Branched-pore model applied to the adsorption of basic dyes on carbon

The branched-pore adsorption model, expressed by an external mass transfer coefficient k_f, a solid diffusivity D_s, a lumped micropore diffusion rate parameter k_b, and the fraction of macropores f, describes kinetic data from initial contact of adsorbent-adsorbate to the long-term ( > 24 hours) adsorption stages with reasonable accuracy.In this work the model is applied for three basic dye systems, namely Basic Red 22, Basic Yellow 21 and Basic Blue 69, all on carbon. A single value of each parameter describes each dye system. The k_f values are 0.18 × 10⁻²±28%, 0.3 × 10⁻²±17% and 0.2 × 10⁻² ± 20% cm s⁻¹, the D_s values are 0.33 × 10⁻⁹ 21%, 0.72 × 10⁻⁹ ± 9% and 0.72 × 10⁻⁹ ± 9% cm² s⁻¹, the k_b values are 0.65 × 10⁻⁶ ± 7.7%, 1.8 × 10⁻⁶ 0.2 × 10⁻⁶ 1% s⁻¹, while the f values are 0.55 ± 9%, 0.60 ± 10 % and 0.18 ± 11%, each for Basic Red 22, Basic Yellow 21 and Basic Blue 69 respectively.The model is based on the internal structure of the carbon particle being divided into a macropore and a micropore region. The latter has an upper-bound capacity of 241, 245 and 656 mg g⁻¹ for Basic Red 22, Basic Yellow 21 and Basic Blue 69 respectively. A sensitivity analysis for each parameter has been carried out.     

Analytical solution using a pore diffusion model for a pseudoirreversible isotherm for the adsorption of basic dye on silica

An analytical solution for a two resistance mass transfer model explaining the adsorption of Astrazone Blue dye (Basic Blue 69) onto Sorbsil silica has been developed. The model includes a film mass transfer coefficient, k_f1 = 80 × 10⁻⁶cm·s−1, and an internal effective diffusivity, D_eff = 18×10⁻⁹cm²·s⁻¹ which controls the internal mass transport processes based on a pore diffusion mechanism.     

Adsorption of dyes onto bagasse pith using a solid diffusion model

The adsorption of four dyes (Basic Blue 69, Basic Red 22, Acid Blue 25, and Acid Red 114) onto bagasse pith has been studied using an agitated batch adsorber. The variables studied were initial dye concentration and pith mass. A mathematical model has been developed based on external mass transfer and solid-phase diffusion. The model has been used to generate theoretical concentration–time decay curves, and these results were adjusted to experimental data by a best fit approach. The external mass transfer coefficients are 2.0 × 10^?3, 1.5 × 10^?3, 8.0 × 10^?4, and 5.0 × 10^?4 cm s^?1 and the solid diffusivities are 1.1 × 10^?8, 1.0 × 10^?8, 6.0 × 10^?9, and 3.0 × 10^?9 cm² s^?1 for Basic Blue 69, Basic Red 22, Acid Blue 25, and Acid Red 114.     

Liquid-phase diffusion and adsorption of pyridine in porous silica-alumina pellets

The adsorption and effective diffusivity of pyridine dissolved in heptane were measured in silica-alumina pellets using a specially developed single-pellet continous-flow diffusion cell. The measured diffusivities varied between 0.43 × 10⁻⁹ and 3.25 × 10⁻⁹ m²·s⁻¹; the temperature dependence of the diffusivities indicated that both pore volume diffusion and surface diffusion play a role in the mass transfer.     

Two-resistance mass transfer model for the adsorption of various dyestuffs onto chitin

The kinetics of the adsorption of various dyestuffs onto chitin have been studied. The dyestuffs used are Neoland Blue 2G, Eriochrome Flavine A, and Solophenyl Brown 3RL and a number of process variables were considered, such as adsorbent mass and dye concentration. The mass transfer model is based on the assumption of a pseudoirreversible isotherm and two resistances to mass transfer. These are external mass transfer and internal pore diffusion mass transfer. The rate of adsorption of dyestuffs onto chitin can thus be described by an external mass transfer coefficient and a pore diffusion coefficient. The external mass transfer coefficients are 5.0 × 10^?5, 5.0 × 10^?5, and 1.0 × 10^?5 m·s^?1 and the pore diffusivities are 3.0 × 10^?10 and 4.0 × 10^?11 m²·s^?1 for Neolan Blue 2G, Eriochrome Flavine A, and Solophenyl Brown 3RL, respectively.     

An Effective Moisture Diffusivity Model Deduced from Experiment and Numerical Solution of Mass Transfer Equations for a Shrinkable Drying Slab of Microalgae Spirulina

From experimental data, Spirulina effective moisture diffusivity was analytically estimated by considering two diffusion regions and the product shrinkage. Then, the moisture diffusivity was deduced from the numerical solutions of mass transfer equations by minimizing the difference between experimental and simulated drying curves and by taking into account the slab thickness variation. The range of moisture diffusivity used for simulations was estimated from minimal and maximal values of experimental effective diffusivities and calculation started with the mean value of experimental effective diffusivities. Identified effective diffusivities ranged from 1.79 × 10^?10 to 6.73 × 10^?10 m²/s. These diffusivities increased strongly with drying temperature and decreased slightly with moisture content. A suitable model correlating effective diffusivity, temperature, and moisture content was then established. Effective diffusivities given by this model were very close to experimental ones with a relative difference ranging from 0.5 to 24%.     

The adsorption kinetics of sodium dodecylbenzenesulfonate on activated carbon. Branched-pore diffusional model revisited and comparison with other diffusional models

Abstract

The adsorption rate of sodium dodecylbenzenesulfonate (SDBS) on three commercial activated carbons (ACs) and an AC synthesized from almond shells was investigated in this study. The mechanisms controlling the overall adsorption rate of SDBS on ACs were found out by using the pore volume and surface diffusion model (PVSDM). The PVSDM showed that the intraparticle diffusion of SDBS in all ACs was mainly attributed to pore volume diffusion and surface diffusion. The surface diffusion coefficient, D_s, in all samples of ACs are influenced by the amount of surfactant adsorbed at equilibrium, q_e, as well as the mean micropore width, L₀. The contribution of surface diffusion to the overall intraparticle diffusion ranged from 45 to 70%, depending on the properties of AC. Moreover, the branched-pore diffusional model was revisited (BPDMR) assuming that the Fick diffusion is the only diffusion mechanism in the macropores and the diffusion in the micropores was represented by the micropore rate coefficient, K_C. Besides, it was proposed that the parameter f representing the mass fraction of SDBS adsorbed on macropores, can be estimated from the textural properties of ACs. Three new strategies were proposed to analyze the experimental data using BPDMR model, and it was demonstrated that the macropore diffusivity in BPDMR is close to the molecular diffusivity of SDBS in water solution. The micropore rate constant, K_C, ranged from 3.90?×?10^?6 to 10.6?×?10^?6 s^?1 and was affected by textural characteristics of ACs. Both models predicted the global adsorption rate of SDBS on ACs satisfactorily.     

Insight into the intraparticle diffusion of residue oil components in catalysts during hydrodesulfurization reaction

Well‐defined and uniform pore structure catalysts were used to study the intraparticle diffusion of fractionated Saudi vacuum residue under hydrodesulfurization (HDS) reaction conditions. HDS rates of residue oil cuts with different molecular weights are determined as functions of pore size, temperature, and pressure in a trickle‐bed reactor. Credible intrinsic and bulk diffusivities of organosulfur compounds in residue oil were obtained for the first time, from the apparent and intrinsic reaction kinetic constants. Intrinsic diffusivities ranged from 2 × 10^?7 to 8 × 10^?7 cm²/s for the residual oil molecules; diffusivity decreases with increasing molecular weight of the residual oil. The intrinsic diffusivity for molecular weights ～1000 Daltons increases with pore size for pores <70 nm, but is nearly independent of pore size for pores >70 nm. The diffusivity dependences on pore size and molecular weight suggest that the onset of restricted diffusion occurs for ratios of molecular diameter to pore diameter of ～0.04. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3267–3275, 2014     

Analysis of intraparticle diffusion on adsorption of crystal violet on bentonite

Abstract

In the present work, kinetics of crystal violet (CV) adsorption on bentonite was studied by pore volume and surface diffusion model (PVSDM), surface diffusion model (SDM), and pore volume diffusion model (PVDM). The adsorption decay curves were obtained in batch system using different adsorbent dosages. The PVDM model did not interpreted the kinetic adsorption since the calculated value of D_p equal to 5.64?×?10^?7 cm² s^?1 predicted a slower adsorption than that obtained by the experimental data. The PVSDM results indicates that the intraparticle diffusion is predominantly due to surface diffusion (93%) and the pore volume diffusion can be negligible. Once the surface diffusion was the limiting step, the estimation with one (D_s) and two (D_sq and α) parameters were tested in the SDM model. The statistical analysis revealed that the one-parameter SDM model was most appropriate to predict the CV adsorption on bentonite. The optimal values of Ds ranged from 6.19?×?10^?10 to 6.49?×?10^?10 cm² s^?1, and decrease with the adsorbent dosage.     

Kinetics and diffusion processes in colour removal from effluent using wood as an adsorbent

The rates of adsorption of a basic dye, Astrazone Blue, and an acidic dye, Telon Blue, on wood have been studied. The rate controlling step is mainly intraparticle diffusion, although a small resistance due to a boundary layer is experienced. The activation energies for the adsorption of Astrazone Blue and Telon Blue on wood are 16.8 kJ mol^?1 and 9.6 kJ mol^?1, respectively. The diffusion coefficients vary from 6×10^?13 cm² s^?1 to 18×10^?13 cm² s^?1 for Astrazone Blue at 18°C and from 3 × 10^?13 cm² s^?1 to 8 × 10^?13 cm² s^?1 for Telon Blue at 18°C. The variation in diffusivities is attributed to boundary layer effects.     

OSMOTIC DEHYDRATION KINETICS OF BLUEBERRIES

Abstract

The kinetics of moisture loss and solids gain during osmotic dehydration of blueberries under different conditions of temperature (37°C - 60°C), concentration of the sucrose solution (47°Brix - 70°Brix) and contact time between fruit and sucrose solution (0.5 h - 5.5 h) were studied, and modeled based on Fick's law of unsteady state diffusion. The study showed that all factors influenced moisture loss and solids gain (p<0.001), both generally increasing with temperature (T) and sucrose concentration (C). Based on the diffusion model, the calculated effective moisture diffusivity (D_m) ranged from 1.98 × 10^?10 to 5.10 × 10^?10 m²/s and the effective solids diffusivity (D_s) ranged from 2.54 × 10^?11 to 2.22 × 10^?10 m²/s. Both D_m and D_s showed increasing trends with temperature and sucrose concentration, and could be modeled as quadratic functions of T and C.     

The Adsorption of basic dye onto silica from aqueous solution-solid diffusion model

The adsorption of Basic Blue 69 dye onto silica in a batch adsorption system has been studied. A two resistance mass transfer model has been developed based on film resistance and homogeneous solid phase diffusion. An analytical solution is presented and experimental results and theoretical data are in good agreement, for a wide range of operating conditions, using a single external mass transfer coefficient and a single effective solid diffusivity. The variables investigated are: initial dye concentration, solid/liquid ratios and adsorbent particle size range. Under constant agitation conditions almost all data can be correlated using a film mass transfer coefficient of 2.0 x 10^?4 cm sec^?1 and a diffusion coefficient of 1.2 x 10^?9 cm² sec^?1.     

Temperature effect on diffusion of carbon dioxide through upper layers of Yucca Mountain

The effective diffusivities of carbon dioxide through the Tiva Canyon tuff and the lower lithophysal zone of the Topopah Spring tuff (outcrop samples of the layer above the proposed nuclear repository site layer) were determined using a steady-state method (counter diffusion). The diffusivity of carbon dioxide through the Tiva Canyon and lithopysal zone tuffs increased with temperature. The following correlation was obtained to estimate the effective diffusivity of carbon dioxide through the Tiva Canyon tuff in cm² s⁻¹ as a function of temperature (K). D_e = 1.22 × 10⁻² − 3.77 × 10⁻⁵T + 9.95 × 10⁻⁸T²The effective diffusivity of carbon dioxide through the lower lithophysal zone of the Topopah Spring tuff (layer right above the proposed repository site) also increased with temperature. For this layer, the following correlation was obtained to estimate the effective diffusivity of carbon dioxide in cm² s⁻¹ as a function of temperature (K). D_e = − 1.11 × 10⁻³ + 1.25 × 10⁻⁵T + 1.83 × 10⁻⁹T²     

Kinetics of Silver Extraction with Triisobutylphosphine Sulfide

Abstract

Kinetics of silver extraction from nitrate solutions with triisobutylphosphine sulfide dissolved in n-octane was studied. Experiments were carried out in a rotating diffusion cell. The rate constants of forward and reverse chemical reactions were evaluated: the former k^? _f = 1.064 × 10^?3 m⁹/(mol³·s) and the latter k^? _f = 2.085 × 10^?1 s^?1. The value obtained for the activation energy shows that the process of silver extraction with triisobutylphosphine sulfide is a predominantly diffusion-controlled process.     

Kinetics of leaching of tunisian phosphate ore particles in dilute phosphoric acid solutions

Van der Sluis et al.'s model was used to determine the rate of the partial dissolution of a Tunisian phosphate rock with dilute phosphoric acid (1.5 mass% P₂O₅). When the temperature rises from 25 to 90°C, for a given particle size, the mass-transfer coefficients, k_L°, vary from 3 × 10^?3 to 8 × 10^?3 m ·s^?1. The corresponding diffusion coefficients, D, lies between 6 × 10^?7 and 27 × 10^?7 m²·s^?1. Activation energy is equal to 14 kJ·mol^?1 and values of k_L°, at 25°C, are in the range of 0.28 × 10^?3 and 4 × 10^?3 m·s^?1 when the agitation speed goes from 220 to 1030 rpm, showing that the leaching process is controlled by diffusion rather than by chemical reaction.     

Reaction and diffusion of reactive disperse dye in nylon 6

The diffusion of a reactive disperse dye with a vinylsulfonyl group accompanied by simultaneous reaction with the amino end groups in nylon 6 was examined by the method of cylindrical film roll at 70°C and pH 2.2–8.0. The experimental diffusion profiles of the active and fixed species of the dye in nylon 6 were confirmed to be described by the diffusion equation accompanied by the chemical reaction with substrate taking the limited amount of the end groups into account, where the active species of dye were assumed to react only with the free base of amino end groups. The completion of the reaction with the amino end groups was observed in the first layer from the surface at pH 6.0–8.0. The value of diffusion coefficient was constant (8.0 × 10^?10 cm²/s) at all the pH's. The product of the second-order rate constant, k₂, of reaction of the dye and the dissociation constant, K_a, of the amino end groups was constant (k₂K_a = 4.0 × 10^?9 s^?1) at pH 2.2–8.0. The k₂ values of the reaction with various substrates for vinylsulfonyl and monochlorotriazinyl-reactive dyes were compared and the practical dyeing conditions were discussed.     

Drying with Chemical Reaction in Cocoa Beans

Desirable flavor qualities of cocoa are dependent on how the cocoa beans are fermented, dried, and roasted. During fermentation and drying, polyphenols such as leucocyanidin and apecatechin are oxidized by polyphenols oxidase to form o-quinone, which later react nonenzymatically with a hydroquinone in a condensation reaction to form browning products and moisture. The objective of this article is to model the cocoa beans drying together with the browning reaction. A Luikov drying model for the moisture and a simple Fick's law diffusion model combined with first-order reactions for both the enzymatic oxidation and nonenzymatic condensation reactions were constructed. Both models were used to identify moisture diffusivity coefficient and total polyphenols diffusivity in cocoa beans from experimental drying and polyphenols degradation data and published kinetic data of the reactions. The theoretical drying model fitted the experimental cocoa bean drying curves with low mean square of residuals. The polyphenols diffusion and reaction model also fitted the experimental polyphenols degradation curves with minimum mean residual squares. The rate of polyphenols degradation in the cocoa beans increases at higher temperature and higher relative humidity. This is because the increasing reaction rate of polyphenols oxidation reaction as well as higher moisture diffusion at higher relative humidity and temperature. The effective moisture diffusivity in cocoa beans is estimated to be between 8.194 × 10^?9 and 8.542 × 10^?9 m²·s^?1, which is of the same order of magnitude as published data. The effective total polyphenols diffusivity is estimated to be between 8.333 × 10^?12 to 1.000 × 10^?11 m²·s^?1 with minimum mean residual squares. It is three orders of magnitude less than the estimated moisture diffusivity because of the larger polyphenols molecules. The estimated polyphenols diffusivity is very close to those published in the literature for sorption and ultrafiltration processes.     

Dehydration of Ethanol-Water Azeotropic Mixture by Adsorption Through Phillipsite Packed-Column

Abstract

Phillipsite is a natural zeolite material available in several locations in Jordan. Phillipsite with and without treatment was used for dehydrating ethanol in the adsorptive distillation process. Molecular sieves 4A was taken as a reference material. According to the breakthrough curves phillipsite treated with 1 M calcium chloride solution gave the best performance. The water uptake using the 1 M-phillipsite was 0.1054 g H₂O/g adsorbent while the water uptake using the 4A molecular sieves was 0.1030 g H₂O/g adsorbent. The Guggenheim, Anderson, and De Boer (GAB) model and the Frenkel, Halsey, and Hill (FHH) model were used to represent the isotherms for water sorption on the adsorbents used. The GAB model fit the experimental data relatively better than the FHH model for all cases, except for the case of using 2 M-phillipsite. Using the Crank diffusion model the effective diffusivity of water vapor in raw phillipsite is 10.40 × 10^?8 mm²s^?1 while it is 6.9 × 10^?8 mm²s^?1 in the 1 M treated phillipsite.     

The Effect of External Mass Transfer Resistance during Drying of Fermented Sausage

The drying mechanism of fermented sausages (sucuks) that were cylindrical rod shaped, 40 cm long and 4 cm diameter, during ripening under natural convection conditions at different temperatures (15 to 30°C) was examined. To simulate the experimental drying curves, three empirical models and a diffusional model assuming negligible external mass transfer resistance were evaluated. The drying rate curves of sucuk samples were also simulated taking into account the influence of the external mass transfer resistance. The equation was solved using the trial-and-error solution algorithm developed in this study and the mass transfer coefficient, k _c , and effective moisture diffusivity, D _eff , were simultaneously determined (1.44 × 10^?8 to 1.93 × 10^?8 m/s and 4.30 × 10^?10 to 6.85 × 10^?10 m²/s, respectively). The proposed model considering the effect of external resistance allowed the accurate simulation of the experimental drying data of sucuks at different temperatures.     

Kinetics of removal of p-toluene sulphonic acid from concentrated solution by granular activated carbon

The removal of p-toluene sulphonic acid (p-TSA) from concentrated solution by granular activated carbon (GAC) was studied in batch experiments. The first order rate constant was found to be 5.5010 × 10^?5 s^?1 for a solution of 1000 mg dm^?3. In order to establish the rate limiting step the pore and film diffusion coefficients were calculated from the half time equations. Film diffusion was found to be rate limiting. The average value of the external mass transport rate constant was 2.91 × 10^?6 cm s^?1. The adsorption isotherm was adequately described by the Langmuir model and belongs to type ‘H’ of Giles' classification.