Liquid membranes numerical model

A mathematical model to be solved numerically has been developed and used to predict the separation effects caused by nonstationary conditions for a liquid membrane transport. Numerical calculations were made to compute pertraction characteristics such as input and output membrane selectivity (ratio of respective fluxes), concentration profiles for cations bound by a carrier in a liquid membrane phase, and the overall separation factors. These quantities are discussed as dependent... 

Wodzki R, Szczepanska G, and Szczepanski P. Unsteady state pertraction and separation of cations in a liquid membrane system Simple network and numerical model of competitive M /H counter-transport. Sep Purif Technol, 2004 36(1) 1-16. 

Theoretical models (analytical and numerical), developed for simulation of the BOHLM and BAHLM transport kinetics, are based on independent experimental measurements of (a) individual mass-transfer coefficients of the solutes in boundary layers and (b) facilitating parameters of the liquid membrane (LMF potential) and lEM potential in the case of ion-exchange membrane (lEM) application. Satisfactory correlation between experimental and simulated data is achieved. 

Advancing front model and three reversible reaction models were applied to describe 2-chlorophenol permeation from aqueous solutions [47]. The numerical implementation seemed more stable in the Bunge and Noble [8] model than in reversible reaction models that allowed changes of effective diffusivity with solute concentration in membrane phase, although results were quite similar for the three models. Kargari et al. [48] studied the selective separation of gold(III) ions from acidic aqueous solutions, using MIBK as carrier and LK-80 as emulsifier. They found only Au + ions is transported across the liquid membrane and nearly all (Pd2+, Cu2+, and Fe ) of other ions remained in the external... 

Emulsion Liquid Membranes. Emulsion liquid membranes have been modeled by numerous researchers. Chan and Lee (77) reviewed the various models. The simplest representation characterizes the emulsion globule (membrane phase) as a spherical shell of constant thickness surrounding a single Internal phase droplet. This representation Is equivalent to assuming that the membrane and internal phase are well mixed. In practice, this Is usually a poor assumption. 

Models Considering Membrane and Liquid Film Diffusion. Models considering membrane and liquid film diffusion are quite complex as they are of second order in nature, and the solution to these models require numerical analysis or a method of moments due to their complexity (Sobotka et al., 1982). Linek et al. (1985), Ruchti et al. (1981), and Dang et al. (1977) suggested that while these models are more complex and involved, their solutions are much superior to any first-order model. However, due to their complexity, they are typically not used and the reader is referred to the literature for more information concerning these models. 

In addition, the numerical models can be used in order to understand the overall effect of CO poisoning on other transport phenomena, such as liquid water transport. In a study by Wang and Chu [24], they developed a transient, one-dimensional, two-phase numerical model of the electrolyte membrane and anode and cathode catalyst layers. Their model was used to look into the effect of CO poisoning on the water distribution in the catalyst layers and the electrolyte membrane. With 100% H2 (i.e., the hydrogen feed was not dilute), 10 ppm CO level, and a cell voltage of 0.6 V, they investigated the liquid water saturation in the catalyst layers and the water content in... 

Mass transfer in emulsion liquid membrane (ELM) systems has been modeled by six differential and algebraic equations. Our model takes into account the following mass transfer of the solute across the film between the external phase and the membrane phase chemical equilibrium of the extraction reaction at the external phase-membrane interface simultaneous diffusion of the solute-carrier complex inside globules of the membrane phase and stripping of the complex at the membrane-internal phase interface and chemical equilibrium of the stripping reaction at the membrane-internal phase interface. Unlike previous ELM models fi om which solutions were obtained quasi-analytically or numerically, the solution of our model was solved analytically. Arsenic removal fi om water was chosen as our experimental study. Experimental data for the arsenic concentration in the external phase versus time were obtained. From our analytical solution with parameters estimated independently, we were able to obtain an excellent prediction of the experimental data. 

Numerous commercial oxygen analysers are available, based on the principle of the Hersch cell, but all being protected from the analyte medium, either gaseous or liquid, by means of a membrane (usually Teflon). This membrane detector is known as the Clark cell (see later under membranes as measurement aids, p. 352) for gas analysis we may mention the Beckman Models 715 (also for liquids), 741, 743 (for flue gas), 755 and 778119. 

In the 1970s, the fluid mosaic concept emerged as the most plausible model to account for the known structure and properties of biological membranes [41]. The fact that membranes exist as two-dimensional fluids (liquid disordered) rather than in a gel state (solid ordered) was clearly demonstrated by Frye and Ededin [42], who showed that the lipid and protein components of two separate membranes diffuse into each other when two different cells were fused. Since that time, numerous studies have measured the diffusion coefficient of lipids and proteins in membranes, and the diffusion rates were found to correspond to those expected of a fluid with the viscosity of olive oil rather than a gel phase resembling wax. 

In Chapter 2 we discussed a number of studies with three-phase catalytic membrane reactors. In these reactors the catalyst is impregnated within the membrane, which serves as a contactor between the gas phase (B) and liquid phase reactants (A), and the catalyst that resides within the membrane pores. When gas/liquid reactions occur in conventional (packed, -trickle or fluidized-bed) multiphase catalytic reactors the solid catalyst is wetted by a liquid film as a result, the gas, before reaching the catalyst particle surface or pore, has to diffuse through the liquid layer, which acts as an additional mass transfer resistance between the gas and the solid. In the case of a catalytic membrane reactor, as shown schematically in Fig. 5.16, the active membrane pores are filled simultaneously with the liquid and gas reactants, ensuring an effective contact between the three phases (gas/ liquid, and catalyst). One of the earliest studies of this type of reactor was reported by Akyurtlu et al [5.58], who developed a semi-analytical model coupling analytical results with a numerical solution for this type of reactor. Harold and coworkers (Harold and Ng... 

The principal object of electrochemical interest is given by another type of electrified interface, contacts of an electronic (liquid or solid metal, semiconductor) and an ionic (liquid solution, SEs, membranes, etc) conductor. For numerous contacts of this kind, one can ensure such ionic composition of the latter that there is practically no dc current across the interface within a certain interval of the externally apphed potential. Within this potential interval the system is close to the model of an ideally polarizable interface, the change of the potential is accompanied by the relaxation current across the external circuit and the bulk media that vanishes after a certain period. For sufficiently small potential changes, d , the ratio of the integrated relaxation current, dQ, to dE is independent of the amplitude and it determines the principal electrochemical characteristics of the interface, its differential capacitance per unit surface area, C ... 

Shirazian, S., Moghadassi, A., Moradi, S. 2009. Numerical simulation of mass transfer in gas-liquid hollow fiber membrane contactors for laminar flow conditions. Simul. Model. Pract. Theory 17 708-718. 

The phase behavior and morphology of phase-separated polymer blends play a vital role in the design of membrane transport properties (Robeson 2010). Numerous applications of polymeric membranes involving gas and liquids are known. Although different transport models have been utilized successfully to relate morphology with transport properties, there is enough room for improvements as membrane applications continue to grow in such areas as gas separation. 

---