Systems with Different Geometries

Fickian diffusional release form a thin polymer film. Equation (4.3) gives the short-time approximation of the fractional drug released from a thin film of thickness S. 

Case II release from a thin polymer film. The fractional drug release q (t) /qoo follows zero-order kinetics [65,66] according to 

Case II radial release from a cylinder. The following equation describes the fractional drug released, q(t) /qoo, when case II drug transport with radial release from a cylinder of radius p is considered [66]  

Case II 1-dimensional radial release from a sphere. For a sphere of radius p with Case II 1-dimensional radial release, the fractional drug released, 

Case II radial and axial release from a cylinder. We quote below a detailed analysis of Case II radial and axial release from a cylinder [67] since (4.4) and (4.5) are special cases of the general equation derived in this section. 

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The use of the dimensionless quantities facilitates comparison between systems with different geometries and scales. For example, although two systems may be different in several respects, they will behave similarly as far as metabolite transport if they have similar Pdclet numbers. Furthermore, the Pdclet number gives an instant idea as to which major transport mechanisms operate in the system under study. If Pe < 1, diffusional transport dominates, while if Pe > 1, convective transport and electrical migration are more important. 

Alder et al. have studied various nonfused bicyclic ring systems with differing ring sizes with respect to the in,out-geometry displayed by these compounds <2001 JCS(P2)>. Compound 293 was synthesized and was found to favor... 

Apart from this, it would be appropriate, although never done in practice, to define homoaromaticity with regard to a molecular property (such as energy, geometry, chemical shifts, etc.) in comparison to the reference(s) used. Various molecular properties reflect the special electronic features of homoaromatic systems with different sensitivity. Thus, for example, it is possible that NMR chemical shifts could suggest weak bond (electron) delocalization while an analysis of the molecular energy does not provide any indication of homoaromatic character. 

Surfactant molecules commonly self-assemble in water (or in oil). Even single-surfactant systems can display a quite remarkably rich variety of structures when parameters such as water content or temperature are varied. In dilute solution they form an isotropic solution phase consisting of micellar aggregates. At more concentrated surfactant-solvent systems, several isotropic and anisotropic liquid crystalline phases will be formed [2]. The phase behavior becomes even more intricate if an oil (such as an alkane or fluorinated hydrocarbon) is added to a water-surfactant binary system and the more so if other components (such as another surfactant or an alcohol) are also included [3], In such systems, emulsions, microemulsions, and lyotropic mesophases with different geometries may be formed. Indeed, the ability to form such association colloids is the feature that singles out surfactants within the broader group of amphiphiles [4]. No wonder surfactants phase behavior and microstructures have been the subject of intense and profound investigation over the course of recent decades. 

Let us imagine an electrolyte with two monovalent ions, A X , such that the couple at the anode is identical to that at the cathode, and only is an electroactive species. A" is produced at the anode and consumed at the cathode. Remember that in this case it is possible to attain steady states different from equilibrium states . For example in a chronopotentiometry, after a while the concentration profile ceases to change. Remember also that electroneutrality requires the anion and cation concentrations to be equal at all points throughout the electrolyte. In systems with unidirectional geometry, linear concentration profiles emerge in the zones where there is no convection, and the slopes depend solely on the current and the diffusion coefficient of the electroactive species A". ... 

The system shows high activity, but differs frran Ti- and V-based catalysts as they produce HDPE with broad MWD. The catalyst contains active sites with different geometries and activities... 

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