Water activity gradient

Equation (2.37) is simplified by assuming that the membrane selectivity is high, that is, DiK jl DjKj/ . This is a good assumption for most of the reverse osmosis membranes used to separate salts from water. Consider the water flux first. At the point at which the applied hydrostatic pressure balances the water activity gradient, that is, the point of osmotic equilibrium in Figure 2.6(b), the flux of water across the membrane is zero. Equation (2.37) becomes... 

It is now appreciated that the water activity gradient within the SC and the water flux through this tissue at rest and following damage, are intimately involved in several aspects of tissue homeostasis, notably in relation to water barrier repair.71 However, the observations on the control of filaggrin catabolism, originally made over 25 years ago, represent some of the earliest studies to demonstrate and emphasize the dynamic nature of SC maturation. 

Diffusion of Water in poly[PFSA] Membranes To describe diffusion of water through the membrane in the presence of a water activity gradient, an appropriate interdiffusion coefficient must be determined. Experimental methods used to study diffusion of water in these polymers, such as radiotracer and pulsed gradient spin-echo NMR techniques, probe intrad-iffusion coefficients, often referred to as tracer or self-diffusion coefficients, determined in the absence of a chemical potential gradient. Intra- and interdiffusion coefficients are related for the case of diffusion of a small molecule in a polymeric matrix as follows [28] ... 

During recent years, the topical delivery of liposomes has been applied to different applications and in different disease models (188). Current efforts in this area concentrate around optimization procedures and new compositions. Recently, highly flexible liposomes called transferosomes that follow the trans-epidermal water activity gradient in the skin have been proposed. Diclofenac in transferosomes was effective when tested in mice, rats and pigs (189). The concept of increased deformability of transdermal liposomes is supported by the results of transdermal delivery of pergolide in liposomes, in which elastic vesicles have been shown to be more efficient (190).The combination of liposomes and iontophoresis for transdermal delivery yielded promising results (191, 192). 

In normal fuel cell operation, protons are the only cation species in the membrane. In the absence of a water-activity gradient, H+ or H3O ions move solely by migration. The potential gradient in the membrane is related to the current density by... 

Previously, we saw how the diffusion and migration fluxes varied across the membrane in the absence of water effects. If we include water effects but maintain uniform X across the membrane, the water will have little effect. Now, we impose a water activity gradient by setting to 11 and Xq to 14. In the absence of current, this will cause water to flow toward the anode. Let us look at the same case as in Figure 8.9 at 0.25 A/cm, shown in Figure 8.10. The potential at the cathode was -45 mV when X was constant, but was -66 mV when Xj was 11. Because the forward flow of protons was impeded by the backflowing water, its migration flux is decreased while its diffusion flux is increased. The ion fraction yn distribution is the same in both cases. 

Equilibrium proton distribution shift with opposite water activity gradients with yin = 0.5 at a current density of 0.15 A/cm2 and including electroosmotic drag. 

Transmembrane transfer of water from the external (continuous) phase into the internal (encapsulated) phase (7c. swelling of the emulsion) is an undesirable process. Some of the primary factors which determine the rate of water transfer are the type and concentration of surfactant in the liquid membrane. The direction of the transmembrane transfer of water in an extracting emulsion is determined by the sign of the water activity gradients. 

Edible films can also stabilize water activity gradients and preserve different textural properties possessed by different food components. For example, an edible fQm could be used to separate the crisp component of a pizza from the moist semi-solid component. 

Under equiUbrium or near-equiUbrium conditions, the distribution of volatile species between gas and water phases can be described in terms of Henry s law. The rate of transfer of a compound across the water-gas phase boundary can be characterized by a mass-transfer coefficient and the activity gradient at the air—water interface. In addition, these substance-specific coefficients depend on the turbulence, interfacial area, and other conditions of the aquatic systems. They may be related to the exchange constant of oxygen as a reference substance for a system-independent parameter reaeration coefficients are often known for individual rivers and lakes. 

The equations above describe how solutes in the soil will move in response to concentration or water potential gradients. Such gradients form when the rhizo-sphere is perturbed by the activities of the root including water and MN abstraction and carbon deposition. These activities need to be mathematically described and form one of the two boundary conditions required to solve the initial-value problem. 

A thorough discussion of the mechanisms of absorption is provided in Chapter 4. Water-soluble vitamins (B2, B12, and C) and other nutrients (e.g., monosaccharides, amino acids) are absorbed by specialized mechanisms. With the exception of a number of antimetabolites used in cancer chemotherapy, L-dopa, and certain antibiotics (e.g., aminopenicillins, aminoceph-alosporins), virtually all drugs are absorbed in humans by a passive diffusion mechanism. Passive diffusion indicates that the transfer of a compound from an aqueous phase through a membrane may be described by physicochemical laws and by the properties of the membrane. The membrane itself is passive in that it does not partake in the transfer process but acts as a simple barrier to diffusion. The driving force for diffusion across the membrane is the concentration gradient (more correctly, the activity gradient) of the compound across that membrane. This mechanism of... 

Continuity of fhe wafer flux fhrough the membrane and across the external membrane interfaces determines gradients in water activity or concentration these depend on rates of water transport through the membrane by diffusion, hydraulic permeation, and electro-osmofic drag, as well as on the rates of interfacial kinetic processes (i.e., vaporization and condensafion). This applies to membrane operation in a working fuel cell as well as to ex situ membrane measuremenfs wifh controlled water fluxes fhat are conducted in order to study transport properties of membranes. 

The simplest practicable approach considers the membrane as a continuous, nonporous phase in which water of hydration is dissolved.In such a scenario, which is based on concentrated solution theory, the sole thermodynamic variable for specifying the local state of the membrane is the water activity the relevant mechanism of water back-transport is diffusion in an activity gradient. However, pure diffusion models provide an incomplete description of the membrane response to changing external operation conditions, as explained in Section 6.6.2. They cannot predict the net water flux across a saturated membrane that results from applying a difference in total gas pressures between cathodic and anodic gas compartments. 

Figure 2.6(a) shows a semipermeable membrane separating a salt solution from the pure solvent. The pressure is the same on both sides of the membrane. For simplicity, the gradient of salt (component j) is not shown in this figure, but the membrane is assumed to be very selective, so the concentration of salt within the membrane is small. The difference in concentration across the membrane results in a continuous, smooth gradient in the chemical potential of the water (component i) across the membrane, from //, on the water side to plo on the salt side. The pressure within and across the membrane is constant (that is, pa = pm= pi) and the solvent activity gradient (y,Imj ,Imj) falls continuously from the pure water (solvent) side to the saline (solution) side of the membrane. Consequently, water passes across the membrane from right to left. 

Osmotic distillation also removes the solvent from a solution through a microporous membrane that is not wetted by the liquid phase. Unlike membrane distillation, which uses a thermal gradient to manipulate the activity of the solvent on the two sides of the membrane, an activity gradient in osmotic distillation is created by using a brine or other concentrated solution in which the activity of the solvent is depressed. Solvent transport occurs at a rate proportional to the local activity gradient. Since the process operates essentially isothermally, heat-sensitive solutions may be concentrated quickly without an adverse effect. Commercially, osmotic distillation has been used to de-water fruit juices and liquid foods. In principle, pharmaceuticals and other delicate solutes may also be processed in this way. 

A process referred to as vapor-arbitrated pervaporation addresses these issues by manipulating the transmembrane activity gradients of water and ethanol in a pervaporation system. Using a permeate side sweep stream that contains water vapor at a partial pressure corresponding to the activity of water on the feed side, permeation of water is halted while ethanol continues to diffuse through the membrane into the sweep stream and is removed. In this way, the native permselectivity of the membrane system can be altered in a controlled fashion to extract one or more volatile components from a solution. 

The majority of recently published papers are based on this kind of effective diffusion model [7, 10]. In the models of Springer et al. [7] and later Nguyen et al. [10], the local membrane state is determined by the local activity of water which is in thermodynamic equilibrium with surrounding water vapor. Diffusion of water driven by the activity gradient balances the electroosmotic flow. Under stationary conditions this results in a characteristic profile of w across the membrane, with lowest values in the proximity of the anode. 

The water flux, J, which is normally expressed as kg (or L) m h is proportional to the water vapor pressure gradient, Apm, between the feed-membrane and strip-membrane interfaces, and the membrane mass transfer co-efficient K, [Eq. (3)]. The vapor pressure gradient between the two interfaces depends on the water activity, a, in the bulk feed and strip streams, and the extent to which concentration polarization reduces that activity at each interface. Whilst can be estimated using established diffusional transport equations, it is more difficult to estimate values for the water vapor pressure at the membrane wall for use in Eq. (3). However, an overall approach using the vapor pressures of the bulk solutions and semi-empirical correlations that take account of the different conditions near the membrane wall can be used to estimate J. 

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