On the influence of particle shape and process conditions in the pressure drop and hydrodynamics in a wall-effect fixed bed

A low tube-to-particle diameter ratio (d_t/d_e,p) fixed bed, packed with spherical and nonspherical catalyst supports, was used to investigate pressure drop at varying temperature (298–673?K) and inlet pressure (245–294?kPa). The d_t/d_e,p ranged from 3 to 6, namely, a large wall-effect fixed bed, with an average void fraction between 0.38 and 0.61. These conditions pertain to multitubular fixed-bed reactors used for exothermic reactions. The pressure drop was notably influenced by the particle size and morphology as well as temperature. The use of particles with d_t/d_e,p?0.55) appeared suitable for pressure drop control. The fluid velocity profiles were calculated by applying the Navier–Stokes–Darcy–Forchheimer equation computing the respective permeability parameters with refitted state-of-the-art pressure drop correlations. The fluid flow exhibited different velocity zones across the fixed bed, the highest velocity zone being located near the reactor wall. The axial velocity component was influenced by the catalyst morphology, as well as temperature and inlet pressure.     

Contribution of interferometry and mechanical parameters in evaluating molecular orientation for drawn polyester

Mechanical and structural parameters related to the optical properties of polyester (PET) (woollen type) fibres drawn at room temperature have been investigated. The changes in the strain were evaluated to obtain the molecular orientation factors 〈P₂(cos θ)〉 and 〈P₄(cos θ)〉. From the optical orientation, the values of f₂(θ), f₄(θ) and f₆(θ) orientation parameters were calculated. The structure and properties of oriented PET have been studied in the light of the rubber elasticity theory. The dielectric constant, magnetic susceptibility, number N′ of chains between crosslinks per unit volume, optical configuration parameter and the segment anisotropy, were among the calculated parameters. The results of the extension were used to calculate the shrinkage factor. Relationships between the calculated parameters and the draw ratios, together with micro-interferograms, are given for illustration. The present study throws light on how the applied stress changes the molecular orientation factors and the structural parameters. © 1999 Society of Chemical Industry     

Applications of Sequentially Estimating the Mean in a Normal Distribution Having Equal Mean and Variance

Abstract

We suppose that we have at our disposal a sequence of independent observations from a N(θ, θ) distribution where θ(>0) is an unknown parameter. Such a model will make good sense to approximate a Poisson(θ) distribution, especially when θ(>0) is moderately large. The Fisher-information contained in the sample mean, the sample variance, and the MLE are included (Appendix A). The derivation of the UMVUE of θ and some remarks regarding computational complexities in numerically evaluating its expression, even for small fixed-sample-size n, are also included (Appendix B). Assuming the availability of a lower bound θ _L (>0) for θ, both purely sequential and two-stage bounded risk methodologies are developed for estimating θ. We have considered the analogs of fixed-sample-size MLE, sample mean, sample median, sample variance, and the UMVUE. First-order asymptotic properties of both purely sequential as well as two-stage sample sizes and the associated risk-bound for an analog of the MLE have been found. Extensive investigations based on computer-simulations have been carried out and the previously stated estimators of θ are compared with one another. The effect of the ratio θ _L /θ on the pilot sample size is critically examined. Overall, we have found that an analog of the fixed-sample-size MLE performs most satisfactorily. In the end, both proposed methodologies are successfully implemented to investigate how these work in two practical situations with the help of real datasets. They show that these methodologies stay fairly robust under mild departures from normality.     

Adsorbed states of K on the diamond (100)(2×1) surface

The adsorbed states of K on the C(100)(2×1) surface have been studied by electron energy loss spectroscopy (EELS), work function change (Δφ) measurement and thermal desorption spectroscopy (TDS). In the region where the K coverage is less than one-half of a monolayer (θ_K≤0.5), a loss is observed from ∼1.2 eV (θ_K=0.2) to 1.0 eV (θ_K=0.5); the work function decreases upon K adsorption until reaching a shallow minimum of Δφ=−3.35 eV at θ_K=∼0.5; and a desorption peak (β) is observed from ∼825 K (θ_K=0.05) to 525 K (θ_K=0.5). These results indicate that the K–substrate bond is highly polarized; the 1.2 eV loss is attributed to the electronic transition from the bonding to antibonding states formed at the K–substrate interface. In the region between θ_K=0.5 and 1, two losses are observed at 0.7 and 1.4 eV (θ_K=0.6); there is only a small increase of the work function; and a desorption peak (α) is observed in addition to the β peak. These results indicate that the K regains its electron and becomes, essentially, neutral. The 1.4-eV loss is ascribed to the transition from the 4s to 4p states of K. The origin of the 0.7-eV loss is discussed. The Δφ and TDS results are analyzed by the depolarization model.     

The Rheology of Wetting By Polymer Melts

Theoretically, the rate of capillary penetration of a polymer melt into a slit, a model for a surface irregularity, has been shown to depend on γcosθ/η) where γ refers to the surface tension of the liquid, η its viscosity and θ a time-dependent contact angle. Analytical expressions relating the depth of penetration with time have been experimentally verified by observations of the penetration of molten polyethylene and poly-(ethylene-vinyl acetate) into aluminum channels. Values of η, calculated from the observed data, agree closely with independent determinations of this material parameter. A theoretical treatment has also been developed which describes the velocity of spreading of a liquid drop over a flat surface. Flow equations for the flow of free films were adapted for this purpose. The spreading velocity is predicted to depend on the product of three factors (1) a scaling factor, (γ/η1R_o), where R_o is the initial radius of curvature, (2) cosθ_∞. (l-cosθ/cosθ_∞) where θ_∞ refers to the equilibrium value of θ, and (3) geometric terms. After demonstrating that a drop of molten polymer may be treated as a spherical cap, the predicted dependence of spreading rate on drop size, cosθ_∞ (nature of the substrate) and the scaling factor was experimentally verified. Some discrepancies noted at long times and high temperatures are discussed.     

Modeling solvent extraction of vegetable oil in a packed bed

A one-dimensional model was developed for solvent extraction of oil from a packed bed of oil-bearing vegetable materials. The equilibrium relationship between the residual oil content of marc and oil concentration of stagnant miscella in pores of the bed material was generated through experiments with rice bran and hexane. The nondimensional parameters recognized from the model describing extraction were initial Reynolds number (Re_i), initial Schmidt number (Sc_i), bed void fraction (ε_b), particle porosity (ε_p), ratio of bed diameter to particle diameter (D_t/d_p), ratio of bed depth to bed diameter (L/D_t), ratio of particle surface area to bed cross-section (a_pAL/A=a_pL), and recycle of solvent and equilibrium distribution coefficient (EDC). For reducing the time required to extract to the same residual oil content of marc, higher values of Re_i, ε_b, and a_pL were beneficial, whereas higher values of Sc_i, ε_p, D_t/d_p, L/D_t, and EDC were detrimental.     

Mass Transfer Characteristics during the Removal of Dissolved Heavy Metals from Waste Solutions in Gas Sparged Fluidized Beds of Ion Exchange Resins

The paper presents experimental results concerning the removal of cupric ions from a simulated wastewater effluent consisting of copper sulphate solution in a gas sparged fluidized bed of cation exchange resin. Variables investigated were: superficial gas velocity, particle diameter, bed height and the physical properties of the solution (adding glycerol). These variables were studied with respect to their effect on the solid-liquid mass transfer coefficient. The coefficient was found to increase with increasing superficial gas velocity. Increasing both particle diameter and bed height were found to reduce the mass transfer coefficient. The experimental data can be correlated by the equation J = 0.68 (Fr Re )^–0.143 (d_p/d)^–0.62 (d_p/L)^0.55valid for the following conditions: 1430 < Sc < 2488; 0.017 < Fr Re < 1.41; 6.33 × 10^–3 < d_p/d < 0.021 and 9.5 × 10^–3 < d_p / L < 0.125.     

Zur unverträglichkeit von polymergemischen. 1. Lichtstreuungsmessungen am system polystyrol/polymethylmethacrylat/benzol

A polystyrene (PS) with M?_w = 9,7 · 10⁴ was investigated by means of light scattering in the isorefractive polymer/solvens-mixture polymethylmethacrylate (PMMA)/benzene. It was found, that the second osmotic virial coefficient A₂ of PS was strongly dependent on the average viscosimetric molecular weight M?_v and on the concentration of PMMA, but scarcely on the temperature in the range of 20°C to 60°C. The θ-Point, where A₂ is zero, was independent of the temperature within experimental error. By defining the PMMA concentration at the θ-Point as c_θ, and by reducing the measured PMMA concentration c to c/c_θ, an unequivocal relation was obtained between A₂ and c/c_θ, which is independent of molecular weight and molecular weight distribution of PMMA. PS shows a high second virial coefficient in dimer and trimer MMA as well as in non-hydrogenated and hydrogenated MMA. The investigated PS constitutes a θ-System in PMMA of a degree of polymerisation of P?_w, ～ 17without the use of benzene.     

Electrochemical wall mass transfer in liquid particulate systems

Ionic mass transfer coefficients between the wall of a 2.081 inch tube and liquid fluidized beds of lead glass, soda glass and lucite spheres have been measured using the diffusion-controlled reduction of ferricyanide ion at a nickel cathode for porosities 0.90 to 0.45 and Schmidt numbers 580 to 2100. The developed fluidization mass transfer coefficient for 41 < D_T/d_p < 105 were correlated by i_D E = 0.274 Re_H^?0.38 for 10 < Re_H <1600 and by J_D E = 0.455 Re_H^?0.44 for 16.7 < D_T/d_p < 27 and 50 < Re_H < 3500. Re_H is the hydraulic Reynolds number = d_H up/μ_E and d_H is D_T E/[1 + (3/2) ((1–E)) (D_T/d_p)). The distinct effect of D_T/d_p ratio is attributed to wall effects and the non-particulate behaviour of the fluidized bed for D_T/d_p < 27. Measurements in the open pipe and packed bed agreed very well with literature values. The packed bed gives highest mass transfer coefficients at given Re_H.     

State of adsorption and coverage by overpotential-deposited H in the H2 evolution reaction at Au and Pt

By means of potential decay measurements using a digital data acquisition and computer processing system, accurate values of overpotential decay rates, dη/dt, may be obtained from which the pseudocapacitance and coverage behaviour of overpotential-deposited (OPD) H species in the cathodic H₂ evolution reaction (HER) at Au electrodes may be quantitatively derived as a function of η. The behaviour of the HER at Au is of interest in that an unusual Tafel slope value of 2.3RT/F is exhibited in acid solution while the value of alkaline solutions is the more familiar value of ca 2.32RT/F.Analysis of the overpotential relaxation behaviour on open-circuit, following interruption of cathodic polarization currents, gives an almost constant and small interfacial capacitance corresponding to a double-layer capacitance. Steady-state OPD H coverage (θ) is hence quite small (θ_H<0.3%). The Tafel slope value of 2.3RT/F requires, however, a potential-dependent H coverage determined by an H electrosorption step almost at equilibrium but with θ_H small. The rate-determining step is suggested to be surface diffusion to preferred desorption sites.Comparative results are presented for the HER at activated Pt where, contrary to the behaviour of Au, a large pseudocapacitance for OPD H is derived that may be associated with some surface hydride formation, the possibility of readsorption of H from a boundary layer supersaturated with H₂ having been minimized by electrode rotation at a sufficiently high rate of 3600 rpm.     

A NON-DRIVING-FORCE APPROXIMATION FOR INTRAPARTICLE DIFFUSION IN CYCLIC ADSORPTION AND DESORPTION WITH SHORT CYCLE TIMES

Simple approximations for intraparticle diffusion rate are obtained for cyclic adsorption-desorption subject to step changes at a cyclic steady state. For slow cycles (θ_c > 0.1), a linear driving-force approximation with a coefficient π² gives good prediction whereas for fast cycles (θ_c ≤ 0.l) a non-driving-force approximation with a constant coefficient (independent of cycle time θ_c) gives satisfactory results. The constant coefficient is an advantage of the non-driving-force approximation over the linear driving-force approximation in which the coefficient increases sharply with decreasing cycle time.     

A Numerical Analysis of Surface Diffusion in a Binary Adsorbed Film

Abstract

Based on the assumptions that the adsorption of a binary gas mixture may be described by Langmuir isotherms and that the rate of diffusion into the interior of the adsorbent is proportional to the gradient in chemical potential, equations are developed to describe the adsorption of a binary mixture by a slab and by a sphere. The equations describing the concentration changes of each component are coupled nonlinear second-order partial differentials and were solved numerically for the following boundary conditions (normalized concentrations θ of the components at the surface): θ_A:θ_B=0.05:0.90, 0.05:0.05, 0.475:0.475, and 0.875:0.095 and ratios of diffusivities, L _A/L _B=2, 10, and 200. Profiles of concentration against distance into a slab or sphere and also curves of total uptake against time (all in dimensionless form) were obtained. The distinctive feature of the results is that the component of higher diffusivity advances ahead of the second component and tends to attain temporary local concentrations much higher than the equilibrium values at the boundary. Consequently, the total uptake of the more-mobile component may pass through a maximum. These effects are most pronounced when the difference in diffusivities is large, when the equilibrium concentration of the component of higher diffusivity is small, and when the total equilibrium concentration of the two components is large. The calculations were applied to previously reported results of the adsorption of nitrogen-methane mixtures by zeolite A and were found to give reasonable correlations between the behavior of mixtures and that of the individual pure components. In the case of near saturation (θ_A+θ_B → 1 at the boundary), the fit with experiment is particularly sensitive to the exact value of (1 ? θ_A ? θ_B).     

HYDRODYNAMICS AND GAS-LIQUID-SOLID INTERFACIAL PARAMETERS OF CO-CURRENT DOWNWARD TWO-PHASE FLOW IN TRICKLE-BED REACTORS†

Design of trickle-fixed bed reactors requires knowledge of the hydrodynamics of two-phase co-current downward flow through fixed porous catalytic media and interfacial parameters. Unfortunately, most of the published papers deal exclusively with the hydrodynamics of an air-water system and the determination of gas-liquid-solid interfacial parameters in highly ionic solutions. In this paper, we present some experimental results on the hydrodynamics, pressure drop, liquid holdup, different flow patterns, gas-liquid interfacial areas and liquid-side mass transfer coefficients for organic non-viscous and viscous liquids and liquid-solid mass transfer coefficients with different packings: glass beads (d_p = 1.16 × 10^?3 m and 4 × 10^?3 m), spherical catalyst (d_p = 2.4 × 10^?3 m) and glass Raschig rings (d_p = 6.48 × 10^?3 m). Comparison between our values and correlations in the literature will be discussed.     

Solidification of a low peclet number fluid flow in a round pipe with the boundary condition of the third kind

This paper presents a theoretical investigation on the solidification of a low Peclet number fluid flow in the thermal entrance region of a round pipe. The velocity is assumed laminar and fully developed throughout the pipe and the fluid temperature is taken to be uniform at X = ?∞. The pipe wall is adiabatic at X ≤ 0 and is cooled convectively at X ≥ 0. The exact solution in the liquid and solid phase are obtained by using the method of separation of variables and constructing two sets of orthonormal functions from the nonorthogonal eigenfunctious at X = ± 0. The solutions including temperature distributions, liquid-solid interfaces and Nusselt numbers for the parameters, Bi = 20, 4, 0.4, 0.04, Pe = 1, 3, 5, 10, 20, 30, ∞ and the superheat ratios, ξ = (1 ? θ_f)/θ_f, θ_f= 0.1, 0.2, …, 0.9 are presented in this paper. The length of ice-free zone x_f corresponding to Pe = ∞ are in excellent agreement with the existing solution.     

Evolution of the Physical Properties of FeCl3 Filled Polystyrene Films

ABSTRACT

The present work investigates the effect of various filling levels (FLs) of FeCl₃ on the structure and physical properties of polystyrene (PS) films. X-ray diffraction scans revealed two main peaks, the amorphous and the polymerization peaks. The infrared transmission spectra depicted the main PS characterizing peaks. The direct current (dc) electrical conduction was attributed to the interpolaron charge carrier hopping. The temperature dependence of dc magnetic susceptibility exhibited Curie–Weiss behavior. The positive values of the paramagnetic Curie temperature (θ_p) indicate the predominance of a ferromagnetic exchange interaction between the magnetic centers at low temperatures, whereas the negative value of θ_p at 9% FL suggests the existence of an antiferromagnetic exchange interaction. The electron spin resonance (ESR) investigations imply the presence of isolated and aggregated Fe⁺³ ions at intermediate and higher FLs, respectively, in the polymeric matrix.     

Interactions of CO and NO with the perovskite-type oxide larho3

Some aspects of the interactions of CO and NO with LaRhO₃ have been studied. The reduction of this oxide with CO occurs where the contracting sphere model is of perovskite structure stable up to a concentration of anion vacancies of ca. 2e^? per molecule. By reduction of LaRhO₃ at 817 K, rhodium was obtained, highly dispersed on a matrix of La₂O_3. After a reduction-oxidation cycle at 871 K the particle size of the perovskite decreased drastically. The activation energy of the reduction (67 kJ mol^?1) was significantly lower than that of other LaMO₃ oxides of group-VIII metals. Coverages of CO(θ_CO) and NO(θ_NO) at room temperature were lower than 3%, θ_NO being substantially higher than θ_CO. The reversibly adsorbed fractions of CO and NO underwent a remarkable decrease after preadsorbing NO and CO, respectively. This competitive adsorption is assumed to be associated with the adsorption of CO and NO on metallic sites. NO preadsorption inhibited the total adsorption of CO more severely than the reverse, indicating that NO is bound more strongly than CO to the LaRhO₃ surface.     

Effects of pressure and type of gas on particle-particle interaction and the consequences for gas—solid fluidization behaviour

The fluidization behaviour of cracking catalyst has been studied up to pressures of 15 bar with different fluidization gases (Ar, N₂, H₂). A number of parameters of both the homogeneous and heterogeneous fluidized bed has been examined experimentally.The experimental results reveal that the minimum fluidization velocity (U_mf) is independent of the pressure. The bubble point velocity (U_bp) and the maximum bed expansion (H_bp) at this velocity increase with increasing pressure. This also holds for the dense phase voidage (ε_d) and the dense phase gas velocity (U_d) in the bubbling bed. The bubble size decreases drastically with increasing pressure. However, the above-mentioned parameters are also strongly dependent on the type of fluidization gas used.The cohesion constant of the powder was measured, using a tilting bed technique. The results reveal that the cohesion constant increases with increasing pressure. Analysis of the results of adsorption measurements of the different gases to the solid reveals for the adsorption as well as for the cohesion and for the beu expansion the same pressure dependence.It is believed that the gas adsorption influences the cohesion between the particles and hence the elasticity modulus introduced by Rietema and Mutsers [1,2]. The increasing elasticity modulus with increasing pressure also explains the increasing bed expansion with pressure.     

Viscosity slope constants for solutions of nylon 6 and polytetrahydrofuran

Measurements of the viscosity slope constant k were made on solutions of nylon 6 and polytetrahydrofuran under different conditions of temperature, solvent, and molecular weight of polymer; θ-conditions were included so that the expansion factor α could be determined in each case. The value of k was influenced somewhat by the particular equation employed to derive it, and generally the Schulz-Blaschke equation (yielding k_SB) was the most reliable. Slope constants (k_calc) calculated according to an expression of Sakai were plotted as a function of α³ and were compared with the corresponding curves in terms of experimental values of k. The agreement was moderately good for PTHF but poor in the case of nylon 6. An expression (due to Imai) involving experimental values of k and α was examined in order to establish a unique value of the slope constant k_θ under θ-conditions by an extrapolation procedure. Although individual value of k_θ for nylon 6 measured under θ-conditions were dependent on molecular weight, the Imai plot yielded a unique value of 0.50 and a slope similar in magnitude to that found for other polymer/solvent systems.     

Simulation of micro- and macro-transport in a packed bed of porous adsorbents by lattice Boltzmann methods

In this study we report 3D simulation of concentration profiles in a fixed bed packed with spherical porous adsorbents using lattice Boltzmann methods (LBMs). The lattice models have been developed to investigate evolution of concentration profiles due to inter- and intra-particle mass transport in an adsorber having small tube-to-sphere diameter (d_t/d_p) ratios. The multi-scaling feature of LBMs permits full 3D simulation of concentration profiles both in the bed voids and within the pores of the adsorbents without using any empirical correlations or without making 1D or 2D approximations that are usually made in traditional numerical methods. The model simulation is carried out for varying packing arrangements and small to large pore diffusivities. The simulation results show significant concentration gradients for small pore diffusivities and large particle size, which must be considered in predicting breakthrough and adsorption times for a tubular adsorber having d_t/d_p<10. The model predicted breakthrough curves are validated with the experimental data obtained by tomography technique in a tubular adsorber packed with zeolite particles.