Diffusion distribution between phases

The distribution of a charged species between two bulk phases, regardless of their composition, is determined by the electrochemical potential38 of the species, jx. The gradient of the electrochemical potential of a species drives its diffusive transfer between phases, and equilibrium with respect to this transfer is described by the equality ... 

The development of surface charge at the interface between soil particles and the soil solution is a reflection of inhomogeneities in the molecular environment of the interface, as discussed in Sec. 3.1. These molecular inhomogeneities also influence the thermodynamic properties of both the charged species in the soil particles and those in the soil solution. In particular, the distribution of a charged species between the two bulk phases, regardless of their composition, is determined by the electrochemical potential of that species, jx. The gradient of the electrochemical potential of a species drives its diffusive transfer between phases, and equilibrium with respect to this transfer is described by the equality... 

The only potential that varies significantly is the phase boundary potential at the membrane/sample interface EPB-. This potential arises from an unequal equilibrium distribution of ions between the aqueous sample and organic membrane phases. The phase transfer equilibrium reaction at the interface is very rapid relative to the diffusion of ions across the aqueous sample and organic membrane phases. A separation of charge occurs at the interface where the ions partition between the two phases, which results in a buildup of potential at the sample/mem-brane interface that can be described thermodynamically in terms of the electrochemical potential. At interfacial equilibrium, the electrochemical potentials in the two phases are equal. The phase boundary potential is a result of an equilibrium distribution of ions between phases. The phase boundary potentials can be described by the following equation ... 

Contaminant volatilization from subsurface solid and aqueous phases may lead, on the one hand, to pollution of the atmosphere and, on the other hand, to contamination (by vapor transport) of the vadose zone and groundwater. Potential volatihty of a contaminant is related to its inherent vapor pressure, but actual vaporization rates depend on the environmental conditions and other factors that control behavior of chemicals at the solid-gas-water interface. For surface deposits, the actual rate of loss, or the pro-portionahty constant relating vapor pressure to volatilization rates, depends on external conditions (such as turbulence, surface roughness, and wind speed) that affect movement away from the evaporating surface. Close to the evaporating surface, there is relatively little movement of air and the vaporized substance is transported from the surface through the stagnant air layer only by molecular diffusion. The rate of contaminant volatilization from the subsurface is a function of the equilibrium distribution between the gas, water, and solid phases, as related to vapor pressure solubility and adsorption, as well as of the rate of contaminant movement to the soil surface. 

The CPC present in the aqueous phase is distributed between the aqueous and organic phases at the SLM-liquid interface. By maintaining low Cl ion concentration in the feed phase and high Cl ion concentration in the stripping phase, the distribution ratio of CPC (P ion form) at the aqueous feed-SLM interface can be made much higher than that at the aqueous strip-SLM interface. Under this condition, the steady-sate overall CPC flux across the membrane can be obtained from Pick s distribution law applied to aqueous diffusion film as well as the membrane itself and from interfacial reaction kinetics which describe the interfacial flux. 

In Chapter 3 we found that all relative transport processes, whether induced by external fields or diffusion, proceed at a rate inversely proportional to the friction coefficient /. Since virtually all separation methods require a certain level of completion of transport, or a certain number of transport steps, the time scale of the separation is linked to the time scale of the required transport both ultimately hinge on the magnitude of /. This conclusion is valid whether one is using methods such as chromatography where the transport processes must maintain the distribution of components between phases at a point near equilibrium, or electrophoresis where transport proceeds only fractionally to equilibrium. 

An experimental test to verify the absence of significant concentration gradients inside the catalyst pellet is based on the inverse proportional relation between the effectiveness factor and the pellet diameter for strong internal diffusion limitations. Hence, a measured rate which is independent of the pellet size indicates that internal diffusion limitations can be neglected. Care should be taken to avoid artifacts. External heat transfer effects also depend on pellet size and for exothermic reactions might compensate the internal diffusion limitations. If the catalyst pellet consists of a support with an non-uniformly distributed active phase, crushing and sieving to obtain smaller pellets is hazardous. 

Adamson (51) proposed a model for W/0 microemulsion formation in terms of a balance between Laplace pressure associated with the interfacial tension at the oil/water interface and the Donnan Osmotic pressure due to the total higher ionic concentration in the interior of aqueous droplets in oil phase. The microemulsion phase can exist in equilibrium with an essentially non-colloidal aqueous second phase provided there is an added electrolyte distributed between droplet s aqueous interior and the external aqueous medium. Both aqueous media contain some alcohol and the total ionic concentration inside the aqueous droplet exceeds that in the external aqueous phase. This model was further modified (52) for W/0 microemulsions to allow for the diffuse double layer in the interior of aqueous droplets. Levine and Robinson (52) proposed a relation governing the equilibrium of the droplet for 1-1 electrolyte, which was based on a balance between the surface tension of the film at the boundary in its charged state and the Maxwell electrostatic stress associated with the electric field in the internal diffuse double layer. 

Transport of solutes through the LM occurs by either passive transport or by carrier-facilitated transport. Phenol, for example, is soluble in both phases, and treatment of an aqueous phenol solution with an emulsion results in a lowering of the external concentration of phenol as it passively diffuses through the hydrocarbon (HC) layer and into the internal aqueous phase. Equilibrium is reached when the concentrations of phenol in both aqueous solutions are equal (assuming no other conditions are present which would alter the distribution between the aqueous and HC phases). One way to alter this equilibrium is to trap phenol inside with a sodium hydroxide solution. Phenol ionizes at high pH, and the phenolate ion cannot permeate a HC layer trace amounts of phenol have been completely removed from wastewaters by this system (10, 11). This exclusion of charged molecules by the aliphatic hydrocarbon LM layer is desirable in some applications, but to employ LM enzyme reactors and/or separation systems with amino acids, it is necessary to incorporate carriers into the HC phase. 

A detailed investigation of the effect of micellar solubilization on the transport of lipids has been made by Westergaard and Dietschy [59]. They studied in vitro uptake of lipids into rabbit intestinal disks by varying the proportions of lipid and bile salts in mixed micelles in 3 different ways. Either lipid concentration was increased with bile salts kept at a constant level, lipid concentration was unchanged while bile salt concentration was varied, or both lipid and bile salt concentration was increased with the molar ratio kept constant. Theoretical calculations of how the mass of the lipid probe was distributed between the aqueous and the micellar compartment showed that there was a good correlation between calculated aqueous monomer concentration and experimentally obtained values for lipid uptake. The rate of uptake is thus proportional to the aqueous monomer concentration of a particular lipid. The conclusion drawn was that diffusion of the lipid molecules in monomeric form through the aqueous phase is an obligatory step before uptake into the plasma membrane, and that the role of bile salt is therefore to overcome the resistance of the unstirred water layer by micellar solubilization. 

The interaction of solute molecules with the ion-exchange stationary phase can be regarded as a sequential two-step process. Initially the solute must diffuse from the mobile phase (usually aqueous) into the stationary phase (often organic). The distribution between the two phases is largely responsible for the retention of a particular solute. Secondly, the solute must interact with, and diffuse through, the stationary phase. 

When the reactants are present in two different phases, one of them must diffuse from its phase into the other for reaction to occur there. If the distribution coefficients of the two reactants do not favor any particular phase, the reaction can occur in both phases, particularly if both are liquid. Clearly, therefore, in general the rates of mass transfer of reactants between phases becomes an important consideration in heterogeneous systems. 

Because two-liquid films are present here, two terms appear for each component, one for phase 1 and the other for phase 2. The distinction between them is explained in Figure 15.1. i is the concentration of A in phase 1, and [>4]j ( the concentration oFA in phase 1 at the interface D 2 refers to the diffusion of A in the phase containing B, phase 2, and Z)b,i to the diffusion of B in the phase containing A, phase 1 and mg are the distribution coefficients of A and B, respectively, between phases 1 and 2 and k[ i2 and are the mass transfer coefficients shown in the figure. 

Diffusion across membranes is hindered for very large molecules (> 9.5 A). Transport to the target site involves partitioning between phases of different lipophilicity, hence the rate constants for the partitioning processes are related to log by different LFERs that may counteract to different extents (differences in kinetics of transport and distribution). 

---