Force for Diffusion

The relationship between the Fickian diffusivity, defined by Eq. (5.1), and the mobility B c), defined by 

In the vapor phase or in a liquid or adsorbed phase at low concentration, Henry s law is obeyed and the activity is directly proportional to concentration. Under these conditions d na/d ncfn 1.0 and the diffusivity approaches a constant limiting value. There is no sound theoretical reason to expect the corrected diffusivity to be independent of sorbate concentration at higher concentration levels outside the Henry s law region, although such behavior has been observed experimentally for a number of systems. For binary liquid phase systems the concentration dependence of Dq is generally less pronounced than that of D, but it is still significant in most systems.  

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As can be seen, conditions in a flowing reactor, even the simplest such as a tube, may be far from the thermodynamic equilibrium conditions predicted by the equilibrium computer programs. However, in the diffusion controlled range, it is possible to use as the driving force for diffusion, the difference between an assumed equi-... 

For diffusion in liquid electrolytes such as molten salts, two forces acting on an ion of interest should be taken into account the gradient of the chemical potential and the charge neutrality. Thus the electrochemical potential rather than the chemical potential should be the driving force for diffusion. 

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 CONCEPT OF SPECIFIC AFFINITY AS A DRIVING FORCE FOR DIFFUSIVE SUBSTRATE TRANSFER... 

Pulmonary absorption of volatile anesthetics across the alveolar-capillary barrier is very rapid because of the relatively high lipid-water partition coefficients and small molecular radii of such agents. The driving force for diffusion is a combination of the blood-air partition coefficient (which is a measure of the capacity of blood to dissolve drug) and the difference in partial pressure between the alveoli and the arterial and venous blood. Agents with high blood-air partition coefficients require more drug to be dissolved in the blood for equilibrium to be reached. 

Another m3dh is that there is a driving force for diffusion. The truth is that diffusion is due to the random motion of atoms. There is no driving force to move atoms along a direction, but random motion is able to produce a directional change of concentrations if there is an initial concentration gradient. 

This is often called the thermodynamic force for diffusion. It is necessary to divide by Avo-gadro s number NA since p, is a molar quantity. Thermodynamics show that... 

The driving force for diffusion is the thermal energy, fcB T, associated with Brownian motion. By contrast, for reactions between ions of charges zAe and zBe, the direct intermolecular potential energy becomes very important and is the Coulomb interaction... 

Chemical potential is analogous to the temperature gradient that drives heat flow or the cell emf potential that drives electrical current flow, in that it provides the driving force for diffusive migration of chemical species from one region of the system to another. 

The driving force for diffusion of C+ from the membrane to the aqueous solution is the favorable solvation of the ion by water. As C+ diffuses from the membrane into the water, there is a buildup of positive charge in the water immediately adjacent to the membrane. The charge separation creates an electric potential difference ( ou,cr) across the membrane. The free-energy difference for C+ in the two phases is AG = —nFE(Mcr, where F is the Faraday constant and n is the charge of the ion. At equilibrium, the net change in free energy for diffusion of C+ across the membrane boundary must be 0 ... 

Stress as a Driving Force for Diffusion Formation of Solute-Atom Atmosphere around Dislocations... 

A driving force for diffusion includes any influence that increases the jump frequency. Examples of driving forces include chemical potential, thermal, and stress gradients. If a chemical potential gradient is present, the flux of species i at the diffusion plane is given by = —D (dc-Jdx), where D is the intrinsic diffusion coefficient of species i. Assuming Henry s law for the tracer element in binary alloys, Darken30 has shown that... 

The vaporization mass loss is composed of two terms (1) vaporization of the M component and associated C as MC, AfmC> (g/cm2) and (2) diffusion-coupled vaporization of excess C, M (g/cm2). The excess C may be viewed as a driving force for diffusion in the case of a coating, it is equal to the difference between the C concentration at the coating gas interface and the congruently vaporizing C concentration. The finite magnitude of M b is... 

Sample dispersion is another cause of the long lag time in flow injection techniques where an aqueous carrier fluid is used [63,64]. Dispersion is caused by axial mixing of the sample with the carrier stream. This increases the sample volume, resulting in longer residence time in the membrane. Dilution reduces the concentration gradient across the membrane, which is the driving force for diffusion. The overall effects are broadened sample band and slow permeation. 

For a system in equilibrium, no net transfer of material occurs between the phases. When a system is not in equilibrium, diffusion of material between the phases will occur so as to bring the system closer to equilibrium. The departure from equilibrium provides the driving force for diffusion of material between the phases. 

An important conclusion from Fig. 6 is that for a small void, it is immaterial wheter or not the initial void contains pure water or an air/water mixture. The diameters at any particular time during the cure cycle are nearly identical when the initial void diameters under 0.1 atm are the same. An air/water void initially containing pure air has a very large driving force for diffusion of water vapor from the resin to the void during the first few minutes of the cycle. This results in diffusion into the void of a large amount of water vapor (relative to the original amount of dry air in the void). Consequently the mole fraction of water vapor in the air/water void quickly approaches unity, and thereafter the rate of diffusion of water vapor across the interface of the air/water void is nearly the same as that for a pure water void. 

Care has to be taken when considering simple concentrations of the permeant since the driving force for diffusion is really the chemical potential gradient. As stated above the maximum flux should occur for a saturated solution of the permeant. However, if supersaturated solutions are applied to the skin, it is possible to obtain enhanced fluxes [27]. This can only be true if the outer skin lipids are capable of sustaining a supersaturated state of the diffusant. Figure 4.4 shows the linear increase in skin permeation with degree of supersaturation, and Fig. 4.5 demonstrates... 

Whole-animal studies assess the percent of the applied dose absorbed into the body using classic techniques of bioavailability, where absorbed chemical is measured in the blood, urine, feces, and tissues with mass balance techniques. Recently, methods have been developed to assess absorption by measuring the amount of chemical in the stratum comeum because it is the driving force for diffusion. Cellophane tape strips are collected 30 minutes after chemical exposure and the amount of drug assayed in these tape strips correlates to the amount systemically absorbed. If the focus of the research is to determine the amount of chemical that has penetrated into skin, core biopsies may be collected and serially sectioned, and a profile of the chemical as a function of skin depth may be obtained. 

For binary diffusion, there is only one independent flow, force or concentration gradient, and diffusion coefficient. On the other hand, multicomponent diffusion differs from binary diffusion because of the possibility of interactions among the species in mixtures of three or more species. Some of the possible interactions are (1) a flow may be zero although its zero driving force vanishes, which is known as the diffusion barrier (2) the flow of a species may be in a direction opposite to that indicated by its driving force, which is called reverse flow and (3) the flow of a species may occur in the absence of a driving force, which may be called osmotic flow. The theory of nonequilibrium thermodynamics indicates that the chemical potential arises as the proper driving force for diffusion. This is also consistent with the condition of fluid phase equilibrium, which is satisfied when the chemical potentials of a species are equal in each phase. 

The choice of mechanism for oral sustained/controlled-release systems is limited by the aqueous solubility of the drug. Thus, diffusional systems are poor choices for low aqueous-soluble drugs since the driving force for diffusion, the concentration in aqueous solution, will be low. The lower limit for the solubility of a drug to be formulated in a controlled-release system has been reported to be O.lmg/mL [11],... 

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