Batch adsorption for pore diffusion with film resistance and an irreversible isotherm

Equations are developed for finite-batch, irreversible adsorption where both pore diffusion and film resistance are significant. Quasi-steady state behavior is assumed and comparisons are made for sheets, cylinders, and spheres. The equations for the three shapes are generalized to a single form. For equal volumes of adsorbent, when the external film controls, spheres attain equilibrium more quickly than cylinders, and cylinders more quickly than sheets. When internal diffusion controls and the ratio of the final to the initial solution concentration is high, this ordering of equilibrium times is preserved; however, if the ratio is very low, the ordering is reversed.     

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.     

Effect of backwashing on activated carbon adsorption using plug flow pore surface diffusion model

A fixed bed is gradually exhausted from top to bottom without backwashing; however, backwashing can rearrange the concentration gradient in the bed. After backwashing, saturated particles which are located at the top of the bed are homogeneously distributed in the bed. The used model to predict adsorption and backwashing effect of organic component is the plug flow pore surface diffusion model (PFPSDM). A sensitivity analysis was performed to determine which parameters have the greatest impact on the model results for components which can represent various organics. In addition, the effects of backwashing were examined by rearranging concentration gradient. For single component sensitivity analysis, the molecular weight was an important parameter. The breakthrough of the smaller molecular weight component was impacted more by backwashing. The SPDFR showed a significant impact on the breakthrough pattern. When surface diffusion was the dominant mechanism, high SPDFR, the breakthrough profile was sharper than when pore diffusion was dominant, low SPDFR. The adsorbability was an important parameter in determining the breakthrough pattern. As expected, the strongly adsorbable component showed the later breakthrough. Backwashing yielded earlier breakthrough for all single components and multi-components examined.     

Analytical solution of the breakthrough curve for rectangular isotherm systems

A general solution including both film and intraparticle diffusion resistances is derived for the breakthrough curve for an adsorption or ion exchange system with irreversible equilibrium. Both fluid and solid resistances are represented by linearized rate expressions but the solution is obtained without recourse to the constant pattern assumption. A numerical solution has also been obtained for intraparticle diffusion with external fluid film resistance. The deviation between the predictions of the two models increases with the magnitude of the intraparticle resistance. Numerical solutions were also obtained for Langmuir and Freundlich isotherms in order to establish the range where the simple rectangular models can be considered as an acceptable approximation.Experimental data for the ion exchange systems of RNaZn(NO₃)₂ and RNaCe(NO₃)₃ and for the adsor     

Pore diffusion model for dye adsorption onto peat in batch adsorbers

The adsorption of Acid Blue 25, Basic Blue 69, Basic Orange 2, and Disperse Blue 7, on peat has been studied using a series of batch adsorption runs. A model has been developed based on external mass transfer and internal diffusion to explain the concentration decay curves. Two system variables, namely, adsorbate concentration and adsorbent concentration, have been studied. The paper presents a rapid analytical solution for predicting the concentration decay curve in batch adsorbers using peat as a cheap adsorbent to remove various classes of dyestuffs from aqueous solution. The analytical solution depends on the assumption of a psdeudo-irreversible isotherm and that the internal diffusion process occurs via a pore diffusion mechanism. External mass transfer coefficients and internal diffusivities have been estimated for the various systems.     

Pore diffusion and external mass transport during dye adsorption on to Fuller's earth and silica

The adsorption of dyes on to Fuller's earth and silica has been studied. A mass transfer model has been developed to describe the adsorption process based on external mass transfer and internal pore diffusion. Theoretical concentration decay curves have been predicted using the model and compared with experimental decay curves.     

高岭土对亚甲基蓝的吸附性能和等温吸附模型研究

以高岭土为吸附剂,研究了其对亚甲基蓝模拟废水的吸附行为、等温吸附模型和吸附动力学。探讨了吸附时间、高岭土投加量、亚甲基蓝初始浓度、盐浓度、p H值等因素对亚甲基蓝吸附效果的影响。结果表明,吸附时间120 min,高岭土投加量10 g/L,低温、碱性条件下就能达到更好的亚甲基蓝吸附效果。高岭土对亚甲基蓝吸附符合Langmuir和Freundlich等温吸附模型,吸附动力学符合准二级动力学模型。     

高岭土对亚甲基蓝的吸附性能和等温吸附模型研究

以高岭土为吸附剂,研究了其对亚甲基蓝模拟废水的吸附行为、等温吸附模型和吸附动力学。探讨了吸附时间、高岭土投加量、亚甲基蓝初始浓度、盐浓度、p H值等因素对亚甲基蓝吸附效果的影响。结果表明,吸附时间120 min,高岭土投加量10 g/L,低温、碱性条件下就能达到更好的亚甲基蓝吸附效果。高岭土对亚甲基蓝吸附符合Langmuir和Freundlich等温吸附模型,吸附动力学符合准二级动力学模型。     

Equal area method to obtain approximate solution of adsorption rate model with nonlinear isotherm

Intraparticle mass transfer coefficients were determined by experimental adsorption data of m-cresol, quinoline and 1-naphthol onto a silica gel in a finite bath. The equal area approximation method of nonlinear isotherm was proposed with the assumption that the internal mass transfer coefficient is constant and equal to average value in the operating region. In the region where a slope of a constant time line is less than that of the operating line(region I), the original nonlinear isotherm was approximated by a quadratic form, and in the inverse case(region II) the isotherm was approximated by a linear form. Thus approximate analytical solutions were obtained. The present experimental conditions were in the region II, and the present approximate solution was in a good agreement with experimental results.     

Influence of pore size distribution on water adsorption on silica gels

The influence of pore size distribution on water adsorption has been analysed for a series of partially dehydroxylated silica gels with different pore structure, assessed from the analysis of nitrogen and CO₂ adsorption isotherms. It has been observed that some silica gels show water adsorption mainly in the first range of relative pressures (relative pressure from 0 up to 0.6), while other silica gels also show water adsorption at higher relative pressures. Comparison of the N₂ and water adsorption isotherms points out that only silica gels containing mesoporosity show water adsorption at relative pressures higher than 0.6. Moreover, a good correlation between the initial part of water adsorption isotherms (relative pressure from 0 up to 0.3) and CO₂ adsorption isotherms has been found (the higher the CO₂ adsorption capacity, the higher the water adsorption capacity at low pressure).     

Water adsorption equilibria on microporous carbons correlated using a modification to the Sircar isotherm

Water vapor adsorption equilibria are measured for several unimipregnated and impregnated microporous carbons, including BPL, ASC, ASC-TEDA and a polymeric beaded carbon. Both the shape of the isotherms and the presence of hysteresis are characteristics of the capillary condensation mechanism. Sircar's isotherm expression, which incorporates capillary condensation with the Kelvin equation, has been modified to correlate the data for both adsorption and desorption. Two gamma distribution functions are required to represent the pore size distribution for the activated carbons while only one gamma distribution function is required to represent the pore size distribution for the polymeric beaded carbon. The pore distributions that result from correlating the isotherm data are consistent with the known structure of these adsorbents.     

An isotherm model describing concave-down scatchard curve for heterogeneous affinity adsorption

A new isotherm model, derived for a concave-down Scatchard curve, is presented to fit the experimental results for pepsin and chymosin adsorption to pepstatin A affinity membranes. The new model is converted into a kinetic expression and used for the fitting of association curves. The results from the new kinetic model show a better agreement with the experimental data than the Langmuir kinetic model. The new kinetic model is also used together with the affinity membrane model to predict the single-solute breakthrough curves, which performs well in matching the experimental curves. ©1997 SCI     

Kinetic,isotherm and thermodynamic study of nitrate adsorption from aqueous solution using modified rice husk

In this article, we prepared anionic sorbent using rice husk (RC). Anionic rice husk (ARC) structural characteristics and adsorption properties for nitrate removal from aqueous solution were investigated. The sorption of NO₃^? by batch method is carried out. The optimum conditions of sorption were found to be: a sorbent dose of 0.4 g in 100 mL of NO₃^? solution, contact time of 90 min, pH = 7. In optimum condition, removal efficiency was 94.3% for the NO₃^?. The nitrate adsorption process was well described by the pseudo-second-order kinetic model, and the experimental isotherm data fitted well with the Langmuir, Freundlich and Dubinin–Radushkevich (D–R) isotherm models. Thermodynamic parameters such as Gibbs free energy change, enthalpy change and entropy change were calculated and the results showed that the adsorption of nitrate on ARC was spontaneous and exothermic in nature. The effect of other anions were also studied and was found that the anions reduced the nitrate adsorption in the order of carbonate > chloride > phosphate > sulphate. ARC was used for the removal of NO₃^? from real wastewater (urban wastewater) that high performance of adsorbent was considerable.     

粗孔微球硅胶负载氢氧化锆对磷酸根吸附性能

以粗孔微球硅胶为载体,采用浸渍法负载ZrOCl2,然后用氨水将ZrOCl2转化为ZrO(OH)2,得到ZrO(OH)2/SiO2吸附剂,研究其对水溶液中磷酸盐的吸附。单独使用粗孔微球硅胶作为吸附剂时对磷酸根没有任何吸附作用。单独使用ZrO(OH)2·2.6H2O(用量0.1g)作为吸附剂时60min吸附量为120.4mg PO43-/g,以纯ZrO(OH)2计的吸附量为160.3mg PO43-/g,当ZrO(OH)2/SiO2负载量为10%时,用量为0.5g,在相同条件下吸附量为36.4mg PO43-/g,以纯ZrO(OH)2计的吸附量为364.3mg PO43-/g。吸附动学实验表明吸附过程符合准二级动力学模型。     

Study of the mechanism of pore diffusion in batch adsorption systems

In this study the film-pore diffusion model was applied to describe system transport kinetics of three basic dye-carbon systems, namely Basic Blue 69, Basic Red 22 and Basic Yellow 21. The mass transfer parameters evaluated were the external mass transfer coefficient k_f (cm s^?1) and the effective diffusivity D_eff (cm² s^?1). A single k_f value was sufficient to describe each dye system: these were 0.15 × 10^?2, 0.20 × 10^?2 and 0.50 × 10^?2 cm s^?1 for BB69, BR22 and BY21, respectively. The effective diffusivity was found to have values much larger than those of pore diffusivities calculated from liquid diffusivities and its value decreased with increasing initial dye concentration. This was attributed to the effect of surface diffusion, hence pore diffusivity was exchanged by the effective pore diffusivity in the model. The present model was solved by the exponential curve fit technique; results were expressed in the form of experimental and theoretical Sherwood Numbers compared in terms of the residual.     

Modeling of adsorption isotherm of a binary mixture with real adsorbed solution theory and nonrandom two‐liquid model

Gas‐phase adsorption equilibria of diluted mixtures of methyl‐ethyl‐ketone and isopropylanol on activated carbon were investigated. Experimental isotherms were determined by a constant volume method. Single‐component adsorption isotherms were fitted by the frequently used Toth model with good accuracy. Then adsorption isotherms were determined for different binary mixtures (with different initial ratio of the two components). Binary mixtures adsorption isotherms were calculated using the adsorbed solution theory. Ideal adsorbed solution theory (IAST) could not represent experimental data, but it was observed that increasing amount of MEK led to higher nonideality of the mixture. Then UNIversal QUAsi Chemical (UNIQUAC) and nonrandom two‐liquids (NRTL) models were considered to describe activity coefficients of the adsorbed phase. The fitted parameters of UNIQUAC model depend on the ratio of the two components, whereas the NRTL model is able to fit all experiments with the same parameters, whatever the initial ratio may be. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Analytical solution for the problem of frictional-elastic collisions of spherical particles using the linear model

In the present paper, the problem of a frictional-elastic impact of two spheres is addressed with a novel approach. The set of equations arising from the linear model of the contact mechanics is analytically integrated considering the combined effects of the elastic and frictional mechanisms. The linear model is very commonly used in simulations based on the soft-sphere distinct element method (DEM) (Geotechnique 29 (1979) 47), where numerical methods are used for the integration of the equations of motion of the particles. The analytical approach presented in this work allows the examination of many important aspects related to the use of the linear model in dynamic simulation of multi-particle systems. The impact characteristics, in terms of the mechanisms governing the evolution of the force-displacement relation, can be classified in terms of the initial conditions, showing the same subdivision as that obtained with the more complex model of Maw et al. (Wear 38 (1976) 101). It is demonstrated how the values of many interesting variables at the end of the impact can be directly related to the impact initial conditions through a one-step calculation procedure. The model results of the tangential coefficient of restitution, rebound angles of the contact point and center of mass are validated with the experimental data on frictional-elastic collisions of Kharaz et al. (Powder Technol. 120 (2001) 281), showing, despite the simplicity of the considered model, an excellent agreement. However, it is demonstrated that the force evolution and time duration of the collisions strongly depend on the model parameters and can be improperly evaluated with incorrect material constants. Further analyses are carried out, for various impact angles, on the amount of energy loss due to the frictional mechanism. Also, an analysis of the direct influence of each model parameter on the properties of the particles at the end of the collision is carried out, with special emphasis on the normal elastic spring constant K_n. This helps clarifying why, in the literature, realistic macroscopic results were obtained even with very small values of K_n.