Membranes diffusion coefficient

Figure 8.1 to Figure 8.3 show the water diffusion coefficient, membrane activity, and the correction factor (1/aJ (da /dA,) needed to use VA for the water driving force instead of Vg. Figure 8.4 shows the variation of water saturation with temperature. 

The release of steroids from silicone implants follows Ficks law of diffusion with the flux of diffusion being affected by a diffusion coefficient, membrane surface area, thickness of the membrane and the concentration gradient across the diffusion path in the membrane. 

If tire diffusion coefficient is independent of tire concentration, equation (C2.1.22) reduces to tire usual fonn of Pick s second law. Analytical solutions to diffusion equations for several types of boundary conditions have been derived [M]- In tlie particular situation of a steady state, tire flux is constant. Using Henry s law (c = kp) to relate tire concentration on both sides of tire membrane to tire partial pressure, tire constant flux can be written as... 

In ulttafUttation, the flux,/ through the membrane is large and the diffusion coefficient, D, is small, so the ratio cjcan teach a value of 10—100 or mote. The concentration of retained solute at the membrane surface, may then exceed the solubility limit of the solute, and a precipitated semisohd gel forms on the surface of the membrane. This gel layer is an additional battier to flow through the membrane. 

Permeability P, can be expressed as the product of two terms. One, the diffusion coefficient, reflects the mobility of the individual molecules in the membrane material the other, the Henry s law sorption coefficient, reflects the number of molecules dissolved in the membrane material. Thus equation 9 can also be written as equation 10. 

Electrically assisted transdermal dmg deflvery, ie, electrotransport or iontophoresis, involves the three key transport processes of passive diffusion, electromigration, and electro osmosis. In passive diffusion, which plays a relatively small role in the transport of ionic compounds, the permeation rate of a compound is deterrnined by its diffusion coefficient and the concentration gradient. Electromigration is the transport of electrically charged ions in an electrical field, that is, the movement of anions and cations toward the anode and cathode, respectively. Electro osmosis is the volume flow of solvent through an electrically charged membrane or tissue in the presence of an appHed electrical field. As the solvent moves, it carries dissolved solutes. 

With regard to the enantioselective transport through the membrane, one advantage of liquid membrane separation is the fact that the diffusion coefficient of a solute in a liquid is orders of magnitude higher as compared to the diffusion coefficient in a solid. The flux through the membrane depends linearly on the diffusion coefficient and concentration of the solute, and inversely on the thickness of the membrane [7]. 

Here solute concentration C and Cp (in permeate) are expressed as mass fractions, D is the diffusion coefficient of the solute and y is the distance from the membrane. Rearranging and integrating from C - Cf when y = / the thickness of the film, to C = Cw, the concentration of solute at the membrane wall, when y=0, gives ... 

The permeability tests for alkali metal ions in the aqueous solution were also conducted. When an aqueous salt solution moves to cell 2 through the membrane from cell 1, the apparent diffusion coefficient of the salt D can be deduced from a relationship among the cell volumes Vj and V2, the solution concentration cx and c2, the thickness of membrane, and time t6 . In Table 12, permeabilities of potassium chloride and sodium chloride through the 67 membrane prepared by the casting polymerization technique from the monomer solution in THF or DMSO are compared with each other and with that the permeability through Visking dialyzer tubing. The... 

Ratio of apparent diffusion coefficient of 67 membrane to the cellulosic membrane. Visking dialyzer tubing. 

For gases, both permeation and diffusion data are best measured by permeation tests, many different types been described elsewhere. The same sheet membrane permeation test can quantify permeation coefficient Q, diffusion coefficient D, solubility coefficient s, and concentration c. The membrane, of known area and thickness, must be completely sealed to separate the high-pressure (initial) region from that containing the permeated gas it may need an open-grid support to withstand the pressure. The permeant must be suitably detected and quantified (e.g., by pressure or volume buildup, infrared (IR) spectroscopy, ultraviolet (UV), gas chromatography, etc.). 

The Desmopressin diffusion coefficient in the cubic phase at 40 C (D=0.24 x 10-10 m2s-l) is about a factor 9 smaller than in 2H20-solution at 25 C (D=2.25 x 10-10 m s" ), a difference which is larger than what is expected from pure obstruction effects a reduction factor of three is expected from the inclusion of a solute in the water channels of the cubic phase (13). Thus, the results indicate an interaction between the peptide and the lipid matrix and/or membrane surface, especially since the peptide and lipid diffusion coefficients are very similar in the cubic phase (Table... 

The permeability coefficient Kpcr is just the flux divided by Cw. It is apparent that the permeability coefficient is linear with P for small distribution coefficients and constant for large P. Thus, for small P the epithelium is the barrier, and for large P the stroma is the barrier. A fit for steroid permeability is shown in Fig. 12, where the regression analysis gave De = 1.4 x 10 9cm2/s and Ds = 2.0 x 10 6cm2/s for 4 = 4 x 10 3 cm and 4 = 3.6 x 10 2 cm [205]. These values for the diffusion coefficients are reasonable compared with those of aqueous gels and lipid membranes. 

Diffusion of cations in a Nation membrane can formally be treated as in other polymers swollen with an electrolyte solution (Eq. (2.6.21). Particularly illustrative here is the percolation theory, since the conductive sites can easily be identified with the electrolyte clusters, dispersed in the non-conductive environment of hydrophobic fluorocarbon chains (cf. Eq. (2.6.20)). The experimental diffusion coefficients of cations in a Nation membrane are typically 2-4 orders of magnitude lower than in aqueous solution. 

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