Interpretation of calcite growth data using the two-step crystal growth model

The crystal growth rates of calcite were evaluated in a dense fluidized-bed crystallizer using a constant-composition method. Several operation variables related to solution properties that affected growth rate, including supersaturation, pH, ionic strength and activity ratio, were systematically investigated. Then the crystal growth-rate data were analyzed by the two-step crystal growth model and thus the mass-transfer and surface-reaction coefficients were obtained. The effects of the solution properties on the two individual coefficients were observed. Good explanations on these effects are needed.     

Effect of pore diffusional resistance on biocatalytic activity of Burkholderia cepacia lipase immobilized on SBA-15 hosts

The present study was focused on elucidating the effects of nanopore diffusional resistance on the activity of Burkholderia cepacia (BC lipase) lipase immobilized in ordered mesoporous silica hosts. BC lipase was immobilized in ordered SBA-15 hosts possessing 55 and diameter pores by physical adsorption. A colorimetric assay of p-nitrophenyl acetate was employed to determine the lipase catalytic activity. The effect of diffusional resistance on catalytic activity of lipase immobilized in SBA-15 hosts was investigated by determining the effective substrate diffusivity as a function of pore size of the SBA-15 host and enzyme loading. Lipase immobilized in SBA-15- exhibited 20-30% of free lipase activity and the activity was further reduced with enzyme loading due to limited accessibility of substrate to the enzyme active sites. Lipase immobilized in SBA-15- hosts showed catalytic activity similar to free lipase activity suggesting that diffusional limitations were minimal. Large pore SBA-15 hosts provided an improved environment for BC lipase to retain its catalytic activity.     

Kinetics of adsorption on activated carbon: application of heterogeneous vacancy solution theory

The kinetics of single component adsorption on activated carbon is investigated here using a heterogeneous vacancy solution theory (VST) of adsorption. The adsorption isotherm is developed to account for the adsorbate non-ideality due to the size difference between the adsorbate molecule and the vacant site, while incorporating adsorbent heterogeneity through a pore-width-related potential energy. The transport process in the bidisperse carbon considers coupled mass transfer in both macropore and micropore phases simultaneously. Adsorbate diffusion in the micropore network is modeled through effective medium theory, thus considering pore network connectivity in the adsorbent, with the activation energy for adsorbate diffusion related to the adsorption energy, represented by the Steele 10-4-3 potential for carbons. Experimental data of five hydrocarbons, CO₂ and SO₂ on Ajax carbon at multiple temperatures, as well as three hydrocarbons on Norit carbon at three temperatures are first fitted by the heterogeneous VST model to obtain the isotherm parameters, followed by application of the kinetic model to uptake data on carbon particles of different sizes and geometry at various temperatures. For the hydrocarbons studied, the model can successfully correlate the experimental data for both adsorption equilibrium and kinetics. However, there is some deviation in the fit of the desorption kinetics for polar compounds such as CO₂ and SO₂, due to the inadequacy of the L-J potential model in this case. The significance of viscous transport in the micropores is also considered here and found to be negligible, consistent with recent molecular simulation studies.     

Effects of crystal growth rate and heat and mass transfer on solute distribution

The effects of crystal growth rate and heat and mass transfer on solute distribution during solidification of binary melt have been theoretically investigated on the basis of a new theory of solute distribution proposed by the present authors. The solute distribution factor f at the solid-liquid (SL) interface is in inverse proportion to the one-half power of the dimensionless growth rate U. The growth rate U is in proportion to the second power of the normalized concentration difference between the SL interface and bulk melt. A new transport factor K, which describes heat and mass transfer in melt, gives an important contribution to the crystal growth and the solute distribution at the SL interface. The transport factor is used successfully to control the solidification of melt. The flow structure in melt exerts essential influence on the solid purity.     

Rod-like crystal growth of dioctyl substituted polyfluorene from nematic and isotropic states

The growth behavior of the rod-like α-form crystals from both the liquid crystal and the isotropic melt state was studied in situ and in real time using a hot-stage atomic force microscopy. The growth rate and direction of the poly(9,9-dioctylfluorene) (PFO) α-form crystals are greatly affected by the orientation of the polymer chains in the liquid crystal matrix. The pre-existence of chain alignment in the liquid crystal matrix serves as a precursor for crystallization, which greatly reduces the growth energy barrier and promotes the overall growth rate of PFO α-form crystals. Our results provide some valuable information for understanding the relationship between morphology and photoexcited emission behaviors.     

The dissolution of a stationary spherical bubble beneath a flat plate

The dissolution of a single stationary bubble held in place by a horizontal plate is commonly observed experimentally. For several decades the standard approach to the analysis of such dissolution data has been to apply a correction factor of ln(2)=0.69 to the Epstein-Plesset equation for an isolated bubble. In this paper, the transport equations for a stationary bubble touching a plate are solved numerically for the common case where the flow field caused by the change in system volume as the bubble dissolves can be neglected. It is found that the total bubble lifetime is not well characterised by the use of the ln(2) factor. However, in most experimental situations, the initial stages of bubble dissolution are not captured. For low gas solubilities the use of a correction factor of 0.69 to the Epstein-Plesset equation is appropriate once the initial transients have dissipated. The correction factor varies from 0.69 to 0.77 across the full range of situations described in this paper. The mathematical model is validated by comparison to experimental data.     

Molecular weight scaling of the spherulite growth rate in isothermally melt crystallized polyethylene nanocomposites

The spherulite growth rate, G_II, was measured for three monodisperse linear polyethylenes filled with up to 4 vol. % of SiO₂ nanoparticles in the crystallization regime II of small undercooling, ΔT. The fumed SiO₂ used did not exhibit any measurable nucleation activity. The G_II scaled with the number average molecular weight, M_n, as M_n^ν with the scaling exponent, ν, equal to (2.2 ± 0.1). This corresponds to the reptation controlled surface self-diffusion of loop-train adsorbed chains with the contour length fluctuation (CLF) and the chain constraint release (CR) contributions. In order to verify the hypothesis of the chain reptation as the molecular mechanism responsible for the chain transport, logG_II was plotted against the logarithm of the number of effective entanglements per chain, logN_eff. The N_eff was the sum of the number of “true” entanglements in the neat resin of a given M_n and the number of apparent “temporary” entanglements due to adsorption/desorption of segments of PE chains onto SiO₂ nanoparticles with their inter-particle distance equal or shorter than the average entanglement length. Adding 2 vol % and 4 vol. % SiO₂, respectively, resulted in an increase of the N_eff by 40% and 80% of apparent “temporary” entanglements, respectively. When plotted against logN_eff, all the experimental logG_II data for a given undercooling, ΔT, collapsed to a single line. The slope of the logG_II vs. logN_eff dependence was independent of ΔT and varied from −2.13 to −2.24, similarly to the slope of the logG_II vs. logM_n dependence. This supported the conclusion that the effects of increasing the M_n and/or adding the non-nucleating nanometer sized SiO₂ on the spherulite growth rate were additive in nature and their effect can be superimposed. The retarded reptation of the chains to the growing crystal front was identified as the primary molecular mechanism of chain transport controlling the reduction of the spherulite growth rate in the model PE/SiO₂ nanocomposites investigated.     

The resistance of interphase mass transfer in colloidal liquid aphron systems

Colloidal liquid aphrons (CLAs) provide very large interfacial area and thus could enhance interphase mass transfer in multiphase processes. This work characterized the mass transfer behavior of CLAs during mass transfer of benzoic acid from cyclohexane in CLAs to water in a small stirred vessel. From experimental data the overall mass transfer coefficient K_L of the surfactant-stabilized CLAs was determined. The influence of stirring speed and concentration of surfactant used for formulating CLAs on K_L was investigated. The experimental results show that surfactant adsorbed on the interface of CLAs influences greatly the value of K_L, and when the surfactant concentration is below its CMC, the overall CLAs mass transfer coefficient K_L (mainly varying with the interfacial mass transfer resistance) could be fitted to the following expression:

K_L=H₁+H₂ln[C+H₃].     

Adsorption of chlorinated hydrocarbons from aqueous solutions by wetted and non-wetted synthetic sorbents: dynamics

In the present investigation the dynamics of the adsorption of several chlorinated hydrocarbons onto wetted and non-wetted synthetic sorbents was studied. A single particle model was developed to describe the adsorption behavior. The values of the mass transfer coefficient, needed to describe the experimental results, were found to be considerably less than those predicted from theory. The difference between measured and expected mass transfer coefficient was found to increase with non-ideality of the solute and to depend on type of sorbent. Apparently, the rate of mass transfer does not only depend on hydrodynamics but also on possible interaction between solute, solvent and sorbent.     

Study on mass transfer of ethyl acetate in polymer adsorbent by experimental and theoretical breakthrough curves

A new polymeric adsorbent with highly hypercrosslinked structure was developed for the removal of VOCs from polluted air. The purpose of this work is to obtain the intraparticle mass transfer coefficient of the adsorbent particles. Adsorption experiments for obtaining breakthrough curves were carried out with a fixed bed system. A dynamic mathematical model for the fixed bed adsorption system was developed. By model fitting, the overall mass transfer coefficient was determined when the deviation error was minimum. Then, the intraparticle mass transfer coefficient of the adsorbent was determined when the external mass transfer resistance was eliminated at higher velocities. Furthermore, a linear relationship of the intraparticle mass transfer coefficient and equilibrium coefficient at lower inlet gas concentrations range was correlated. Moreover, an equation for predicting external mass transfer coefficient at low Reynolds number range at room temperature was obtained.     

Determination of diffusion coefficient from transitory uptake or release kinetics: Incidence of a recirculation loop

The determination of the diffusion coefficient of a solute in a solid matrix (polymers, gels, adsorbents) is often determined based on batch kinetics experiments performed when a given amount of matrix is put into a stirred cell containing a defined volume of diluting fluid (gas or liquid). There is, however, a strong trend to develop smaller and smaller volume set-ups (due to, for instance, the cost of either the solute or the matrix in biological or pharmaceutical fields). Furthermore, a continuous monitoring of the solute concentration in the release (or exhaustion) medium is obviously attractive and frequently applied, in place of a sequential manual sampling protocol. This option demands, however, most often a continuous recirculation loop to be implemented on the cell volume, so that a continuous detector (such as spectrophotometric, conductimetric or refractive index) can be used. The objective of this work is to analyze the influence of such a recirculation loop, which may affect significantly the hydrodynamics (fluid residence time distribution) as well as the dynamics (delayed signal) of the experimental kinetics, in order to evaluate the impact on the diffusion coefficient determination. Numerical simulations covering a broad range of situations have been performed, and an experimental validation on a system consisting of alginate hydrogel beads as a model matrix and pullulan molecules (molecular weight ranging between 730 and 880 000) as model solute is reported. Practical guidelines are finally proposed in order to estimate, through ab initio shortcut methods, the error induced by the recirculation loop, based on explicit experimental parameters (cell/loop volume, recirculation loop residence time, solute diffusion time constant).     

Particle growth kinetics of calcium fluoride in a fluidized bed reactor

Crystallization process in a fluidized bed reactor to remove fluoride from industrial wastewaters has been studied as a suitable alternative to the chemical precipitation in order to decrease the sludge formation as well as to recover fluoride as synthetic calcium fluoride.In the modeling, design and control of a fluidized bed reactor for water treatment it is necessary to study the particle growth kinetics. Removal of fluoride by crystallization process in a fluidized bed reactor using granular calcite as seed material has been carried out in a laboratory-scale fluidized bed reactor in order to study the particle growth kinetics for modeling, design, control and operation purposes.The main variables have been studied, including superficial velocity (SV, ), particle size of the seed material (L₀, m) and supersaturation (S). It has been developed a growth model based on the aggregation and molecular growth mechanisms. The kinetic model and parameters given by the equation fits well the experimental data for the studied range of variables.     

Thin-layer drying of porous materials: Selection of the appropriate mathematical model and relationships between thin-layer models parameters

Experimental investigation of the drying kinetics of various types of materials was carried out in laboratory-scale dryers under different conditions of temperature, microwave heating power and pressure. Leather samples (mechanically and vacuum-dewatered bull napa and wet blue cutting), paperboards (grafopack, testliner), wood (alder, birch, willow) and two pharmaceutical powders (chlorpropamide and hydrochlorotiazide) were dried in a microwave dryer. Thin clay slabs, Al–Ni catalyst and chlorpropamide were dried in a convection dryer, while chlorpropamide and ketoprofen were dried in a vacuum dryer. In order to compare drying kinetics, experimentally obtained data, X = f(t), were correlated with the Lewis “thin-layer” equation, the modified Page equation and Fick's second law. The drying constant, effective diffusion coefficient, mass transfer coefficient and modified Page model parameters were estimated by fitting the selected mathematical models to experimental data. High levels of correlation between measured and calculated data were obtained for all materials and dryers using modified Page model. The application of the Lewis and Fick's equation is justified only for drying of clay, catalyst and leather. Mass transfer coefficient depends linearly on the drying constant. The relation between the modified Page model parameter and the drying constant can be represented by a unique power function.     

Asymptotically exact driving force approximation for intraparticle mass transfer rate in diffusion and adsorption processes: nonlinear isotherm systems with macropore diffusion control

An asymptotically exact nonlinear driving force model of intra-particle mass-transfer rate for nonlinear isotherm systems with macropore diffusion control is presented. The obtained expression is compared with the solutions of the Fickian diffusion and adsorption model and excellent accuracy over the entire time (fractional uptake) domain is demonstrated. In the case of an irreversible isotherm the model reduces to the equations resulting from the shrinking core model a fact that guarantees its accuracy for highly nonlinear systems. The high accuracy of the model is further demonstrated by comparison with experimental data under various operational conditions.     

Optimal experimental protocol for identification of dissolution parameters in presence of fast reaction

To model the reactive solid phase contribution, knowledge of the solubility and mass transfer should be extracted from empirical measurements. Often unknown factors may complicate the interpretation of the data. In this paper we consider an example of this kind and present a practical procedure that allows one to avoid these difficulties. A simplified model is derived for the mass transfer and kinetics. This model provides the insight that leads to an optimal protocol for estimation of the parameters of interest.     

A Simple Determination Method of Adsorption Kinetics from a Liquid Phase Fixed‐Bed Breakthrough Curve

The mass transfer zone (MTZ) method using the linear driving force (LDF) approximation is the most common and frequently used technique for the analysis of adsorption kinetics from a fixed‐bed breakthrough curve and for adsorptive process design. However, the adsorption kinetics obtained by the MTZ method includes approximations and estimation errors. This report describes a new analytical method for determining the intraparticle diffusivity (D_S) and the fluid‐film mass transfer coefficient (k_F) from an experimental breakthrough curve without using the LDF approximation and empirical correlations for estimating k_F . The proposed method has the advantage of less trial and error on the curve‐fitting process and helps better determine D_S and k_F . The estimation procedure of the Biot number that represents the ratio of D_S to k_F is the key of this method. The values of D_S and k_F for the adsorption of phenols onto activated carbon were determined from experimental breakthrough curves using the new analytical method. The results indicate that the method presented in this study yields reliable values.     

Kinetics and equilibrium of dissolved oxygen adsorption on activated carbon

The macroscopic adsorption behavior of dissolved oxygen on a coconut shell-derived granular activated carbon has been studied in batch mode at 301 and 313 K for initial dissolved oxygen concentrations of 10-30 mg/l and oxygen/carbon ratios of 2-180 mg/g. BET (Brunauer, Emmett, and Teller) surface area, micropore volume, and pore size distribution were determined from N₂ isotherm data for fresh and used samples of carbon. The surface groups were characterized using Boehm titrations, potentiometric titrations, and FTIR study. The material is characterized by its high specific surface area , microporocity (micropore volume ), its basic character ( total basic groups) and its high iron content (15,480 ppm Fe). BET n-layer isotherm describes adsorption equilibrium suggesting cooperative adsorption and important adsorbate-adsorbate interactions. Kinetic data suggest a process dependent on surface coverage. At low coverage a Fickian, intraparticle diffusion rate model assuming a local equilibrium isotherm (oxygen dissociation reaction) adequately describes the process. The calculated diffusion coefficients (D) vary between and for initial oxygen concentration of 10 and 20 mg/l, respectively. Sensitivity analysis shows that the oxygen dissociation equilibrium constant determines the equilibrium concentration, whereas the diffusion coefficient controls the kinetic rate of the adsorption process having no effect at the final equilibrium concentration. A combined kinetic mass transfer model with concentration-dependent diffusion (parabolic form) has been developed and successfully applied on the dissolved oxygen adsorption system at high surface coverage. For equilibrium uptake of the estimated mean mass transfer coefficient and adsorption rate constant are and , respectively.     

Reaction kinetics and mass transfer studies of biomass char gasification with CO2

Gasification kinetics of wheat straw char with CO₂ was investigated using Thermogravimetric apparatus (TGA). The main objective was to identify the diffusional and surface reaction phenomena that may occur during biomass char gasification experiments with CO₂. The effects of temperature (750–900 °C) and particle size (<60–925 μm) on gasification rate of char-CO₂ reaction were determined. The 50% conversion (r₅₀) rate showed that the reactivity increases with temperature, and it decreases as the particle size increases. The important diffusional parameters such as effective diffusivity, effectiveness factor and Thiele modulus were calculated based on the experimental data and the results showed that the impact of physical factors is prominent at high temperatures and large particle sizes. It was found that char gasification within the temperature range studied followed the chemically controlled reaction regime and the influence of pore diffusion was negligible for fine powder particles.     

Effect of surface resistance on cyclohexane uptake curves in Silicalite-1 crystals

Adsorption kinetics of cyclohexane in a variety of Silicalite-1 samples were measured by gravimetric uptake experiments. The kinetic appears as dependent upon the history of the crystals. Samples stored for several months before calcination (with their micropores full of template) exhibit a kinetic drop by almost an order of magnitude. Surprisingly, physico-chemicals analysis do not show any differences between these samples (no modification of their crystallinity or morphology, and no residual carbon is detected in the pore network). The kinetic drop is therefore attributed to a modification of the crystals surface, induced by a long-time contact with the template or cyclohexane molecules.Aged and as-synthesized (non-calcined) samples were etched by an HF solution, so as to “purify” the surface of the crystals. After a few minutes of treatment, the aged samples recover their initial adsorption kinetic, confirming that the kinetic drop is induced by the partial blocking of the entrance of the pores. Moreover, some of the as-synthesized crystals also show a rise of their adsorption kinetic, showing that surface resistance can be present ab initio, depending on the synthesis conditions.In an attempt to produce an accelerated aging effect, hydrothermal treatments were performed on non-calcined crystals. However, the treatments conditions are too severe, and induce variations in the crystal structure.