Diffusion, biphasic

Biphasic Diffusion. Much of the confusion about routes of entry has been resolved by Scheuplein (i). His work shows that any one of the routes can be dominant under appropriate conditions. For instance, dominance may vary with time (Figure 2). Scheuplein observed biphasic diffusion with rapid onset and initial dominance of flux via ducts, hair. 

Many situations can be described in terms of biphasic diffusion, where a given species diffuses through the electrolyte and the electrode phases. For this situation, which parallels that for codiffusion of electroactive species in solution phase (Blanch and Anson, 1991 Oldham, 1991), two limiting cases can be distinguished, following the description of Andrieux et al. (1984) for redox polymer films ... 

In a series of papers, Gupta et al. (109-112) studied the in vitro release properties of heat-stabilized BSA microspheres containing adriamycin. The biphasic release of drug was attributed to its location in the microsphere. The initial release results from surface desorption and diffusion through pores, while the later release arises from drug within the microsphere, which becomes available as the microsphere hydrates. 

Various factors that influence the release of drugs from particulate carriers are listed in Table 10. Drugs can be released by diffusion or by surface erosion, disintegration, hydration, or breakdown (by a chemical or an enzymatic reaction) of the particles. The release of drugs from microspheres follows a biphasic pattern that is, an initial fast release followed by a slower... 

As for a single phase system, the rate of the reaction is still dependent on the probability of reactants meeting and therefore on the concentration of the reagents. However, in the biphasic system, the critical concentration of these components is no longer their total concentration in the whole system but the concentration where the reaction takes place. This concentration will be dependent on a number of factors, and the most influential are the rate of diffusion of the reactants to the catalyst and the relative solubility of the reagents in each phase. These two factors are interdependent, and will be considered in turn. 

For diffusion in a biphasic system, there is the additional complication of the phase boundary. Therefore, diffusion in each phase will be described by Equation 2.11, but in the region of the phase boundary different rules apply to take into account the mass transfer of the reactant from one phase to the other. Where the solubility of the solute is the same in both phases, the rate of diffusion across the phase boundary J for a solute moving from the higher concentration [A]i to the lower concentration [A]2 through a film of thickness l is given by Equation 2.12, which also describes an exponential decrease in concentration, but... 

In most biphasic systems, the solubility of the solute differs between the two phases. In this case, it is not the absolute concentration of the reagent that affects the rate of diffusion, but the concentration relative to the saturation of the solution. In the extreme example shown in Figure 2.12, although the actual concentration of solute A is higher in phase 1 than in phase 2, diffusion will proceed in the direction of phase 1 from phase 2, because phase 1 is less saturated by solute A than phase 2. The saturation is determined by the solubility of the solute in... 

As for the rate of diffusion, the equilibrium constant for a reaction in a biphasic system is not determined by the overall concentration of each reagent, but by their concentrations in the reaction phase. In some cases this can drive the forward reaction to completion, and in other cases it can be inhibitory, depending on the relative concentrations of the reactants and products. In model 1, where the reaction takes place at the phase boundary, the effective concentration of the reactants and products will be that in phase 1, and assuming each has an equivalent solubility, the equilibrium position will approach that of a homogeneous system. Where the reaction takes place in the bulk solvent, as in model 2, the equilibrium position is very much dependent on the solubility of the reagents in phase 2. For example, if the product is less soluble in phase 2 than the reactant, as the product is formed it will diffuse back into phase 1, reducing its concentration in phase 2 where the reaction is occurring and therefore the reaction will... 

In a homogeneous system, the rate of diffusion in the system can be directly related to the rate of the reaction as it governs the number of times the catalyst will interact with the reactants over a set time. In a biphasic system, diffusion still affects the rate of reaction, as this is dependent on the catalyst and reactants meeting. However, the rate of diffusion also affects the time it takes for the reactants to reach the place where the reaction takes place. How diffusion affects rate depends on the catalytic turnover. 

As the measured rate of the reaction in a biphasic system can be dramatically affected by diffusion, the measured rate of reaction is termed the observed rate of... 

In many biphasic systems, constant stirring creates a fine emulsion, where droplets of one solvent become suspended in the other. In this emulsion the surface area between the two phases is increased, providing a bigger surface for either the catalytic reaction to occur or the reactants to diffuse across to react in the bulk solvent. 

The fact that diffusion models describe a number of chemical processes in solid particles is not surprising since in most cases, mass transfer and chemical kinetics phenomena occur simultaneously and it is difficult to separate them [133-135]. Therefore, the overall kinetics of many chemical reactions in soils may often be better described by mass transfer and diffusion-based models than with simple models such as first-order kinetics. This is particularly true for slower chemical reactions in soils where a fast reaction is followed by a much slower reaction (biphasic kinetics), and is often observed in soils for many reactions involving organic and inorganic compounds. 

This chapter starts with a short introduction on the skin barrier s properties and the methods employed for analyzing experimental data. This is followed by an overview of several selected approaches to predict steady-state diffusion through the skin. Then a few approaches that approximate the structural complexity of the skin by predicting drug diffusion in biphasic or even multiphasic two-dimensional models will be presented. Finally, the chapter concludes with a short summary of the many variables possibly influencing drug permeation and penetration. 

While Heisig et al. solved the diffusion equation numerically using a finite volume method and thus from a macroscopic point of view, Frasch took a mesoscopic approach the diffusion of single molecules was simulated using a random walk [69], A limited number of molecules were allowed moving in a two-dimensional biphasic representation of the stratum corneum. The positions of the molecules were changed with each time step by adding a random number to each of the molecule s coordinates. The displacement was related... 

Batch operation For the design of batch reactors for biphasic conversion the type of stirring device is an essential aspect to generate a narrow distribution with small droplet sizes which is equivalent to high surfaces [36]. Together with the diffusion ability (diffusion coefficient) of the used sol-... 

As already shown by Wiese et al. [17] mass transport rates in biphasic catalysis can be dramatically influenced by hydrodynamics in a tube reactor with Sulzer packings. Above all, the volume rate of the catalyst phase in which the substrates are transported by diffusion plays a decisive role in accelerating the mass transport rate. This effect was also investigated for citral hydrogenation in the loop reactor. Overall reaction rates and conversions as a function of the catalyst volume rate can be seen in Fig. 15. 

However, biphasic catalysis, such as the above-mentioned process, is hmited by the solubility of the reaction compounds in the aqueous phase. Hence, only compounds with sufficient water solubility are suitable for biphasic catalytic apphca-tion. More hydrophobic substrates caimot diffuse to the catalytic active species, which is solubilized in the aqueous phase, and the reaction cannot take place. 

On the basis of the Hatta number, the transformations carried out in biphasic systems can be described as slow (Ha < 0.3), intermediate (with a kinetic-diffusion regime 0.3 < Ha < 3.0), and fast (Ha > 3). These are diffusion limited and take place near the interface (within the diffusion layer). Slow transformations are under kinetic control and occur mostly in a bulk phase, so that the amount of substrate transformed in the boundary layer in negligible. When diffusion and reaction rate are of similar magnitude, the reaction takes place mostly in the diffusion layer, although extracted substrate is also present in the continuous phase, where it is transformed at a rate depending on its concentration [38, 50, 54]. 

The proposed model consists of a biphasic mechanical description of the tissue engineered construct. The resulting fluid velocity and displacement fields are used for evaluating solute transport. Solute concentrations determine biosynthetic behavior. A finite deformation biphasic displacement-velocity-pressure (u-v-p) formulation is implemented [12, 7], Compared to the more standard u-p element the mixed treatment of the Darcy problem enables an increased accuracy for the fluid velocity field which is of primary interest here. The system to be solved increases however considerably and for multidimensional flow the use of either stabilized methods or Raviart-Thomas type elements is required [15, 10]. To model solute transport the input features of a standard convection-diffusion element for compressible flows are employed [20], For flexibility (non-linear) solute uptake is included using Strang operator splitting, decoupling the transport equations [9],... 

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