MODELING MASS TRANSFER OF FITC-LABELED DEXTRAN FROM POLYELECTROLYTE MICROCAPSULES

Layer-by-layer adsorption of oppositely charged polyelectrolytes has been used for the manufacturing of hollow microspheres or capsules for controlled release studies. Using this self-assembly technique, microsphere core material was encapsulated with poly styrenesulfonate (PSS) and poly allylamine (PAH) multilayers or PAH and polyvinyl sulfate (PVS) multilayers and the core dissolved to produce hollow microcapsules. The microspheres were loaded with fluorescein-isothiocyanate (FITC)-labeled dextran of different molecular weights for different lengths of time to quantify the release properties. After loading, the capsules were immersed in water and the FITC-dextran was allowed to diffuse into the mother liquor. The FITC-dextran concentration of the mother liquor was measured over a period of hours and days. In this study, one- and two-compartment models were developed, based on a species mass balance, to predict the concentration of dextran release from the microcapsules over time. The two-compartment model was found to be superior to the one-compartment model in its fit to the observed data. The model was applied to experimental data in order to characterize the release properties of microcapsules with different numbers of layers and constituent architectures.     

THE TWO-THIRDS POWER MODEL FOR PREDICTING DIFFUSION COEFFICIENTS IN LIQUIDS

Most of the models found in the literature for predicting diffusion coefficients in liquids take the viscosity of the solution as inversely proportional to the diffusivity. A model (previously derived for sucrose-water system)which considers the viscosity raised to the two-third power, is evaluated here using published data for the Benzene—Cylohexane, Ethanol-Water and Acetone-Chloroform systems. These results, and results for the sucrose-water system are compared with the experimental values, and with those obtained using the Hartley—Crank equation. Better agreement with the experimental values at low and in the middle of the concentration range was found when diffusivities were calculated using the model proposed than when using the Hartley-Crank equation.     

EXPERIMENTAL AND THEORETICAL STUDY OF THE PORE STRUCTURE AND DIFFUSION PROPERTIES OF AN EVOLVING HETEROGENEOUS MATERIAL: APPLICATION TO RADIOACTIVE BITUMINIZED WASTE

Placed in a geological repository, radioactive bituminized waste (BW) could be altered in the long term by water, leading to the release of chemical and radioactive elements. The main difficulty, in terms of experimental characterization, comes from the fact that the BW material evolves in time due to the swelling associated to the water osmotic flux. To overcome this difficulty, a new approach is proposed in this work, based on the leaching of BW samples in aqueous solutions where the chemical activity of water is controlled. These specific leaching conditions allow one to control the swelling of the degraded BW matrix. The chemical activity of water being fixed, the pore structure of the leached BW samples was quantitatively studied by ESEM pictures further treated by image analysis. In parallel, diffusion cells using radioactive tracers were used in order to measure mass transfer characteristics in the leached BW. Coupling image analysis with diffusion experiments for each degradation state leads to a diffusion coefficient-porosity relation that is then compared to standard diffusion models in biphasic materials.     

EXPERIMENTAL AND THEORETICAL STUDY OF THE PORE STRUCTURE AND DIFFUSION PROPERTIES OF AN EVOLVING HETEROGENEOUS MATERIAL: APPLICATION TO RADIOACTIVE BITUMINIZED WASTE

Placed in a geological repository, radioactive bituminized waste (BW) could be altered in the long term by water, leading to the release of chemical and radioactive elements. The main difficulty, in terms of experimental characterization, comes from the fact that the BW material evolves in time due to the swelling associated to the water osmotic flux. To overcome this difficulty, a new approach is proposed in this work, based on the leaching of BW samples in aqueous solutions where the chemical activity of water is controlled. These specific leaching conditions allow one to control the swelling of the degraded BW matrix. The chemical activity of water being fixed, the pore structure of the leached BW samples was quantitatively studied by ESEM pictures further treated by image analysis. In parallel, diffusion cells using radioactive tracers were used in order to measure mass transfer characteristics in the leached BW. Coupling image analysis with diffusion experiments for each degradation state leads to a diffusion coefficient-porosity relation that is then compared to standard diffusion models in biphasic materials.     

DIFFUSION FROM A CYLINDRICAL DOMAIN THROUGH A MEMBRANE

The method of integral transforms is used to solve the problem of permeation from a polymer-thickened cylinder which is in contact with a permeable membrane at one end. The opposite side of the membrane is kept at zero concentration by a sweeping medium. It is assumed that the diffusion in the cylinder is one-dimensional and that the coupling conditions at the interface are given by the mass and solubility conservations. The mass dux through the membrane is formally approximated. The model can be applied to problems associated with such areas as the testing of protective clothing and controlled release devices.     

混合电解质溶液在多孔颗粒内扩散的数学模型

建立了混合电解质溶液在多孔颗粒内扩散的数学模型,并由此计算了交互扩散效应的大小;讨论了单一扩散系数的菲克定律描述电解质混合物扩散的适用性;用模型处理了HCl-KCl-H_2O体系的实验数据,得出了有效主扩散系数和有效交互扩散系数.     

A TWO-REGION MATHEMATICAL MODEL FOR BATCH DRYING OF GRAINS IN A TWO-DIMENSIONAL SPOUTED BED

A two-region non-equilibrium model of a two-dimensional spouted bed dryer has been developed. The model, based on heat and mass transfer interactions between the spout and downcomer regions, predicts the air and grain temperatures and moisture content throughout each elementary thin layer of grain in the spouted bed. The model was validated with the experimental results on batch drying of corn. Drying and heating processes are shown to occur in both the spout and downcomer regions. Overall, the agreement between experimental and simulated results is satisfactory.     

MATHEMATICAL MODEL OF FCC CATALYST DEACTIVATION

A model is proposed that explains both lab-scale and commercial unit FCC catalyst deactivation, taking vanadium mobility between particles into account. Equilibrium catalyst density fractionation is also simulated, helping in the interpretation of the commercial unit results.     

A TWO-REGION MATHEMATICAL MODEL FOR BATCH DRYING OF GRAINS IN A TWO-DIMENSIONAL SPOUTED BED

A two-region non-equilibrium model of a two-dimensional spouted bed dryer has been developed. The model, based on heat and mass transfer interactions between the spout and downcomer regions, predicts the air and grain temperatures and moisture content throughout each elementary thin layer of grain in the spouted bed. The model was validated with the experimental results on batch drying of corn. Drying and heating processes are shown to occur in both the spout and downcomer regions. Overall, the agreement between experimental and simulated results is satisfactory.     

A MATHEMATICAL MODEL FOR CONTINUOUS DRYING OF GRAINS IN A SPOUTED BED DRYER

A mathematical model for a continuous spouted bed dryer has been presented to predict moisture content, air and grain temperatures as well as energy consumption. To better understand the interactive influence of processes in each region of the spouted bed, solution schemes for the spout and downcomer were treated separately. The behavior of dryer was investigated experimentally and found that the dryer behaved differently from an ideal plug flow. The drying rate as simulated by the model is almost constant during grain movement in the dryer. Absence of airflow in the downcomer leads to a tempering process that takes place in the downcomer while intense heat and mass transfer occurs mainly in the spout due to the high airflow rate there. Furthermore, by considering the predicted grain temperature history as one of the indicators of product quality, one can, in principle, design appropriate successive processes in a continuous spouted bed dryer to minimize product damage.     

A MATHEMATICAL MODEL FOR CONTINUOUS DRYING OF GRAINS IN A SPOUTED BED DRYER

ABSTRACT

A mathematical model for a continuous spouted bed dryer has been presented to predict moisture content, air and grain temperatures as well as energy consumption. To better understand the interactive influence of processes in each region of the spouted bed, solution schemes for the spout and downcomer were treated separately. The behavior of dryer was investigated experimentally and found that the dryer behaved differently from an ideal plug flow. The drying rate as simulated by the model is almost constant during grain movement in the dryer. Absence of airflow in the downcomer leads to a tempering process that takes place in the downcomer while intense heat and mass transfer occurs mainly in the spout due to the high airflow rate there. Furthermore, by considering the predicted grain temperature history as one of the indicators of product quality, one can, in principle, design appropriate successive processes in a continuous spouted bed dryer to minimize product damage.     

均相玻璃态高分子中溶剂扩散系数的数学模型

以自由体积理论为基础 ,提出改良的玻璃态高分子中溶剂扩散系数的数学模型 .模型推导过程中考虑了溶剂可塑化效应对高分子凝聚态的影响 ,并以明确的物理概念计算玻璃态聚合物的自由体积 .对橡胶态适用的自由体积参数在此模型中保持有效 ,所引入的表达溶剂可塑化效应的唯一参数 β可以通过计算玻璃化温度来确定 .所以 ,本模型中无可调节参数存在 ,具有完全可预测性 .以芳香族溶剂苯、甲苯、乙苯在玻璃态聚苯乙烯和聚甲基丙烯酸甲酯中的扩散系数为例对模型进行验证 ,理论计算结果和实验值取得良好一致     

AN INVESTIGATION ON THE MATHEMATICAL MODEL OF ELECTRODE DIFFUSION PROCESS IN THE DETERMINATION OF DISSOLVED OXYGEN BY POLAROGRAPHIC METHOD

The mathematical model of diffusion process in polarographic determination of dissolved oxygen hasbeen thoroughly studied with an electric simulator.It is found that the combination of microelectrodeand impulse operating technique is a possible way to improve the characteristics of present Clark electrode.The quantitative relations between the electrode size and operating condition are given in this paper indimensionless form,and the range of the optimum condition has been discussed.     

二元醇/水溶液在渗透蒸发均质膜中的扩散模型

用交联聚乙烯酸膜对不同浓度的乙二醇/水溶液在不同温度下分别进行了渗透蒸发实验研究．针对小分子在致密膜中的扩散行为提出了一个新见解,并借用改进的Vigne方程得到了一个新的热力学扩散系数方程,用此方程结合Lee-Thods方程、Wilke-Chang方程、Vrentas和Duda改进的自由体积理论、扩散方程和溶胀平衡方程预测了水和乙二醇分子在不同温度下通过交联聚乙烯醇膜的渗透蒸发行为,其预测结果与实验值基本一致．     

IMPROVEMENT OF DEEP-BED CROSSFLOW MODEL BY A DIFFUSION COMPONENT FOR THE GRAIN PARTICLE AND LOG MODEL FOR EVALUATION OF RECIRCULATING CROSSFLOW DRYER

This paper presents the improved versions of -bed cross now and log simulation models. A diffusion model descries ibing internal diffusion of moisture within a grain kernel to compute moisture removal rate is developed and incur porsted in crossflow model to improve its flexlbillty and versetility. The lag model is suilably modified and employed to evaluate its accuracy and applicability compared to crossflow drying model for evaluating recirculating crossflow drying operation. Experiments were conducted on large scale recirculating crossflow dryer for corn drying. Simulation results are compared with experimental results to test the validity of drying models.     

THE EXACT PENETRATION MODEL OF DIFFUSION IN MULTICOMPONENT IDEAL GAS MIXTURES. ANALYTICAL AND NUMERICAL SOLUTIONS

An exact analytical solution is derived for the penetration model of diffusion in multicomponent ideal gas mixtures at constant pressure and temperature. It takes the form of a matrizant solution to the continuity and Maxwell-Stefan equations transformed by introduction of a similarity variable, and includes as special cases the corresponding binary and linearized theory solutions

Direct numerical implementation of the analytical solution is computationally inefficient, but an alternative finite-difference algorithm is developed in which the transformed equations are solved by Euler's method with a simple shooting technique. Sample calculations are reported for two ternary diffusion problems

It is concluded on the basis of the theoretical and numerical results that the linearized theory predictions should provide an excellent approximation to the exact solution of the penetration model.     

THE EXACT PENETRATION MODEL OF DIFFUSION IN MULTICOMPONENT IDEAL GAS MIXTURES. ANALYTICAL AND NUMERICAL SOLUTIONS

An exact analytical solution is derived for the penetration model of diffusion in multicomponent ideal gas mixtures at constant pressure and temperature. It takes the form of a matrizant solution to the continuity and Maxwell-Stefan equations transformed by introduction of a similarity variable, and includes as special cases the corresponding binary and linearized theory solutions

Direct numerical implementation of the analytical solution is computationally inefficient, but an alternative finite-difference algorithm is developed in which the transformed equations are solved by Euler's method with a simple shooting technique. Sample calculations are reported for two ternary diffusion problems

It is concluded on the basis of the theoretical and numerical results that the linearized theory predictions should provide an excellent approximation to the exact solution of the penetration model.     

3个表征换热器换热特性的变量

引　言换热器广泛应用于制冷、化工及能源等工业生产领域 ,是许多工艺过程必不可少的设备 .换热器换热性能分析评价指标目前已有数十种 ,如温度效率Ｅ、传热单元数ＮＴＵ、可用能流率等[1] .Ｂｅｊａｎ提出以熵产生单元数为换热器性能评价指标[2 ] ,也有学者提出火用效率指标[3,4 ] .但这些多是从换热器设计、选型的角度出发 ,独立考虑某一指标 ,对指导换热器实际经济运行用处不大 ,缺乏实用性 .换热器长期使用中难免会出现玷污、流体温度及流量变化 ,必将改变换热器的换热性能[5,6 ] .这些现象对不同换热器的换热性能影响程度不同 ,有关这…     

UCKRON II TEST PROBLEM THE EFFECTS OF PORE DIFFUSION

The UCKRON I test problem was reworked with the inclusion of diffusional limitations to the kinetics. For this purpose, the rate expressions, i.e. the full kinetic model and the Langmuir-Hinshelwood model, proposed in the previous workshop, were assumed to represent the true kinetics.

A simple mathematical model based on simplified effective diffusivities and the “Dusty-Gas” model were used to take account of pore diffusion resistance within the catalyst particle. These models predicted effectiveness factors based on the reaction at the bulk conditions. The effectiveness factors were then correlated against temperature and the partial pressure of reacting species.

These correlations were then used to predict the temperature profiles within the water cooled plug flow reactor for various values of cooling media temperature.     

MIXING WITH DIFFUSION AND FAST CHEMICAL REACTION IN SIMPLE SHEAR FLOW: A COMPARISON OF STRETCH MODEL TO TWO-DIMENSIONAL DIFFUSION WITH PERIODIC BOUNDARY CONDITIONS

The lamellar stretch model for describing mixing with simultaneous diffusion and fast chemical reaction is evaluated for simple shear flow between two parallel plates by comparing the predicted concentration profiles to those computed from the governing partial differential equation. A direct algorithm is devised to solve the sparse matrix originating from the discretization of the PDE. Under conditions where initial striation thickness equals the characteristic dimension of the flow geometry, the lamellar stretch model turns out to be quite accurate for k ≥ 10⁶ or k ≤ 1, where k is the product of the Reynolds number and the Schmidt number. In the intermediate range of k values, where mechanical and diffusional mixing are of comparable importance, the model is less accurate