Analysis and interpretation of residence time distribution experimental curves in FM01-LC reactor using axial dispersion and plug dispersion exchange models with closed-closed boundary conditions

The liquid phase mixing flow pattern at low (20 < Re < 120) and intermediate liquid flow rate (120 < Re < 400) was studied by means of residence time distribution (RTD) experimental curve in an up-flow Filter Press electrochemical reactor (FM01-LC) bench scale. For this purpose, a plastic turbulence promoter was used with stainless-steel and platinised titanium structural meshes as electrodes in channel configuration. To visualize and determine the mixing flow pattern in the liquid phase, the stimulus-response technique was employed using dextran blue (D_M = 1.058 × 10⁻¹¹ m² s⁻¹, 25 °C, in water) as model tracer. A theoretical analysis and approximation RTD experimental curves with axial dispersion model (ADM) and plug dispersion exchange model (PDE), with “closed-closed vessel” boundary conditions were used in order to establish a better approximation of the axial dispersion, stagnant zones, channelling and by-pass (preference flow) effects present at low and intermediate Re. RTD curves show that the liquid flow pattern in the FM01-LC deviates considerably from axial dispersion model at low Re, where the FM01-LC exhibits large channelling, stagnant zones, and dead zone. The PDE model represents fairly this deviation from ideal flow (less dead zone).     

The measurement and characterisation of residence time distributions for laminar liquid flow in plastic microcapillary arrays

Residence time distributions (RTDs) for a thermoplastic microreactor system were experimentally measured using fibre optic probes and step change concentration inputs. The distributions were then compared to models assuming plug flow superimposed by axial dispersion. The disc-shaped plastic microreactors contained microcapillary arrays of up to 19 parallel channels with diameters around 230 μm and lengths of 10 m. Two different systems were investigated, with either 1 or 19 active capillaries. The magnitude of axial dispersion in those two systems was characterised using Peclet numbers, which were in the range of 15-221 depending on flow rate, demonstrating that molecular dispersion along a single 10 m capillary can provide near plug flow characteristics. The multiple-capillary array showed small perturbations of this plug flow like RTD behaviour as the 19 microcapillaries displayed slight variations in diameter. These results confirm that the flow inside the presented plastic multiple capillary device provides a near plug flow behaviour for the use in continuous microreactors.     

Solids mixing in a down-flow circulating fluidized bed of 0.418-m in diameter

The axial and lateral solids mixing in a down-flow circulating fluidized bed of 0.418-m diameter was investigated by a pneumatic injection phosphor tracer technique (PIPTT). The axial and lateral solids dispersion were determined by measuring the solids RTD at same axial but different lateral positions using point sources for tracer injection. A two-dimensional dispersion model described the measured RTD curves satisfactorily. The results were compared to those obtained in the small scale downers and the scale-up effect was investigated. The axial solids Peclet number Pe_a is around 110 and invariable with changing U_g, G_s and ?_s, while the lateral solids Peclet number Pe_r is linearly increasing with ?_s. And Pe_r is found to decrease with the square root of inner diameter (ID) in comparison with the results obtained in small ID downers. Correlation of Pe_r, Pe_r = (15 + 70.7 ?_s)D^− 0.5, is proposed.     

The intensification of gas-liquid flows with a periodic, constricted oscillatory-meso tube

The experimental study of gas dispersion in a vertical periodically, constricted, oscillatory meso-tube (OMT) is herein presented. Water was continuously pumped through the OMT in the laminar flow regime along with an oscillatory flow component superimposed into the net flow in a range of fluid oscillation frequency (f) and centre-to-peak amplitude (x₀) of and 0-3 mm, respectively, in the presence of a very low superficial gas velocity . Bubble images were recorded with a CCD camera and analysed with Visilog^® software. A bimodal distribution of bubble size was in general observed but the bubble size was found strongly dependent on the oscillatory flow mixing conditions imposed into the fluid. A number fraction of micro-bubbles (with an equivalent diameter, D_eq, equal or bellow 0.2 mm) up to 60% was generated with increasing values of x₀ (i.e. 3 mm) and values of f in the range . Furthermore, it is demonstrated that the Sauter mean diameter, D₃₂, and the specific interfacial area, a, can be fined tune by setting both f and x₀ in this studied range. The high number fraction of micro-bubbles was concluded to have a positive impact in enhancing the liquid-side mass transfer coefficient, k_L. Globally, the differences in bubbles sizes were found to play a marginal effect in the global enhancement of the k_La in the meso-tube in comparison with the intensive contact experimented by the bubbles rising in the oscillatory flow. The higher order of magnitude of the k_L values found in this work (up to ) is promising for running numerous industrial gas-liquid flows processes through smaller and better, while aeration of biotransformations can be run more efficiently, as supported by our recent proof-of-concept studies carried out in the platform.     

Residence time distribution and dispersion of gas phase in a wet gas scrubbing system

Residence time distribution (RTD) of exhaust gas in a wet scrubbing system was investigated for application to the removal of SO _x , NO _x or dust included in exhaust gas. The mixing of gas phase in the wet scrubbing system was also examined by considering the axial dispersion coefficient of gas phase. Effects of gas amount (velocity), liquid amount (velocity) and solid floating materials on the residence time distribution (RTD) and axial dispersion coefficient of exhaust gas were discussed. The addition of solid floating materials could change the RTD and thus dispersion of exhaust gas in the scrubbing system. The mean residence time and axial dispersion coefficient of exhaust gas were well correlated in terms of operating variables.     

Characterisation of fluid mixing in novel designs of mesoscale oscillatory baffled reactors operating at low flow rates (0.3-0.6 ml/min)

For the first time two mesoscale oscillatory baffled designs (central and integral baffles with their volumes of 5.2 ml and 4.4 ml, respectively) were experimentally characterised at net flow rates as low as 0.3 ml/min (Re_n ∼ 1.25), giving a residence time of around 15-17 min over a wide range of oscillation conditions. The purpose was to identify the lower limits of operability, thereby determining the maximum residence time per unit reactor volume for these mesoscale units. The characteristics of fluid flow were found to be strongly affected by Strouhal number at these low net flows. For the integral baffles, the oscillation conditions exhibited little influence on the fluid mixing. For the central baffles, there were three distinct flow regimes, depending on Strouhal numbers which affect the fluid characteristics differently. At two regimes of Sts, St ≥ 0.8 and 0.13 ≤ St ≤ 0.2, an increase in frequency did not alter the axial dispersion. At St ≥ 0.8, the fluid experienced less uniform mixing, representing by right-skewed residence time distribution (RTD) curves. At 0.20 ≤ St ≤ 0.13, the fluid mixing was significantly improved, indicated by narrow and symmetrical RTD curves with Re_o up to 700. At 0.4 ≤ St ≤ 0.27 and St ≤ 0.1, the degree of plug flow was a function of Re_o. The maximum number of tanks achieved at these low flow rates was in the range 30-35, occurring at a velocity ratio (Re_o/Re_n) of 39-40.     

Mixing characteristics for the single and air-water two-phase flows in miniaturized parallel multichannel-based devices

Investigation on the miniaturized parallel multichannel-based devices packed with glass beads to improve the mass exchange execution is the critical focal point of the current study. One of the essential parameters to specify the miniaturized devices' flow distribution is the residence time distribution (RTD). In the present context, the RTDs of a liquid tracer were investigated for the air-water multiphase flows (concurrent) across the multichannel-based miniaturized devices (comprising of 11 similar dimensional parallel channels). The devices were variable in height and packed with glass beads. The conductivity estimations generated the RTD curves and were addressed by the axial dispersion model (ADM). The fluid-flow rates differed within the range of 5–23 ml min⁻¹. The axial dispersion coefficients and the rate of the specific energy dispersion were investigated. The effects of pressure difference and geometry on the hydrodynamic attributes and mixing properties were well-illustrated, and the new correlations were suggested.     

Effects of heating rate on microstructures and microwave dielectric properties of (1 − x)ZnAl2O4–xTiO2 (x = 0.21) ceramics

(1 − x)ZnAl₂O₄–xTiO₂ (x = 0.21) ceramics were synthesized at 1500 °C for 3 h using the solid-state reaction at a heating rate from 1 to 7 °C/min. The effects of heating rate on the microstructure, phase composition and oxidation state of titanium in the ceramics were investigated. The XRD results show that this system is composed of two phases, i.e. ZnAl₂O₄ spinel and rutile. The “black core” phenomenon resulting from reduction of Ti⁴⁺ ion valence appears after the ceramics are sintered at the speed of 1 and 3 °C/min. As the heating rate increases, the density and quality factor (Q·f) increase initially and reach the maximum value when the heating rate is 5 °C/min, and then reduce quickly to the minimum, while the dielectric constant (?_r) and temperature coefficient of resonator frequency (τ_f) nearly do not change. The optimal microwave dielectric properties can be achieved in (1 − x)ZnAl₂O₄–xTiO₂ (x = 0.21) ceramics sintered at a heating rate of 5 °C/min with an ?_r value of 11.6, a Q·f value of 74,000 GHz (at about 6.5 GHz), and a τ_f value of −0.4 ppm/°C.     

Microwave dielectric properties of Ba3Ti4−x(Zn1/3Nb2/3)xNb4O21 for low temperature co-fired ceramics

The effects of substitution of (Zn_1/3Nb_2/3) for Ti on the sintering behavior and microwave dielectric properties of Ba₃Ti_4−x(Zn_1/3Nb_2/3)_xNb₄O₂₁ (0 ≤ x ≤ 4) ceramics have been investigated. The dielectric constant (?_r) and the temperature coefficient of the resonant frequency (τ_f) of Ba₃Ti_4−x(Zn_1/3Nb_2/3)_xNb₄O₂₁ ceramics decreased with increasing x. However, the Q × f values enhanced with the substitution of (Zn_1/3Nb_2/3) for Ti. It was found that a small amount of MnCO₃-CuO (MC) and ZnO-B₂O₃-SiO₂ (ZBS) glass additives to Ba₃Ti_4−x(Zn_1/3Nb_2/3)_xNb₄O₂₁ (x = 2) ceramics lowered the sintering temperature from 1250 to 900 °C. And Ba₃Ti_4−x(Zn_1/3Nb_2/3)_xNb₄O₂₁ (x = 2) ceramics with 1 wt% MC and 1 wt% ZBS sintered at 900 °C for 2 h showed excellent dielectric properties: ?_r = 53, Q × f = 14,600 GHz, τ_f = 6 ppm/°C. Moreover, it has a chemical compatibility with silver, which made it as a promising material for low temperature co-fired ceramics technology application.     

Microwave dielectric properties of the (1 − x)Mg2TiO4-xCaTiO3-y wt.% ZnNb2O6 ceramics system

Composite ceramics based on (1 − x)Mg₂TiO₄-xCaTiO₃-y wt.% ZnNb₂O₆ (x = 0.12-0.16, y = 0-8) were prepared by a conventional mixed-oxide route. Zn²⁺ partially replaced Mg²⁺ in Mg₂TiO₄ and formed the spinel-structured (Mg_1−δZn_δ)₂TiO₄ phase. Nb²⁺, is known to be solid soluble in CaTiO₃, was found to change its shape from cubic to pliable. A bi-phase system (Mg_1−δZn_δ)₂TiO₄ and CaTiO₃ exhibited in all samples, where a small amount of second phase Mg_1−δZn_δTiO₃ was also detected. The microwave dielectric properties of specimens were strongly related to ZnNb₂O₆ and CaTiO₃ content. As y increased, ?_r and τ_f decreased, however, Q × f decreased to a minimum value and started to increase thereafter. It was also found that ?_r and τ_f increased and Q × f decreased with increasing x. The optimized microwave dielectric properties with ?_r = 18.37, Q × f = 31,027 GHz (at 6 GHz), and τ_f = 0.51 ppm/°C were achieved for (1 − x)Mg₂TiO₄-xCaTiO₃-y wt.% ZnNb₂O₆ (x = 0.12, y = 4) sintered at 1360 °C for 6 h.     

Structural evolution, sintering behavior and microwave dielectric properties of (1 − x)Li3NbO4-xLiF (0 ≤ x ≤ 0.9)

Sintering behavior, microstructure and microwave dielectric properties of (1 − x)Li₃NbO₄-xLiF (0 ≤ x ≤ 0.9) ceramics have been studied in this paper. Continuous solid solution with rock salt structure formed across the entire compositional range. Phase transformed from ordered body-centered cubic phase to short range ordered face-centered cubic phase with the addition of LiF. The x > 0.4 compositions could be densified at 850 °C/2 h. The optimized Q × f value for each composition increased with the increase of LiF content and saturated at about 75,000 GHz when x ≥ 0.15, whereas the optimized dielectric permittivity decreased with the increase of LiF content. All specimens exhibited negative τ_f value. The chemical compatibilities with copper (Cu) in the case of x = 0.4 composition and silver (Ag) in the case of x = 0.5 composition were also investigated, respectively. No chemical reaction has taken place between the matrix phase and Ag or Cu after sintering at 850 °C/2 h or 950 °C/2 h, respectively.     

Influence of A-site Ba substitution on microwave dielectric properties of (BaxMg1−x)(A0.05Ti0.95)O3 (A=Zr,Sn) ceramics

The microwave dielectric properties of (Ba_xMg_1−x)(A_0.05Ti_0.95)TiO₃ (A=Zr, Sn) ceramics were investigated with regard to substitution of Ba for Mg of A-site. The microwave dielectric properties were correlated with the Ba content. With an increase in Ba content from 0.01 to 0.1, the dielectric constant and the τ_f value increased, but the Q×f value decreased. The sintered (Ba_xMg_1−x)(Zr_0.05Ti_0.95)TiO₃ (called B_xMZT) ceramics had a permittivity in the range of 19.1−20.6, quality factor from 180,000 to 25,000 GHz, and variation in temperature coefficient of resonant frequency from −35 to −39 ppm/°C with increasing composition x. For sintered (Ba_xMg_1−x)(Sn_0.05Ti_0.95)TiO₃ (called B_xMST) ceramics, the dielectric constant increased from 19 to 20.5, Q×f value increased from 120,000 to 37,000 (GHz), and the τ_f value increased from −50 to −3.3 ppm/°C as the x increased from 0.01 to 0.1. When A=Sn and x=0.1, (Ba_0.1Mg_0.9)(Sn_0.05Ti_0.95)TiO₃ ceramics exhibited dielectric constant of 20.5, Q×f value of 37,000 (GHz), and a near-zero τ_f value of −3.3 ppm/°C sintered at 1210 °C for 4 h.     

RTD studies in trickle bed reactors packed with porous particles

The residence time distribution (RTD) for liquid phase in a trickle bed reactor (TBR) has been experimentally studied for air-water system. Experiments were performed in a 15.2 cm diameter column using commerical alumina extrudates with D/d_p ratio equal to 75 to eliminate the radial flow differences. The range of liquid and gas flow rates covered was 3.76 < Re_L < 9.3 and 0 < Re_G < 2.92. The axial dispersion model was used to compute axial dispersion coefficient. The effect of liquid and gas flow rates on total liquid holdup and axial dispersion was investigated. The total liquid holdup has been correlated to liquid and gas flow rates.     

The influence of axial pressure on relaxor properties of BaBi2Nb2O9 ceramics

On the basis of our studies it results that dielectric properties of BaBi₂Nb₂O₉ ceramics are sensitive to axial pressure applied. The pressure causes an increase of dispersion in the real part of dielectric permittivity ?′(T,f) and a rise in the temperature T_m at which the maximum in ?′(T,f) dependence occurs. The applied pressure induces in the ?′(T) dependence an additional step-like anomaly, which appears at the temperature T_A < T_m. The applied pressure shifts both T_m and T_A at the same rate, i.e. dT_A/dX = dT_m/dX = +14 °C/kbar at high axial pressure range, above the threshold pressure X_thresh. The Vogel–Fulcher relationship is employed to determine the axial pressure influence on relaxor properties of BBN ceramics. The simulated order parameter q takes non-zero values below Burn‘s temperature T_B, where the polar clusters appear on cooling. For pressures higher than 0.8 kbar, the T_B changes at the rate dT_B/dX = −200 °C/kbar. The decrease in the difference between Burn's T_B and the freezing T_f temperatures induced by the applied axial pressure is observed. This could be ascribed to the narrowing of temperature range of relaxor behavior.     

Microwave dielectric properties of BaO-2(1 − x)ZnO-xNd2O3-4TiO2 (x = 0-1.0) ceramics

Microwave dielectric properties of (1 − x)BaZn₂Ti₄O₁₁-xBaNd₂Ti₄O₁₂ (x = 0-1.0) ceramics were investigated by the solid-state reaction with the purpose of finding a microwave ceramics with high dielectric constant (?_r), high quality factor (Q × f) and low temperature coefficient of resonant frequency (τ_f). A two phase system BaZn₂Ti₄O₁₁-BaNd₂Ti₄O₁₂ was formed and SEM photographs show equiaxed BaZn₂Ti₄O₁₁ grains and columnar BaNd₂Ti₄O₁₂ grains. The microwave dielectric properties were strongly determined by the chemical composition. As increasing x from 0 to 1.0, the phase composition varied from pure BaZn₂Ti₄O₁₁, to the two phase system BaZn₂Ti₄O₁₁-BaNd₂Ti₄O₁₂ and then to pure BaNd₂Ti₄O₁₂. Therefore, the ?_r raised from 29.1 to 82.0 and the Q × f values decreased from 54,630 GHz to 8110 GHz, and the τ_f values increased from −29 ppm/°C to 94 ppm/°C. 0.8BaZn₂Ti₄O₁₁-0.2BaNd₂Ti₄O₁₂ ceramics sintered at 1250 °C for 2.5 h had ?_r = 39.1, Q × f = 37,850 GHz and τ_f = −9 ppm/ °C.     

Mass transfer in vertical liquid-solids flow of coarse particles

Wall-to-bed mass transfer in the hydraulic transport of spherical glass particles was studied. The experiments were performed by transporting spherical glass particles 1.20, 1.94 and 2.98 mm in diameter with water in a 25.4 mm I.D. tube. The mass transfer coefficients were determined by following rate of dissolution of a segment of the transport tube prepared from benzoic acid.In the runs in hydraulic transport, the Reynolds number of the tube varied between 1826 and 27597. The loading ratio (G_p/G_f) was between 0.026 and 0.474, and the fluid superficial velocity was between 0.267 · U_t and 4.904 · U_t, where U_t represents the single particle terminal velocity. For these ratios, the voidage ranged from 0.7123 to 0.9228.Also, wall-to-bed mass transfer in the single phase flow regime was studied. In the runs without particles, the Reynolds number of the tube varied between 122 and 39132. The data for the mass transfer factor (j_D) in single phase flow are correlated for turbulent flow regime, using the Chilton-Colburn's type equations, j_D = f(Re). Those investigations were conducted in aim to compare with results for wall-to-bed mass transfer in hydraulic transport.The data for wall-to-bed mass transfer (j_D) in hydraulic transport of spherical particles were correlated by treating the flowing fluid-particle suspension as a pseudofluid, by introducing a modified suspension-wall friction coefficient (f_w) and a modified Reynolds number (Re_m). The data for wall-to-bed mass transfer in the hydraulic transport of particles show that an analogy between mass and momentum transfer exists.     

Electrical and magnetic properties of magnesium-substituted lithium ferrite

Magnesium-substituted lithium ferrite of different composition (Li_0.5Fe_2.5−xMg_xO_4−δ) were prepared for x = 0.0–1.0 by conventional ceramic technique. The crystal structure characterization and morphology were investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM). Initial permeability and quality factor were measured in the frequency range of 1 kHz to 100 MHz. The permeability decreased gradually from μ (f = 10 MHz) = 34.0 for Li_0.5Fe_2.5O₄ to μ (f = 10 MHz) = 11.5 for Li_0.5Fe_1.5Mg_1.0O₄. Electrical conductivity measurements were carried in the range of 250–700 °C in air. The maximum electrical conductivity, σ_700 °C = 0.1274 S/cm has been found to be for Li_0.5Fe_2.5O₄ specimen. With increasing Mg-substituted content, the decreased in the electrical conductivity.     

More studies on the PVOH-LiH2PO4 polymer system

Polymer electrolytes based on poly(vinyl alcohol) (PVOH) and lithium dihydrogen-phosphate (LiH₂PO₄) with molar ratio of x = 0.07, 0.10 and 0.14 were prepared in order to investigate the mechanism of ionic motion. Admittance spectroscopy measurements were used to study electrical conductivity relaxation on both anhydrous and hydrated samples in the 5 Hz to 13 MHz frequency range and temperatures ranging from 25 to 150 °C. The conductance, G, shows dispersion above a crossover frequency, f_p. This behavior is typical of systems in which correlated ionic motions in the bulk material are responsible for ionic conductivity. For hydrated samples, results reveal that the temperature dependence of the dc-conductivity, σ₀ and the characteristic frequency, f_p, shows Arrhenius-type behavior with the same energy, E_σ. However, for anhydrous conductivity, a Vogel-Tamman-Fulcher (VTF) behavior is shown for both σ₀(T) and f_p(T), with the same pseudo activation energy, B and B_σ, respectively, thus indicating that they are correlated with chain mobility.     

Liquid phase axial mixing in bubble columns operated at high pressures

Liquid phase axial mixing was measured in a 100 mm i.d. bubble column operated in the pressure range of 0.1-0.5 MPa. Water, ethanol and 1-butanol were used as the liquid phase and nitrogen as the gas phase. The temperature and superficial gas velocity were varied in the range of 298-323 K and 0.01-0.21 m/s, respectively. The axial dispersion coefficient increased with an increase in the gas density due to pressure. The temperature had surprisingly a small effect. A CFD model was developed for the prediction of flow pattern in terms of mean velocity and eddy diffusivity profiles. The model was further extended for the prediction of residence time distribution and hence the axial dispersion coefficient (D_L). The predictions of axial dispersion coefficient agree favorably with all the experimental data collected in this work as well as published in the literature. The model was extended for different gas-liquid systems. The predicted values of axial dispersion coefficient were found to agree very well with all the experimental data.     

Application of residence time distribution technique to the study of the hydrodynamic behaviour of a full‐scale wastewater treatment plant plug‐flow bioreactor

The hydrodynamic behaviour of a full‐scale wastewater treatment plant (WWTP) bioreactor treating municipal wastewater, situated in Granollers (Barcelona, Spain), has been studied by means of a residence time distribution (RTD) technique using lithium (chloride) as tracer. The bioreactor studied is designed to work as a plug‐flow reactor and it is divided into two independent lanes (1 and 2), each one composed of four compartments in series resulting in a total volume of 3970 m³ per lane. During the RTD experiments, working flow was 1000 m³ h^?1 per lane, which implied an ideal mean residence time of 3.97 h. When a lithium chloride tracer was injected in the bioreactor, both lanes showed a similar highly non‐ideal hydrodynamic behaviour, which had an important effect on the reactor's performance. This global RTD was complemented by means of local RTDs in different locations of the bioreactor in order to determine qualitatively the reactor's mixing regime. Different non‐ideal models (namely axial dispersion, tanks‐in‐series and some simple compartment models) have been tested for the modelling of the experimental RTD. The best model fitting RTD data for Lanes 1 and 2 was a configuration consisting of four mixed tanks in series. The RTD study proposed in this work will permit improvement of the reactor's mixing performance, which is of special interest in future projects including simultaneous removal of carbon, nitrogen and phosphorus. Copyright © 2005 Society of Chemical Industry