Diffusion layer, aqueous

C. Steady Diffusion Across a Membrane with Aqueous Diffusion Layers... 

A stagnant diffusion layer is often assumed to approximate the effect of aqueous transport resistance. Figure 4 shows a membrane with a diffusion layer on each side. The bulk solutions are assumed to be well mixed and therefore of uniform concentrations cM and cb2. Adjacent to the membrane is a stagnant diffusion layer in which a concentration gradient of the solute may exist between the well-mixed bulk solution and the membrane surface the concentrations change from Cm to c,i for solution 1 and from cb2 to cs2 for solution 2. The membrane surface concentrations are cml and cm2. The membrane has thickness hm, and the aqueous diffusion layers have thickness ht and h2. 

Applying the concentration profile of Eq. (32) obtained from a thin film to both aqueous diffusion layers at steady state, we have... 

Figure 4 Diffusion across a membrane with aqueous diffusional layers. cbI and cb2 are the concentrations of bulk solutions 1 and 2, respectively. The thicknesses of the aqueous diffusion layers are /i, and h2. The membrane has a thickness of hm. Equilibrium is assumed at the interfaces of the membrane and the aqueous diffusion layers. At steady state, the concentrations remain constant at all points in the membrane and in the aqueous diffusion layers. The concentration profiles inside the membrane and aqueous diffusion layers are linear, and the flux is constant.

In Eqs. (40)-(42), cM and cb2 are experimentally measurable and the aqueous diffusion layer thickness can be estimated theoretically. Therefore, the only unknowns are the solute concentrations at the interfaces, csl and cs2. Their estimation is shown below. 

The steady flux across each aqueous diffusion layer is... 

Therefore, the film thickness is the z-axis intercept of the tangent curve of the concentration profile. The calculated thickness of the aqueous diffusion layer is... 

Table 1 Calculated Thickness of the Aqueous Diffusion Layer Based on Eq. (82), Assuming a Diffusion Coefficient of 5 X I0 6 cm2/sec... 

Membrane diffusion illustrates the uses of Fick s first and second laws. We discussed steady diffusion across a film, a membrane with and without aqueous diffusion layers, and the skin. We also discussed the unsteady diffusion across a membrane with and without reaction. The solutions to these diffusion problems should be useful in practical situations encountered in pharmaceutical sciences, such as the development of membrane-based controlled-release dosage forms, selection of packaging materials, and experimental evaluation of absorption potential of new compounds. Diffusion in a cylinder and dissolution of a sphere show the solutions of the differential equations describing diffusion in cylindrical and spherical systems. Convection was discussed in the section on intrinsic dissolution. Thus, this chapter covered fundamental mass transfer equations and their applications in practical situations. 

JH Kou, D Fleisher, GL Amidon. Calculation of the aqueous diffusion layer resistance for absorption in a tube Application to intestinal membrane permeability determination. Pharm Res 8 298-305, 1991. 

Natural surfactants such as sodium taurocholate and sodium glycocholate are not able to eliminate the limiting character of the aqueous diffusion layer adjacent to the luminal side of the membrane [29, 30]. For that reason in the presence of these natural surfactants at their CMC, the absorption Hpophihdty correlations are as hyperbolic as the ones obtained without additives. Figure 4.3 displays the difference between the correlations obtained in the presence of polysorbate 80 and sodium taurocholate [27, 28]. 

Under efficient stripping condition (Cmf Cmr) and neglecting the aqueous diffusion layer (Cmf Cf), Equation 31.1 gets simplified to... 

U(VI) HDEHP pH solutions 5 M H3PO4 Transport rates controlled by aqueous diffusion layer in Feed side [67]... 

Aqueous Boundury (Diffusion) Luyer. The aqueous boundary layer (often referred to as the stagnant, unstirred, or aqueous diffusion layer) is an important hydrodynamic barrier that a drug must traverse before reaching the surface of the mucosal membrane. " Before a molecule in the intestinal lumen passes through the membrane, it must first cross the aqueous boundary layer located at the intestinal lumen and membrane interface (Fig. 2). The liquid in this layer, in reality, is not static, as the term unstirred implies, but represents a film at the surface where diffuse and natural convective mixing occurs. This unstirred layer can be a rate-limiting step for the absorption of hydro-phobic molecules. However, hydrophilic molecules such... 

The effect of particle size and dissolution rate has been known since the pio-neeringworkofNoyes and Whitney (1897), and Hixson and Crowell (1931) subsequently derived a highly useful equation that expresses the rate of dissolution based on the cube root of the weight of the particles. When the Hixson-Crowell model is applied to micronized particles, for which the thickness of the aqueous diffusion layer around the dissolving particles is comparable to or larger than the radius of the particle, the change in particle radius with time is given by ... 

Different explanations were discussed for this effect [175, 475], which even is obtained in simple n-octanol/water in vitro systems (Figure 28) [476]. Without questioning the relevance of different reasons in certain cases, the pH shift can easily be explained by the assumption of an aqueous diffusion layer at the aqueous/organic interface. Neutral species rapidly enter the organic phase from the aqueous/organic interface. They are steadily regenerated by the dissociation equilibrium from ionized species within the aqueous diffusion layer, much faster than the neutral molecules can diffuse from the bulk solution into this layer. 

In facilitated transport of metal ions through LM, the metal ions are transported through the membrane against their own concentration gradient, termed as the uphill transport. The driving force in such processes is provided by the chemical potential difference of the species other than the diffusing ones on either side of the membrane. The permeability of the transported species is decided by the parameters such as membrane thickness, pore structure, aqueous diffusion coefficient of the species, aqueous diffusion layer thickness, and distribution and diffusion coefficients of the transported species in the LM phase. The diffusion of the species in the carrier solvent depends on the membrane characteristics (viz., porosity and tortuosity) and viscosity of the solvent, while the aqueous diffusion of the metal ions depends upon the flow rate and diffusivity of metal species in the aqueous phase. On the other hand, the overall transport rates of the species can be controlled through various parameters such as feed composition, carrier concentration, and receiver phase composition. 

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