Resistance In Series Model Research Articles

Membrane-based solvent extraction and stripping of lactate in hollow-fibre contactors

This work reports lactate extraction with Aliquat 336, an ion-exchange carrier, using membrane contactors with hydrophobic microporous membranes. The overall mass-transfer coefficients were evaluated by either assuming a constant distribution coefficient or using the equilibrium equation. The mass-transfer coefficients calculated using the equilibrium relationship between C f ∗ and C O, proved to be more rigorous, since the variation of the distribution coefficient with solute concentration is accounted for throughout the extraction process. Assuming the resistance in series model, the membrane resistance was identified as the limiting step on the mass-transfer process. In order to increase the membrane mass-transfer coefficient, it is necessary to increase the diffusion coefficient of the lactate-amine complex; this can be achieved by reducing the viscosity of the organic phase either through a temperature increase or reduction of the carrier concentration. Using a plate-and-frame module with a well-defined hydrodynamic characterization of both phases, the mass-transfer coefficients can be rigorously evaluated; these were compared with the values obtained with hollow-fibre modules. Simultaneous extraction and stripping of lactate was accomplished using two hollow-fibre modules in series. This configuration assures that saturation of the carrier does not occur, as it is permanently regenerated; furthermore, the carrier concentration can be reduced while still maintaining the mass-transfer rate, thus decreasing the associated operating costs of the process.

Gas permeation through poly(dimethylsiloxane)-plasma polymer composite membranes

The permeation of CO 2, O 2, N 2, and CH 4 through composite membranes consisting of poly(dimethylsiloxane) (PDMS) substrates coated with fluorine rich plasma polymers was studied. Measurements were made with different thicknesses of plasma polymer (0 to 1 μm) and at different temperatures between 35 and 75°C, which allows us to determine the permeability coefficients and permeation activation energies of each layer. The results are compared to a simple resistance in series permeation model. For CH 4 and N 2 the permeabilities of the composite membranes deviate from the resistance in series model. This is most likely due to plasma modification of the PDMS surface during the early stages of plasma polymerization.

A cross-flow microfiltration model based on integration of the mass transport equation

The two opposite fluxes which lead to the build-up of a filtration cake have been studied in the case of the cross-flow microfiltration process. The back transport of particles was estimated according to the mechanism of shear induced diffusion. Mass balancing, associated with the resistance in series model, gave a differential equation which was integrated formally versus time. The result was an expression for the permeate flow that takes into account the operating parameters (transmembrane pressure and tangential flow velocity) and the suspension properties (the radius of particles, the concentration of the solution and the specific resistance of the cake). Experiments have been performed with baker's yeast suspended in a saline solution in order to validate this model.

Aqueous-aqueous extraction of organic pollutants through tubular silicone rubber membranes

The extraction of organic pollutants from one dilute aqueous solution to another dilute aqueous solution through silicone rubber membranes has been investigated. Overall mass transfer coefficients have been measured using a single membrane tube held in a glass module, and have been described using a resistances in series model. This has allowed the relative contributions of the liquid film boundary layer resistances and the membrane resistance to be elucidated, and has shown that both liquid film resistances and permeation through the membrane itself can limit the overall extraction rate. Under some conditions the membrane resistance can become negligible relative to the liquid film resistances. An important parameter for determining the magnitude of the membrane resistance is the membrane/aqueous phase partition coefficient, K. This parameter can be estimated from the Hildebrand solubility parameter of an organic compound, or quickly ascertained by performing a set of simple adsorption experiments.

Flux decline behaviour with low molecular weight solutes during ultrafiltration in an unstirred batch cell

Experimental studies were carried out on the flux decline behaviour of various solutes during ultrafiltration (UF) in an unstirred batch cell. A theoretical model was developed to predict the flux decline pattern during UF using the integral model as well as the resistance in series model. The model was found to predict the flux profiles during UF of low and high molecular weight solutes quite accurately. The model was further compared to other theories from literature which showed departure for the case of low molecular weight solutes. The model describes the UF flux behaviour of PEG-6000 as well as that of PVA in an unstirred batch cell. Thus, it may serve to predict the limiting flux phenomena during UF of low molecular weight solutes as well as that of high molecular weight solutes. These predictions may be useful in modelling the UF system. It was found that for high molecular weight solutes, a gel-layer was formed after some finite time. The model was tested with experimental flux values at high pressures for different solutes [black liquor, polyethyleneglycol and poly (vinyl alcohol)] and the results were found to be in good agreement.

Flux-based measures of adsorption to ultrafiltration membranes

This paper discusses models of membrane and adsorbed layer resistances which are commonly used to describe changes in permeability due to ultrafiltration or static exposure of the membrane surface to protein solutions. A comparison is made between resistances in a series model, and in “interacting” models. In the former, the additional fouling resistance is independent of initial membrane resistance. The models are tested on previously published data [1] on permeability and adsorption isotherms of the DDS GR61PP membrane using a whey protein mixture and individual whey proteins. Making use of the variability of initial membrane resistances, regression analysis shows that the resistances in series model is not appropriate for the data.