Transport model membrane behavior

Liquid crystals are widely believed to be closely related to membranes of living cells and have been used as model systems in studies to understand membrane behavior. Among dynamic processes of interest here are transport of various species across membranes and various motions and deformations of membranes. 

The purpose of a transport model is to mathematically relate performance (typically flux (see Chapter 3.4) of both solvent and solute) to operating conditions (typically pressure and concentration driving forces).1 The objective is to predict membrane behavior under certain conditions. 

Titanium, as an example for the transport model verification, was chosen because of the extensive experimental data available on LLX and membrane separation [1,2,74—76] and of its extraction double-maximum acidity dependence phenomenon [74]. This behavior was observed for most extractant families basic (anion exchangers), neutral (complexants), and acidic (cation exchangers). So, it is possible to study both counter- and cotransport mechanisms at pH > 0.5 and [H] > 7 mol/kg feed solution acidities, respectively, using neutral (hydrophobic, hydrophilic) and ion-exchange membranes. 

A variety of RO membrane models exist that describe the transport properties of the skin layer. The solution-diffusion model( ) is widely accepted in desalination where the feed solution is relatively dilute on a mole-fraction basis. However, models based on irreversible thermodynamics usually describe membrane behavior more accurately where concentrated solutions are involved.( ) Since high concentrations will be encountered in ethanol enrichment, our present treatment adopts the irreversible thermodynamics model introduced by Kedem and Katchalsky.(7.)... 

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. 

Computer simulations of both equilibrium and dynamic properties of small solutes indicate that the solubility-diffusion model is not an accurate approximation to the behavior of small, neutral solutes in membranes. This conclusion is supported experimentally [57]. Clearly, packing and ordering effects, as well as electrostatic solute-solvent interactions need to be included. One extreme example are changes in membrane permeability near the gel-liquid crystalline phase transition temperature [56]. Another example is unassisted ion transport across membranes, discussed in the following section. 

There are a variety of membrane structures available. Correspondingly, the variety of transport expressions or transport models is considerable. The nature and magnitude of the driving forces and the frictional resistances can vary, leading to enormous variations in individual species fluxes. It is not possible to cover the whole spectrum of such behavior here. Rather we focus on a few cases of considerable use in practical separation techniques/processes to illustrate integrated flux expressions for membranes. 

Combined solution-diffusion film theory models have been presented already in several publications on aqueous systems however, either 100% rejection of the solute is assumed or detailed experimental flux and rejection results are required in order to find parameters by nonlinear parameter estimation (Murthy and Gupta, 1997). Consequently, it is difficult to apply these models for predictive purposes. Peeva et al. (2004) presented the first consideration of concentration polarization in OSN. They coupled the solution-diffusion membrane transport model, Eq. (16.4), with film theory to describe flux and rejection of toluene/ docosane and tolune/TOABr binary mixtures. This approach was able to integrate concentration polarization and nonideal solution behavior into OSN design models and predict fluxes over a wide range of solvent mixtures from a limited data set of the pure solvent fluxes. The only parameters to be estimated, other than physical properties, are the mass transfer coefficients, which may be measured, and the permeabUilies, which may... 

Abstract Mathematical modeling is widely used for the design and control of industrial processes and, in particular, membrane processes the approach is based on the formulation of transport models to analyze the transport phenomena occurring in the membrane module as well as within the membrane. However, analysis of such complex behaviors is rather onerous and time consuming for practical purposes and some of the interactions between the fluid and the membrane structure or related to the actual kinetics, in the case of membrane reactors, are not yet completely understood. For these reasons, several simplified approaches have been proposed in the Uterature to describe the behavior of real membrane systems. 

In reality, this behavior is only observed in the limit of small jg. At currents o 1 A cm-2 that are relevant for fuel cell operation, the electro-osmotic coupling between proton and water fluxes causes nonuniform water distributions in PEMs, which lead to nonlinear effects in r/p M- These deviations result in a critical current density, p at which the increase in r/pp j causes the cell voltage to decrease dramatically. It is thus crucial to develop membrane models that can predicton the basis of experimental data on structure and transport properties. 

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