GREEN'S FUNCTION FORMALISM IN GENERALIZED TAYLOR DISPERSION THEORY†

Green's function formalism is applied to obtain the asymptotically long-time solution of the multidimensional, phase-space, convective-diffusion equation governing transport and temporal evolution of the conditional probability density P of a Brownian tracer particle. In the long-time limit, P (as well as its infinite sequence of polyadic moments) is shown to be derivable from a pair of time-independent scalar fields characterizing the local-space transport process. These two functions are employed to obtain the global phenomenological coefficients occurring in the physical-space (global) equation governing the asymptotically long-time, locally-averaged, conditional probability density distribution     

A GENERAL THEORY OF TAYLOR DISPERSION PHENOMENA IV. Direct Coupling Effects

A previous generalized theory of Taylor dispersion phenomena is here extended so as to include “coupling” phenomena. Such direct coupling arises from the fact that—in certain circumstances—global transport processes may be driven by local gradients, and conversely. An obvious example of such direct coupling effects arises in problems pertaining to the gravitational settling and concomitant “sedimentation dispersion” of asymmetric Brownian particles lacking a center of symmetry. In the presence of such asymmetry the parlicle's translational and rotational motions are inseparably coupled to one another. This specific problem will be ueated in a companion paper as an example of the general coupling theory developed herein.     

MULTICOMPONENT LIQUID PHASE ADSORPTION IN BATCH PART I FORMULATION AND DEVELOPMENT OF COMPUTATION ALGORITHMS

Algorithms were developed which can be used to predict the dynamics of multicomponent adsorption in batch. These algorithms were developed on the following bases: (a) the rate of adsorption is controlled by both external and intraparticle diffusion, (b) the intraparticle diffusion is described by either the pore or the surface diffusion models, and (c)the multicomponent adsorption equilibrium behavior can be predicted from the ideal adsorbed solution (IAS)theory. The availability of these algorithms makes it possible to predict concentration histories of batch adsorption processes involving an arbitrarily large number of adsorbates from a minimum amount of base information obtained from single-species adsorption measurements.     

MULTICOMPONENT LIQUID PHASE ADSORPTION IN BATCH PART I FORMULATION AND DEVELOPMENT OF COMPUTATION ALGORITHMS

Algorithms were developed which can be used to predict the dynamics of multicomponent adsorption in batch. These algorithms were developed on the following bases: (a) the rate of adsorption is controlled by both external and intraparticle diffusion, (b) the intraparticle diffusion is described by either the pore or the surface diffusion models, and (c)the multicomponent adsorption equilibrium behavior can be predicted from the ideal adsorbed solution (IAS)theory. The availability of these algorithms makes it possible to predict concentration histories of batch adsorption processes involving an arbitrarily large number of adsorbates from a minimum amount of base information obtained from single-species adsorption measurements.     

MICROWAVE DRYING OF MULTICOMPONENT SOLS

ABSTRACT

Extensive studies on microwave drying of multicomponent materials have been carried out in order to determine dielectric properties of metalsiloxane sols, define the healing and drying characteristics of metalsiloxane sols and gels, develop the mathematical model of thermal processing, and design the continuous microwave dryer that could be used in an industrial scale     

固定化静止酵母细胞的扩散─反应特性的模拟

测定了聚丙烯酰胺包埋酵母的固定化细胞中葡萄糖和乙醇的有效扩散系数，研究了葡萄糖和乙醇对于悬浮静止酵母细胞反应动力学的影响．计算了固定化静止细胞中酵母细胞的存活分数，考察了具有不同细胞包埋量及不同厚度的固定化细胞的反应特性。用组分的有效扩散系数、悬浮细胞的反应动力学及固定化细胞的细胞存活分数很好地模拟了具有内扩散影响的固定化细胞的反应结果。     

低分子量中性溶质体系的纳滤膜的透过特性

根据浓差极化模型和非平衡热力学模型,对４种品牌的纳滤膜（ＮＦ４０膜、ＮＴＲ７４５０膜、Ｄｅｓａｌ５膜和Ｇ２０膜）在醇类和糖类中性溶质体系的透过实验数据进行回归计算,求得膜定数（即膜的反射系数和溶质透过系数）,再由这些膜定数结果根据细孔模型估算了４种品牌的纳滤膜的细孔结构参数,这４种膜的细孔半径范围在０．４～０．８ｎｍ。结果讨论表明细孔模型适用于纳滤膜的结构评价。     

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.     

MULTICOMPONENT LIQUID PHASE ADSORPTION IN BATCH PART II EXPERIMENT ON CARBON ADSORPTION FROM SOLUTIONS OF PHENOL,O-CRESOL,AND 2,4-DICHLOROPHENOL

Experiments were conducted on carbon adsorption from solutions of phenol, o-cresol, and 2,4-dichlorophenol in various combinations. The equilibrium data were found in general agreement with predictions based on the ideal adsorbed solution (IAS) theory. The kinetic measurements suggest that the adsorption process can be described by the film-surface diffusion (FSD) model. By using the algorithms developed in Part I and based on the rate and equilibrium data obtained from single adsorbate adsorption measurements, concentration histories of the individual adsorbate of carbon adsorption from solutions containing phenol, o-cresol and 2,4-dichlorophenol can be predicted with sufficient accuracy.     

MULTICOMPONENT LIQUID PHASE ADSORPTION IN BATCH PART II EXPERIMENT ON CARBON ADSORPTION FROM SOLUTIONS OF PHENOL, O-CRESOL, AND 2,4-DICHLOROPHENOL

Experiments were conducted on carbon adsorption from solutions of phenol, o-cresol, and 2,4-dichlorophenol in various combinations. The equilibrium data were found in general agreement with predictions based on the ideal adsorbed solution (IAS) theory. The kinetic measurements suggest that the adsorption process can be described by the film-surface diffusion (FSD) model. By using the algorithms developed in Part I and based on the rate and equilibrium data obtained from single adsorbate adsorption measurements, concentration histories of the individual adsorbate of carbon adsorption from solutions containing phenol, o-cresol and 2,4-dichlorophenol can be predicted with sufficient accuracy.     

Characterization and modelling of diffusion and reaction of low molecular weight reactants in molten polymer

A model reactive system was defined for studying experimentally and by simulation the competition between reaction and diffusion of two low molecular weight reactants, 2,3-epoxypropyl-phenylether (EPPE) and dipentylamine (DPA). Both reactants are miscible in a high-viscous molten polymer, poly(ethylene-co-vinyl acetate) (EVA). The comparison of the experimental rates of reaction for initially homogeneous samples and bi-layer unpremixed samples proved that the reaction was diffusion controlled. A kinetic model of the epoxy-amine reaction was coupled to mutual diffusion coefficients of reacting species in a transport model and the simulations were compared with experimental results. The diffusion/reaction process was finally related to typical mixing conditions encountered in reactive polymer processes. For the model reactive system, the simulations have established that actual mixing conditions with shear rate values encountered in polymer processing machines, were able to homogenize the system in less than 10 s. In other words, the reaction should no longer be controlled by molecular diffusion as soon as a relatively low intensity mixing is applied (shear rate > 10 s⁻¹).     

Rheological study of mixing in molten polymers: 2-mixing of reactive systems

Three reactive polymer systems have been examined with a new mixing device adapted on a classical rheometer in order to investigate reactive mixing situations encountered in polymer blends. After having characterized the bulk polymerization of ε-caprolactone (ε-CL), the polymerization of 40 wt% of ε-caprolactone into a copolymer of ethylene and vinyl acetate (EVA) was run into the rheo-mixer. The kinetics of the reaction in dispersed media was observed slightly different from that in bulk since the characteristic time of ε-caprolactone diffusion into EVA is much lower than its time of mixing. On the other hand, it was observed that the molecular weight distribution of the poly(ε-caprolactone) is broader in dispersed media (I_p=2.6) than in bulk (I_p=1.6). A broadening of the molecular weight distribution in dispersed media was pointed out due to the fact that ε-CL monomer is partitioned between the EVA and PCL phases leading to a non-homogeneous concentration of monomer in the reactive phase.The polycondensation of 40 wt% of a epoxy-amine system into a polystyrene matrix was also investigated and the morphology of the resulting material examined. A gradient of structure and conversion was detected in a blend obtained from the assembly of two initially non-reactive layers. The gradient reveals that the amine diffuses faster than the epoxy leading to non-stoichiometry of the reactive functions across the sample. When the blend was polymerized under shear, the kinetic of the reaction remained unchanged regardless the level of shear. However, the morphologies were significantly different, pointing out the importance of the coalescence and droplet deformation phenomena. Spherical droplets were observed at 0.15 s⁻¹, elongated droplets and fibers at 1.5 and 15 s⁻¹.     

DESORPTION CURVES AND TRANSPORT PROPERTIES OF POLYMERS

The desorption of hydrocarbons in LDPE film is analyzed with the help of a continuous-random-walk model. It is shown that for obtaining the mechanical relaxation modulus of the sample, one has to know the complete desorption curve. The existence of a universal desorption is suggested by the normalized desorption curves for the investigated systems.     

ADSORPTION OF ORGANIC SOLUTES INTO ACTIVATED CARBONS-BATCH STUDIES

In this paper, a new model is proposed for the adsorption of organic solutes into solids having a bimodal pore size distribution. This model takes into account, the pore and surface diffusion in the macropore and also the adsorption capacities in both macropore and micropore. The model equations are solved numerically (Crank-Nicholson) and in special cases, the asymptotic solutions for micropore uptake control and macropore uptake control are presented. This model is applied to data obtained by Peel, Benedek and Crowe (1981) and is shown to describe the experimental data well. It has been observed that surface diffusion plays a significant role in the adsorption of phenol on activated carbon.