Liquid-membrane equilibrium

There are two aspects to liquid-membrane equilibrium. The first one is concerned with the osmotic equilibrium between two solutions on two sides of a semipermeable membrane permeable to the solvent and impermeable to the solute the second one covers partitioning of the solute between the solution and the membrane. Both porous and nonporous membranes are of interest. The second aspect is also useful for porous sorbent/gel particles. 

If the membrane happens to be porous (or microporous) and uncharged, the nature of the liquid-membrane equilibrium will be determined by the relative size of the solute molecules with respect to the pore dimensions in the absence of any specific solute-pore wall interaction. Similar considerations are also valid for liquid-porous sorbent equilibria. If the solute dimensions are at least two orders of magnitude smaller, then the solute concentration in the solution in the pore should be essentially equal to that in the external solution. However, the solute concentration in the porous membrane/porous sorbent/gel will be less than that in the external solution due to the porosity effect. Assuming that the solute exists only in the pores of the memhrane/porous sorbent with a porosity e , the value of kirn should be equal to the membrane or sorbent porosity e if the solute characteristic dimensions are at least two orders of magnitude smaller than the radius of the pore. 

Pervaporation. Pervaporation differs from the other membrane processes described so far in that the phase-state on one side of the membrane is different from that on the other side. The term pervaporation is a combination of the words permselective and evaporation. The feed to the membrane module is a mixture (e.g. ethanol-water mixture) at a pressure high enough to maintain it in the liquid phase. The liquid mixture is contacted with a dense membrane. The other side of the membrane is maintained at a pressure at or below the dew point of the permeate, thus maintaining it in the vapor phase. The permeate side is often held under vacuum conditions. Pervaporation is potentially useful when separating mixtures that form azeotropes (e.g. ethanol-water mixture). One of the ways to change the vapor-liquid equilibrium to overcome azeotropic behavior is to place a membrane between the vapor and liquid phases. Temperatures are restricted to below 100°C, and as with other liquid membrane processes, feed pretreatment and membrane cleaning are necessary. 

Figure 8.21. Comparison of selectivity of pervaporation membranes and liquid-vapour equilibrium for...

In conclusion, it should be mentioned that extraction parameters (the equilibrium constants of exchange reactions and ion-pair stabilities) were introduced into the theory of ion-selective electrodes in [2, 31,33, 34, 35,69]. The theory of ISEs with a liquid membrane and a diffusion potential in the membrane was extended by Buck etal. [11, 13, 14, 73, 74] and Morf [54]. 

We now come to internal metal contacts in ISEs without an internal solution. As discussed above, systems without internal electrolytes are used very often, with both solid and liquid membranes. Obviously, the condition of thermodynamic equilibrium requires that common electrically-charged particles (ions or electrons) be present in electrically-charged phases that are in contact (see chapter 2). ISEs with a silver halide membrane to which a silver contact is attached are relatively simple. In the system... 

The previous chapters dealt with ISE systems at zero current, i.e. at equilibrium or steady-state. The properties of the interface between two immiscible electrolyte solutions (ITIES), described in sections 2.4 and 2.5, will now be used to describe a dynamic method based on the passage of electrical current across ITIES. Voltammetry at ITIES (for a survey see [3, 8, 9, 10, 11, 12,18]) is an inverse analogue of potentiometry with liquid-membrane ISEs and thus forms a suitable conclusion to this book. 

Inspection of Eq. (13.6) shows that the selectivity behavior of a liquid membrane is specified completely by the membrane selectivity constant, Ky, which in turn is dependent on the equilibrium constant of Eq. (13.5) and on the mobility of ions i and j within the membrane. For the case in which the membrane consists of a neutral carrier [129], the exchange reaction can be presented as ... 

The main advantage of this process becomes clear when applying Eq. (15.1) to the three-phase system. As the liquid membrane phase does not accumulate the solute, the distribution ratio that is relevant to the efficiency of this process is that between phases 1 and 3. At equilibrium, this equation applies to both pairs of phases 2-1 and 3-2 ... 

In order to develop the liquid membrane techniques, i.e., emulsion Hquid membrane (ELM), supported liquid membrane (SLM), non-dispersive extraction in hollow fiber membrane (HFM), etc., for practical processes, it is necessary to generate data on equilibrium and kinetics of reactive extraction. Furthermore, a prior demonstration of the phenomena of facilitated transport in a simple liquid membrane system, the so-called bulk liquid membrane (BLM), is thought to be effective. Since discovery by Li [28], the liquid membrane technique has been extensively studied for the separation of metal ion, amino acid, and carboxyHc acid, etc., from dilute aqueous solutions [29]. 

Figure 19.3 schematically describes in more detail the transport phenomena occurring during pervaporation. First, solutes partition into the membrane material according to the thermodynamic equilibrium at the liquid-membrane interface (Fig. 19.3a), followed by diffusion across the membrane material owing to the concentration gradient (Fig. 19.3b). A vacuum or carrier gas stream promotes then continuous desorption of the molecules reaching the permeate side of the membrane (Fig. 19.3c), maintaining in this way a concentration gradient across the membrane and hence a continuous transmembrane flux of compounds.

This development, of course, says nothing about the metal ion flux across the membrane under non-equilibrium conditions this is described by Fick s law. At steady state, the flux jMRn, in mol/cm2 s, of metal complex MR, across the liquid membrane is given by... 

Because some of the reactions involved in establishing equilibrium at the membrane surface are slow compared to diffusion, the calculated concentration gradients formed in the liquid membrane do not have a simple form. The equations for partial reaction rate control have been derived by Ward and Robb [23],... 

Liu, J.-F., J.A. Jonsson, and P. Mayer. 2005. Equilibrium sampling through membranes of freely dissolved chlorophenols in water samples with hollow fiber supported liquid membrane. Anal. Chem. 77 4800M-809. ... 

Romero, R. and J.A. Jonsson. 2005. Determination of free copper concentrations in natural waters by using supported liquid membrane extraction under equilibrium conditions. Anal. Bioanal. Chem. 381 1452-1459. 

The pore size distribution or its mean value of a porous inorganic membrane can be assessed by a number of physical methods. These include microscopic techniques, bubble pressure and gas transport methods, mercury porosimetry, liquid-vapor equilibrium methods (such as nitrogen adsorption/desorption), gas-liquid equilibrium methods (such as permporometry), liquid-solid equilibrium methods (thcrmoporometry) and molecular probe methods. These methods will be briefly surveyed as follows. 

The above quantities are accessible by standard measurements of liquid membrane transport and are frequently reported in the corresponding literature. To emphasize the kinetic source of separations studied, all computations have been carried out after assuming the same equilibrium constants for cation-exchange reactions appearing in the pertraction system, i.e.. 

Uddin MS and Kathiresan M. Extraction of metal ions by emulsion liquid membrane using bi-functional surfactant equilibrium and kinetic studies. Sep Purif Technol 2000 19 3-9. 

As far as the spread molecules are concerned, the system is closed in the thermo-d5mamic sense, (even if colloquially these substances are referred to as surfactants ). Upon compression or expansion they cannot leave or enter the monolayer because they are insoluble in the liquid (although we continue calling it solvent or water ). This layer is, via a barrier, separated from a surface that does not contain surfactants. However, water molecules and molecules dissolved in it, including electrolytes, can pass underneath the barrier, so for these components the system is open. The ensuing stationary state is a typical example of a membrane equilibrium, that is an equilibrium between two phases when (at least) one of the components is present in one of the phases only (sec. 1.2.12). 

Liquid membrane separation is a rate process and the separation occurs due to a chemical potential gradient, not by equilibrium between phases. 

The solute transport is driven by solute concentration gradient, by Liquid membrane facilitation potential (LMF), K, and by Donnan equilibrium coupling, Kj. is denoted as an internal LM carrier driving force coefficient, derived from extraction distribution constants for solute between... 

Bhavani, R., Neena, T. and John, W. (1994). Emulsion liquid membranes for waste-water treatment Equilibrium models for some typical metal-extractant systems. Environ. Sci. Technol., 28, 1090-8. 

A mathematical model to be solved numerically has been developed and used to predict the separation effects caused by nonstationary conditions for a bulk liquid membrane transport. Numerical calculations compute such pertraction" characteristics 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 all being dependent on time. The computations of fluxes and separation factors as dependent on time have revealed high separation efficiency of unsteady-state pertraction as compared with steady or near-steady-state process (with reactions near equilibrium). 

Inclusion of this technique to the BOHLM has to be explained. Solvent extraction or partition of the solute between two immiscible phases is an equilibrium-based separation process. So, the membrane-based or nondispersive solvent extraction process has to be equilibrium based also. Liquid membrane separation is a rate process and the separation occurs due to a chemical potential gradient, not by equilibrium between phases [114]. According to these definitions, many authors who refer to their works as membrane-based or nondispersive solvent extraction processes are not correct. 

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