Membrane formation by isothermal precipitation in polyamide-formic acid-water systems II. Precipitation dynamics

An analysis is presented, which describes the isothermal ternary diffusion process encountered in the formation of the aliphatic polyamide membranes such as Nylon-66 by direct immersion-precipitation of a polymeric solution in a nonsolvent bath. A material coordinate is employed to derive the mass transfer equations for the membrane solution. The convective mass transfer in the coagulation bath is taken into account by solving the hydrodynamic boundary layer equations. Diffusion coefficients were measured and used to deduce ternary phenomenological coefficients. The computed results are found to agree with measured precipitation times and with membrane morphologies observed by scanning electron photomicrographs. © 1995 John Wiley & Sons, Inc.     

Mass transfer modeling of asymmetric membrane formation by phase inversion

A derivation is presented of a ternary diffusion model to describe the mass transfer processes associated with the quench bath period of the phase inversion process for membrane formation. The complete governing equations, initial conditions, and boundary conditions in the casting film and coagulation bath are presented. Equations for ternary chemical potentials and diffusion coefficients are consistently based on constant specific volume formulations. The model is applied to the analysis of mass transfer paths and their effects on membrane structure formation. Precipitation times are determined for given sets of conditions by superposing calculated mass transfer paths on the ternary phase diagram and observing when the miscibility gap is crossed. Comparisons are made with an earlier reported study on the membrane-forming system: water-acetone-cellulose acetate (CA). Agreement between predicted and measured precipitation times is found to be excellent. The polymer film composition profile at the moment of precipitation is shown to be a useful indicator of both skin and sublayer structures, allowing distinctions to be made between conditions leading to spongelike and fingerlike morphologies. The influence of model parameters on the mass transfer paths and associated polymer profiles is also discussed.     

Some hydrodynamic boundary layer influences on mass transfer coefficients

As an initial approach to the quantitative understanding of the importance of various components of intestinal' contents as factors in mass transfer resistance, studies have been performed in diffusion cells containing polydimethylsiloxane membranes under circumstances sensitive to the boundary layers. (1) The effect of temperature change on permeability was measured. Under the conditions of the study, demonstration of a clear transition from membrane control to boundary control with rising temperature proved elusive. (2) When membrane thickness was systematically decreased, a gradual transition from membrane to boundary control was demonstrated, yet practical restrictions of the experimental conditions and system limited the degree to which either membrane or diffusion layers could be manipulated into a rate controlling role. (3) The effect of solution viscosity on mass transfer was also studied. Methylcellulose and sucrose were used as polymeric and low molecular weight viscosity inducing agents respectively. It was readily shown that viscosity has a much greater influence on the flux of a permeant through decreased diffusion coefficients than through increased boundary layer thicknesses, as is predicted by diffusional theories.     

Transport of Acids through Polyether-Sulfone Anion-Exchange Membrane

Diffusion dialysis of sulfuric acid and hydrochloric acid into water with a polyether-sulfone anion-exchange membrane was studied. Transport of sulfuric acid and hydrochloric acid through the membrane has been quantified by diffusion coefficients and mass transfer coefficients. The mass transfer coefficients were investigated as a function of the rotational speed of the stirring rate of both sides of the membrane and with different pH ranges. It was observed that the diffusion dialysis seems to be dependent on the rotational speed of the stirrer; in contrast, the membrane mass transfer coefficients are independent of rotational speed, but they are slightly affected by the initial acid concentration in donor phase. Copyright 2001 Academic Press.     

In situ determination of adsorption kinetics of proteins in a finite bath

A method for fast in situ measurement of adsorption kinetics based on a finite bath was developed. We modified the conventional finite bath by replacing the external loop by a dip probe which enables in situ measurement of the concentration change in the contactor. Deposition of adsorbent particles on the reflection surface of the dip probe compromised measurements. Different membranes, a polyamide, a polypropylene and a nylon membrane were tested to protect the internal reflection surface of the dip probe from fouling with adsorbent particles. The nylon membrane provided efficient protection and high mass transfer evaluated by response time experiments. Unspecific adsorption of the model protein on the membrane could also be excluded. To corroborate the measurements of the dip probe the results were compared to a conventional finite bath and to a shallow-bed. The uptake curves for human polyclonal IgG at different concentrationes (0.1-3 g/l) on rProtein A Sepharose FF and MabSelect were used as model system. The effective diffusion coefficients were determined using a pore diffusion model. These values were in good agreement for all methods.     

A distributed parameter diffusion-reaction model for the alcoholic fermentation process

A distributed parameter model is developed for the yeast floc in the alcoholic fermentation process. The model takes into consideration the external mass transfer resistances, the mass transfer resistance through the cellular membrane, and the diffusion resistances inside the floc. The two-point boundary value differential equations for the membrane are manipulated analytically, whereas the nonlinear twopoint boundary value differential equations of diffusion and reaction inside the floc have been approximated using the orthogonal collocation technique. The evaluation of the necessary diffusion coefficients have involved a relatively large number of assumptions because of the present limited knowledge regarding the complex process of diffusion and biochemical reactions in these systems.     

A new modeling of asymmetric membrane formation in rapid mass transfer system

Mass transfer process involved in the immersion precipitation of polyurethane/dimethylformamide (DMF)/water system was investigated. The set of diffusion equations describing the local composition of the membrane solution as a function of space coordinate and time were solved by numerical method, and the composition path in the phase diagram was obtained. Instead of boundary conditions based on the instantaneous equilibrium assumption between membrane solution and coagulation bath, new boundary conditions were set up by using mass transfer formalism at the interface which is especially valid in the condition that the mass transfer rate is extremely rapid. Phase separation phenomena during immersion precipitation were taken into account to continue the calculation after phase separation. The calculated results showed that the chance of phase separation via spinodal decomposition increases with the strength of nonsolvent, addition of nonsolvent to the dope solution, and the use of more hydrophobic polymer. The proposed model is the improvement of the previous works eliminating the equilibrium assumption at the interface and extending the calculation after phase separation.     

Mathematical modeling of controlled-release systems of herbicides using lignins as matrices

The herbicides applied in soils can be easily lost, owing to leaching, volatilization, and bio-and photodegradation. Controlled-release systemsusing polymeric matrices claim to solve these problems. The movement of the herbicides in the soilisalso an important phenomenon to be studied in order to evaluate the loss processes. The development of mathematical models is a relevantrequirement for simulation and optimization of such systems. This study reviews mathematical models as an initial step for modeling data obtained for controlled-release systems of herbicides (diuron, 2,4-dichlorophenoxyacetic acid, and ametryn) using sugarcane bagasse lignin as a polymeric matrix. The release kinetic studies were carried out using several acceptorsystems includinga water bath, soil, and soil-packed columns. Generally, these models take into account phenomena such as unsteady-state mass transfer by diffusion (Fick'slaw) and convection, consumption by several processes, and partitioning processes, resulting in partial differential equations with respect to time and space variables.     

Kinetische Betrachtung der Verteilung von elektrisch neutralen Ionophoren zwischen einer Flüssigmembran und einer wässerigen Phase

Kinetic Study of the Distribution of Electrically Neutral Ionophores between a Solvent Polymeric Membrane and an Aqueous Phase The kinetic behaviour of a series of ligands in the transfer from a solvent polymeric membrane into a stirred aqueous phase was investigated and compared with theoretical kinetic models. It was found that the transfer of ligands with low lipophilicity was controlled by the diffusion in the membrane phase, and that of ligands with high lipophilicity was controlled by the exchange reaction at the phase boundary and/or the diffusion through the unstirred Nernst diffusion layer. The diffusion coefficients in the membrane decrease drastically on increase of the content of the polymer in the membrane and are nearly independent of the size and lipophilicity of the ligand, whereas the overall transfer coefficient through the boudary region does not depend on the polymer content but decreases with increasing lipophilicity of the ionophore.     

Simplified model for extraction of rare-earth ions using emulsion liquid membrane

By considering the resistances of rare-earth ions in both the external and membrane phases, the interfacial reaction and the membrane breakage, a mathematical model for the extraction of rare-earth ions by batch emulsion liquid membrane process is established. Further, two simplified mass transfer equations are also derived from the proposed model in each of the specified cases. The validity of both the model and the resulting equations are tested by batch extraction of Sm³⁺ with emulsion liquid membrane containing di-2-ethylhexyl phosphoric acid as a carrier in kerosene. The experimental results show that both the proposed model and the resulting equations can simulate mass transfer process satisfactorily.     

海藻酸钠-壳聚糖-粉末活性炭生物微胶囊的传递性能研究

测定不同分子量的聚乙二醇(PEG)溶液透过海藻酸钠-壳聚糖-粉末活性炭(SA-CA-PAC)生物微胶囊的性能,确定了SA-CA-PAC膜的截留分子量在PEG4000以下。研究了葡萄糖、乳糖、氨基酸等小分子的物质在SA-CA-PAC微胶囊中的扩散性能,用数学模型计算出了这些物质在微胶囊的混合扩散系数Dm以及相应的微胶囊膜层中扩散系数D1,结果表明小分子量的物质具有较好的扩散性能,且Dl<相似文献   

Diffusion relaxation times of nonequilibrium isolated small bodies and their solid phase ensembles to equilibrium states

The possibility of obtaining analytical estimates in a diffusion approximation of the times needed by nonequilibrium small bodies to relax to their equilibrium states based on knowledge of the mass transfer coefficient is considered. This coefficient is expressed as the product of the self-diffusion coefficient and the thermodynamic factor. A set of equations for the diffusion transport of mixture components is formulated, characteristic scales of the size of microheterogeneous phases are identified, and effective mass transfer coefficients are constructed for them. Allowing for the developed interface of coexisting and immiscible phases along with the porosity of solid phases is discussed. This approach can be applied to the diffusion equalization of concentrations of solid mixture components in many physicochemical systems: the mutual diffusion of components in multicomponent systems (alloys, semiconductors, solid mixtures of inert gases) and the mass transfer of an absorbed mobile component in the voids of a matrix consisting of slow components or a mixed composition of mobile and slow components (e.g., hydrogen in metals, oxygen in oxides, and the transfer of molecules through membranes of different natures, including polymeric).     

Competitive facilitated transport through liquid membranes

A mathematical model is presented which solves the dimensionless, transient, non-linear partial differential equations governing the competitive facilitated transport of two gases through a liquid membrane. The model incorporates the mass transfer coefficients in the boundary conditions for the free gas concentrations. Several studies were carried out. A comparison of this model with a steady-state “equilibrium core” model was excellent. Through varying the dimensionless parameters, it was found that gas I would have a higher steady-state facilitation factor than gas 2 if k₁ >k₂ and k_-1k_-2. The boundary conditions and mass transfer coefficients were also varied to see their effects on the facilitation factors. The idea of pumping one of the gases against its concentration gradient was shown to be theoretically possible.     

Investigation of the concentration dependence of mass transfer coefficients in reversed-phase liquid chromatography

In order to investigate the concentration dependence of mass transfer coefficients in RPLC, experimental breakthrough curves obtained by staircase frontal analysis (FA) were fitted to the simplified models such as multiplate (MP) model, equilibrium dispersive (ED) model, and transport model, and the sophisticated models such as lumped pore diffusion (POR) model and general rate (GR) model. The MP model was used to obtain the initial guesses of the parameters of the ED and the transport models. Then the best values were obtained by minimizing the differences between theoretical and experimental values with a nonlinear fitting procedure. The values of the parameters of the POR and the GR models can be calculated by using the expressions derived from the plate height equations, which was further validated by using the fitting method. It was found that the mass transfer coefficients would depend on the solute concentration. This can be ascribed to the surface diffusivity, which correlates with the concentration and is lumped into the mass transfer coefficients for both simplified and sophisticated models.     

Breaking the limitation of composition change during isothermal mass-transfer processes at the spinodal

A governing equation describing the mass-transfer fluxes in practical membrane formation is derived using Markoffian and Onsager's thermodynamic systems. This equation unambiguously demonstrates that isothermal mass-transfer fluxes at the spinodal composition may not be zero for systems operated in the gravitational field. This study suggests that the mass transfer equations derived by Cheng and Gryte are a special case of the present study and are not fully capable of describing the mass transfer in practical membrane formation. Experimental results published in previous literature qualitatively support our assessment. The limitations of using Markoffian and Onsager's thermodynamic systems for membrane formation study are also reviewed. In conclusion, new thermodynamic theories for polymer solutions are needed to quantitatively describe the mass transfer fluxes in practical membrane formation.     

Complications in the Use of the Taylor Dispersion Method for Ternary Diffusion Measurements: Methanol + Acetone + Water Mixtures

The Taylor dispersion technique is used to measure the ternary mutual diffusion coefficients of aqueous nonelectrolyte solutions at 25°C. The dispersion of the injected solutes is recorded by a differential refractometer and an ultraviolet-visible detector. The diffusion coefficients are calculated directly by fitting the theoretical dispersion equations to about six experimental curves simultaneously. If the ternary diffusion effects in the measured dispersion profiles are not confused by the inaccuracy of the experimental method or an unfavorable relative detector sensitivity, the diffusion coefficients are precise. For the system methanol + acetone + water, it is shown that the Taylor dispersion method is unsuitable for the determination of all the diffusion coefficients if the methanol mole fraction is less than 0.45 or the acetone mole fraction if more than 0.001.     

Modeling of asymmetric membrane formation by dry-casting method

Many polymeric membranes are produced by phase inversion technique invented by Loeb and Sourirajan in 1962. The dry-casting method is one of the major phase inversion techniques in which a homogeneous polymer solution consisting of solvent(s) and nonsolvent(s) is cast on a support and then evaporation of the casting solution takes place under convective conditions. In this paper, we model membrane formation by the dry-casting method. The model takes into account film shrinkage, evaporative cooling, coupled heat, and mass transfer and incorporates practical and reliable diffusion theory as well as complex boundary conditions especially at the polymer solution/air interface. The predictions from the model provide composition paths, temperature, and thickness of the solution. By plotting the composition paths on the ternary phase diagram, we ascertain the general structural characteristics of the membranes prepared from particular casting conditions. The predictive ability of the model was evaluated by comparing the results with the experimental data obtained from gravimetric measurements for cellulose acetate (CA)–acetone–water system. In an attempt to illustrate the importance of diffusion formalism on the predictions, recently proposed multicomponent diffusion theory and its simplified forms were utilized in the model. The computational results show that the critical factor for capturing the accurate behavior of membrane formation is the diffusion formalism utilized in the model.     

Kinetics of thorium(IV) and lanthanum(III) extraction from aqueous salt solutions with composite material based on trialkylamine and polymeric support at various temperatures

The kinetics of thorium(IV) and lanthanum(III) extraction from aqueous salt solutions with a composite material based on trialkylamine and a polymeric support at 293.15–333.15 K was studied. The mass transfer coefficients were found, and the apparent activation energy of the extraction reaction was estimated.