Activity gradient

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 simplifying assumptions that make Tick s law useful for other processes are not vaHd for pei vaporation. The activity gradient across the membrane is far more important than the pressure gradient. Equation (22-110) is generally used to describe the pei vaporation process ... 

In a container or a loop in which a molten metal is flowing but where there is not necessarily a temperature gradient, a type of corrosion can occur by transfer of material along an activity gradient ( activity being used here in the thermodynamic sense—see Section 20.1). Again it is convenient to discuss this phenomenon under two headings ... 

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... 

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. 

This may be separated into two terms, one involving an activity gradient (dilfusion) and the other an electrical field (migration)... 

The fluxes due to the influence of both an electrical field and an activity gradient may be given by the following relations... 

In this case a fused salt electrolyte, incorporating ZnCl2 dissolved in a eutectic mixture of LiCl and KCl, is used to determine the activity gradient between pure liquid Zn and a ternary Zn-In-Pb alloy, also in the liquid state. The EMF arises from the potential between pure Zn at imit activity to Zn in the alloy where the activity has a value, ci. The ruling equation then becomes... 

Zhang (1993) proposed the modified effective binary approach (also called activity-based effective binary approach). In this approach, the diffusive flux of a component is related to its activity gradient and all other components are treated as one combined component. The diffusive flux for any component i is expressed as (by analogy with Equation 3-61)... 

Writing the diffusive flux of a component i in terms of activity gradients of all independent components in an N-component system, the flux equation is... 

The second law of thermodynamics dictates that ct is positive when Vp2 0 therefore, I>0. Hence, based on Equation Al-15, diffusion in binary solutions is always down the chemical potential (or activity) gradient. Comparing J2 in Equation Al-14 with Pick s law and assuming constant molar density p, we have... 

The concentrations in the solid phases, Cj and c, are determined by the solnbilities and diffusivities of hydrogen in A and B, and so they are not eqnal. The thermodynamic activity of hydrogen has a single valne at the interface, however. (Refer to Section 3.0.1 for a description of thermodynamic activity.) Hence, the treatment of diffusion flux in a composite wall is simplified by considering activity gradients rather than concentration gradients. If the dissolution of hydrogen gas in the solid follows the reaction... 

Charge-transfer mechanism - The nature of the charge-transfer mechanism is important in that under reaction conditions the electroactive species need not be at a constant activity (i.e. there may be activity gradients). It is therefore... 

The net inward flux densities at the inner and outer surfaces are equal. At the inner surface this is proportional to the activity gradient, and at the outer surface it is proportional to the potential difference. In the latter case we call the proportionality constant H. Hence, we have... 

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. 

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... 

SFE has a wide range of applications, which include the extraction of PAHs, PCBs, phenols, pesticides, herbicides, and hydrocarbons from environmental samples, contaminants from foods and feeds, and active gradients from cosmetics and pharmaceutical products. Table 3.6 lists some examples from the literature. 

Majority MAE applications have been in the extraction of PAHs, PCBs, pesticides, phenols, and total petroleum hydrocarbons (TPHs) from environmental samples. MAE has also been used in the extraction of contaminants and nutrients from foodstuffs, active gradients from pharmaceutical products, and organic additives from polymer/plastics. Table 3.14 lists some typical applications. Readers interested in the details of MAE applications can find more information in some recent reviews [85-87],... 

Another interesting approach is to use nanofiber scaffolds as a crystallization matrix to mimic biological composites. Xia and coworkers were able to produce meshes with a gradient of calcium phosphate content to mimic the tendon-to-bone insertion site [206], The variation in composition led to an interesting spatial gradient in stiffness of the scaffold. This was also reflected in an activity gradient of seeded mouse preosteoblast cells. 

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. 

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. 

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