed by the calculation of the Weisz–Prater modulus whose values are not $<<$1 nor $>>$1. The results obtained are subjected to a statistical test leading to analyzing whether there are significant differences both in the Thiele modulus, as well as in the effectiveness factor with respect to the radius and length of the reactor. It has been determined that there are no significant differences between the effectiveness factor with respect to the radius of the reactor; however, according to the analysis of variance, there are significant differences in the effectiveness factor with respect to length and, likewise, there are significant differences in the Thiele modulus and the Weisz–Prater modulus with respect to radius and length. Full article

The theoretical model for a packed porous catalytic particle of the slab, cylindrical, and spherical geometries shape in fixed-bed electrochemical reactors is discussed. These particles have internal mass concentration and temperature gradients in endothermic or exothermic reactions. The model is based on a nonlinear reaction–diffusion equation containing a nonlinear term with an exponential relationship between intrinsic reaction rate and temperature. The porous catalyst particle’s concentration is obtained by solving the nonlinear equation using Akbari-Ganji’s method. A simple and closed-form analytical expression of the effectiveness factor for slab, cylindrical, and spherical geometries was also reported for all values of Thiele modulus, activation energy, and heat reaction. The accordance with results of a reliable numerical method shows the good accuracy that their approximate solution yields. Full article

Hierarchical crystals with short diffusion path, conventional microcrystals and nanocrystals of ZSM-5 zeolites were used for biodiesel production from waste frying oils and were assessed for their catalytic activity in regard to their pore structure and acidic properties. Produced zeolites were characterized using XRD, nitrogen adsorption–desorption, SEM, TEM, X-ray fluorescence, and FTIR. Pore size effect on molecular diffusion limitation was assessed by Thiele modulus calculations and turnover frequencies (TOF) were used to discuss the correlation between acidic character and catalytic performance of the zeolites. Owing to the enhanced accessibility and mass transfer of triglycerides and free fatty acids to the elemental active zeolitic structure, the catalytic performance of nanosponge and nanosheet hierarchical zeolites was the highest. A maximum yield of 48.29% was reached for the transesterification of waste frying oils (WFOs) using HZSM-5 nanosheets at 12:1 methanol to WFOs molar ratio, 180 °C, 10 wt % catalyst loading, and 4 h reaction time. Although HZSM-5 nanosponges achieved high conversions, these more hydrophilic zeolites did not function according to their entire acidic strength in comparison to HZSM-5 nanosheets. NSh-HZSM5 catalytic performance was still high after 4 consecutive cycles as a result of the zeolite regeneration. Full article

A diffusion-reaction coupled model was presented to investigate the effects of multiscale pore structure characteristics on gas sensing properties. A series of CoTiO₃ powders with different pore size distributions were fabricated by sol-gel method. Experimental results on cobalt titanate thick films show that a well-defined multiscale pore structure is particularly desired for the improvement of sensing performance, instead of just increasing the specific surface area. The theoretical responses of sensing elements with different pore size distributions were derived and compared with experimental data on CoTiO₃ sensors exposed to ethanol. The calculated sensitivities considering the influence of pore size changes were also found to be in agreement with the experimental results. A dimensionless Thiele modulus Th was introduced for assessing the critical point corresponding to the transformation from surface reaction-controlled sensitivity into diffusion-controlled sensitivity. Full article

A novel methodology to estimate the effectiveness factor (EF) of an immobilized enzyme catalyst is proposed here. The methodology consists of the determination of the productivity of both the immobilized enzyme catalyst and its corresponding soluble enzyme, plotted as a function of the reaction conversion. The ratio of these productivities corresponds to the EF estimator of the catalyst. Conversion curves were simulated in a batch reactor with immobilized enzyme and soluble enzyme for different values of the S₀/K_M ratio and Thiele modulus (Φ) to demonstrate this hypothesis. Two different reaction orders were tested: first-order kinetic and Michaelis–Menten-based kinetic with product inhibition. The results showed that the ratio of productivities between the immobilized and soluble enzymes followed the behavior profile presented by the EF with satisfactory agreement. This simple methodology to estimate the EF is based on routine conversion experiments, thus avoiding the exhaustive kinetic and mass transfer characterization of the immobilized enzyme catalyst. Full article

A novel approximate solution for catalyst effectiveness factors is presented. It is based on carefully selected approximate reaction rate profiles, instead of typical assumption of composition profiles inside the catalyst. This formulation allows analytical solution of the approximate model, leading to a very simple iterative solution for effectiveness factor for general nonlinear reaction stoichiometry and arbitrary catalyst particle shape. The same model can be used with all practical Thiele modulus values, including multicomponent systems with inert compounds. Furthermore, the correct formulation of the underlying physical model equation is discussed. It is shown that an incorrect but often-used model formulation where convective mass transfer has been neglected may lead to much higher errors than the present approximation. Even with a correctly formulated physical model, rigorous discretization of the catalyst particle volume may have unexpectedly high numerical errors, even exceeding those with the present approximate solution. The proposed approximate solution was tested with a number of examples. The first was an equimolar reaction with first order kinetics, for which analytical solutions are available for the standard catalyst particle geometries (slab, long cylinder, and sphere). Then, the method was tested with a second order reaction in three cases: (1) with one pure reactant, (2) with inert present, and (3) with two reactants and non-stoichiometric surface concentrations. Finally, the method was tested with an industrially relevant catalytic toluene hydrogenation including Maxwell-Stefan formulation for the diffusion fluxes. In all the tested systems, the results were practically identical when compared to the analytical solutions or rigorous finite volume solution of the same problem. Full article

In the aftermath of oil spills in the sea, clouds of droplets drift into the seawater column and are carried away by sea currents. The fate of the drifting droplets is determined by natural attenuation processes, mainly dissolution into the seawater and biodegradation by oil-degrading microbial communities. Specifically, microbes have developed three fundamental strategies for accessing and assimilating oily substrates. Depending on their affinity for the oily phase and ability to proliferate in multicellular structures, microbes might either attach to the oil surface and directly uptake compounds from the oily phase, or grow suspended in the aqueous phase consuming solubilized oil, or form three-dimensional biofilms over the oil–water interface. In this work, a compound particle model that accounts for all three microbial strategies is developed for the biodegradation of solitary oil microdroplets moving through a water column. Under a set of educated hypotheses, the hydrodynamics and solute transport problems are amenable to analytical solutions and a closed-form correlation is established for the overall dissolution rate as a function of the Thiele modulus, the Biot number and other key parameters. Moreover, two coupled ordinary differential equations are formulated for the evolution of the particle size and used to investigate the impact of the dissolution and biodegradation processes on the droplet shrinking rate. Full article

Ni- and Cu/alumina powders were prepared and characterized by X-ray diffraction (XRD), scanning electronic microscope (SEM), and N₂ physisorption isotherms were also determined. The Ni/Al₂O₃ sample reveled agglomerated (1 μm) of nanoparticles of Ni (30–80 nm) however, NiO particles were also identified, probably for the low temperature during the H₂ reduction treatment (350 °C), the Cu/Al₂O₃ sample presented agglomerates (1–1.5 μm) of nanoparticles (70–150 nm), but only of pure copper. Both surface morphologies were different, but resulted in mesoporous material, with a higher specificity for the Ni sample. The surfaces were used in a new proposal for producing copper and nickel phthalocyanines using a parallel-plate reactor. Phthalonitrile was used and metallic particles were deposited on alumina in ethanol solution with CH₃ONa at low temperatures; ≤60 °C. The mass-transfer was evaluated in reaction testing with a recent three-resistance model. The kinetics were studied with a Langmuir-Hinshelwood model. The activation energy and Thiele modulus revealed a slow surface reaction. The nickel sample was the most active, influenced by the NiO morphology and phthalonitrile adsorption. Full article