Diffusional path

Since the left side of Eq. (7) represents the release rat of the system, a true controlled-release system with a zero-order release rate can be possible only if all of the variables on the right side of Eq. (7) remain constant. A constant effective area of diffusion, diffusional path length, concentration difference, and diffusion coefficient are required to obtain a release rate that is constant. These systems often fail to deliver at a constant rate, since it is especially difficult to maintain all these... 

The rate of drug diffusing out of the resin is controlled by the area of diffusion, diffusional path length, and rigidity of the resin, which is a function of the amount of cross-linking agent used to prepare the resin. 

FIGURE 19.12 Considerations for the interpretation of SSITKA data. Case 1 Three formates can exist, including (a) rapid reaction zone (RRZ)—those reacting rapidly at the metal-oxide interface (b) intermediate surface diffusion zone (SDZ)—those at path lengths sufficient to eventually diffuse to the metal and contribute to overall activity, and (c) stranded intermediate zone (SIZ)—intermediates are essentially locked onto surface due to excessive diffusional path lengths to the metal-oxide interface. Case 2 Metal particle population sufficient to overcome excessive surface diffusional restrictions. Case 3 All rapid reaction zone. Case 4 For Pt/zirconia, unlike Pt/ceria, the activated oxide is confined to the vicinity of the metal particle, and the surface diffusional zones are sensitive to metal loading. 

The rate is independent of particle size. This is an indication of neghgible pore-diffusion resistance, as might be expected for either very porous particles or sufficiently small particles such that the diffusional path-length is very small. In either case, i -> 1, and ( rA)obs = ( rA)inl for the surface reaction. 

The BM has an enormous surface area compared to the epithelium due to connective tissue papillae on which the effective diffusional path length may depend. 

Pore dimensions may have a more subtle effect on decay rate depending on component dimensions and production method of the manufactured material. Products made from pasted starch, LDPE, and EAA (2) typically appeared as laminates of starch and plastic when examined by scanning electron microscopy (Figure 1). The dimensions of inter-laminate channels (i.e., pores) were not uniform and ranged from about 50 to 325 m in cross-section (22). Since flux is dependent on diffusional path area, the smaller pores can be an impediment to movement of solutes from the interior to the surface of the films. Figure 5 illustrates two films in which the laminate units are the same thickness, but differ in length. When the starch is removed... 

Here, Da is diffusion coefficient in the amorphous phase alone, oc is the volume fraction of crystalline polymer, and t is a scalar quantity that denotes the tortuosity of diffusional path of the solute. The value of Da may be estimated by the Peppas-Reinhart model if the amorphous regions of the polymer are highly swollen. This substitution yields... 

In the presence of the spacer (Fig. 17.35a), an initially high photocurrent value ( 6 mA/cm2) is achieved, but, due to the larger spacing between the two electrodes, the diffusion of the electron mediator is not fast enough to supply new reduced mediator to the Ti02/dye interface from which, under irradiation, is constantly depleted. Thus, a steady photocurrent value, significantly lower than the initial spike, is attained after a few seconds. In Fig. 17.35b, the reduced diffusional path for the electron mediator allows for a more effective mass transport that accounts for the generation of a stable photocurrent without the observation of photoanodic relaxation processes. 

The resistance to mass transfer of reactants within catalyst particles results in lower apparent reaction rates, due to a slower supply of reactants to the catalytic reaction sites. Ihe long diffusional paths inside large catalyst particles, often through tortuous pores, result in a high resistance to mass transfer of the reactants and products. The overall effects of these factors involving mass transfer and reaction rates are expressed by the so-called (internal) effectiveness factor f, which is defined by the following equation, excluding the mass transfer resistance of the liquid film on the particle surface [1, 2] ... 

Diffusional Path in Mucus Layers and Possible Drug Interactions... 

FIGURE 3.1 Concentration profiles in a passive sampling device. The driving force of accumulation is the difference in chemical potentials of the analyte between the bulk water and the sorption phase. The mass transfer of an analyte is governed by the overall resistance along the whole diffusional path, including contributions from the individual barriers (e.g., aqueous boundary layer, biofilm layer, and membrane). 

The tortuosity term is intended to account for increases in diffusional path length due to windiness. Classical descriptions of the tortuosity predict a value of 1 to 3 for random porous media (.2.). Since the tortuosities inferred by these models are orders of magnitude greater than expected, other physical properties of the system must be important in determining release rates. Since continuum diffusion models provide an incomplete description of the release from these devices, the microscopic details of the system must be considered explicitly. 

FIGURE 16 Concentration gradient from the tablet between matrix and bulk fluid for dissolution. Cs, drug solubility C, uniform concentration h, thickness of stagnant film X = diffusional path length. 

The titration profiles for dicalcium phosphate are not monotonic, but exhibit stages of dehydration consistent with the scheme shown in Eq. (7). It is also evident that the release of moisture is faster from the milled form (Fig. 14, curve B) of the excipient. This is consistent with the increased total surface area and shorter diffusional path expected with smaller particle size. 

The parameters that determine the release rate of a drug from a delivery device include polymer solubility, polymer diffusivity, and thickness of the polymer diffusional path, and the drug s aqueous solubility, partition coefficient, and aqueous diffusivity. Finally, the thickness of the hydrodynamic diffusion layer. 

Criteria for immobilized liquid membrane (ILM) support selection can be divided into two categories structural properties and chemical properties. Structural properties include geometry, support thickness, porosity, pore size distribution and tortuosity. Chemical criteria consist of support surface properties and reactivity of the polymer support toward fluids in contact with it. The support thickness and tortuosity determine the diffusional path length, which should be minimized. Porosity determines the volume of the liquid membrane and therefore the quantity of carrier required. The mean pore size determines the maximum pressure difference the liquid membrane can support. The support must be chemically inert toward all components in the feed phase, membrane phase, and sweep or receiving phase. 

The other support parameter determining the diffusional path length is the tortuosity, which is a measure of the deviation of the structure from cylindrical pores normal to the support surface. 

Support tortuosity should be minimized to reduce the diffusional path length. However, many membrane preparation techniques, such as casting, produce support materials with tortuous pores. Operating Pressure Considerations... 

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