Specific permeability coefficient

Combining Equations 2.90 and 2.92 gives the specific permeability coefficient, B° ... 

Column gas velocity is dependent upon the column length, carrier gas viscosity, pressure drop through the column and the column permeability. Column permeability is expressed by the specific permeability coefficient, B0, which may be calculated by the following expression. 

As mention previously, dermal absorption of contaminants in water can be significant. The permeability of the skin to a chemical is influenced by an agent s molecular weight, electrostatic charge, hydrophobicity, and solubility in aqueous and lipid media. Chemicals that can penetrate the skin easily, are generally nonio-nized, lipid soluble, low molecular weight substances. Chemical-specific permeability coefficients should be used to estimate dermal absorption of a chemical from water. 

If we now introduce the specific permeability coefficient Bq (viscous flow parameter) of a porous medium as follows (Carman, 1956) ... 

Eq. (7.5-14) is the famous Darcy equation with B being the specific permeability coefficient. The Darcy equation implies that the flow mechanism is by viscous drag and the fluid is inert to the porous medium, that is the effects of chemical, adsorptive, electrical, electrochemical interactions between fluid molecules and the capillary are absent (Carman, 1956). 

Drag theory considers the physical basis of permeability in terms of the frictional resistance of the walls of the material s pores reducing the free flow of fluid through the material, the degree of resistance being dependent on the viscosity of the fluid.+ The drag on the fluid by a pore wall is estimated from the Navier-Stokes equations, and the sum of aU the resistances of the pore walls is assumed to be the total resistance of the material to the fluid flow. This total resistance would be the reciprocal of the specific permeability coefficient, k, of Equation [8.6]. 

As described above, some solutes such as gases can enter the cell by diffusing down an electrochemical gradient across the membrane and do not require metabolic energy. The simple passive diffusion of a solute across the membrane is limited by the thermal agitation of that specific molecule, by the concentration gradient across the membrane, and by the solubility of that solute (the permeability coefficient. Figure 41—6) in the hydrophobic core of the membrane bilayer. Solubility is... 

This equation teaches us that the total stead-state flux (total rate of permeation across a membrane in the steady state of permeation), dM/dt, is proportional to the involved area (A) and the concentration differential expressed across the membrane, AC. In an experiment, flux is the experimentally measured parameter while A and AC are fixed in value when setting up an experiment. The value of the permeability coefficient, Ptotai, is what is calculated upon completion of an experiment using Eq. (8). The permeability coefficient, besides having the specific attributes ascribed to it, is... 

Upon taking PABL and Pe into account, the transmonolayer permeability coefficient (PM) was quantified and, in turn, delineated into its component permeabilities for the transcellular and paracellular pathways (Table 11). Specifically, Pparaceii was found as... 

Here, we briefly describe the automated Caco-2 assay used at the research site in AstraZeneca R D Molndal. The solubility of the test compounds is measured (or theoretically predicted) before they are run in the Caco-2 assay. In order to be able to make correct determinations of the permeability coefficient, the substance must be dissolved when added to cell monolayer in the transport experiment. Compounds with insufficient solubility are therefore not tested. We generally apply a test concentration of 10 pM, but in specific projects or under certain circumstances a concentration of only 1 pM is applied. The test compounds are first prepared in DM SO solution (1 mM) on a parent plate and are then diluted in transport buffer to give a final drug concentration of 10 pM (solution containing 1% DMSO) when added to the cell monolayers. 

Equation 6 Calculation of optimum ratio of particle size and column length, with selectivity factor, a capacity factor of second component of critical pair under analytical chromatography conditions, fe 02 diffusion coefficient, (cm /s) (typical value for MW 1000 10 cm /s) viscosity, p (cP) specific permeability (1.2 X 10 for spherical particles), feo third term of the Knox equation, C and maximum safe operating pressure, Ap, (bar). 

To be specific, permeability is the product of the partition coefficient K and diffusion coefficient D of a solute within a material. The partition coefficient is usually defined as the ratio of solute concentration in the material to the concentration in the solution it is a measure of the interaction between the polymer and the solute. The partition coefficient should decline as a gel shrinks and the average pore size declines, if other interactions between the solute and the gel are unchanged. The diffusion coefficient is also expected to decline as water content falls and obstruction to movement increases. While K is an equilibrium property, D is a transport property, and so these parameters can be evaluated independently. 

Some of the variables that are important for the subsequent discussion are recalled here. The membrane properties are related to the mass transport of the different chemical species through the membrane itself or its separating layer (for an asymmetric or multilayer membrane). Permeability and selectivity were defined for the mass transport by permeation both depend on the membrane nature and morphology that impose the specific transport mechanism driving the permeation of which it is characteristic. Table 13.2 reports the permeability coefficient, selectivity and permeating driving force of some permeation mechanisms. 

The measurement of sorption, diffusion and permeability coefficients takes place as a rule using one of three methods sorption of the gases in the polymer, permeation through a membrane (film or sheet) into a sealed container or permeation through a membrane into a gas stream. As far as possible sorption methods should be used together with permeation methods that are specific for the measured gas/polymer system in order to uncover any possible anomalies or errors in the measurements by comparison of results. 

Figure 11 depicts the numerical solutions for the time dependence of the resin pressure profile in the vertical direction for one-dimensional flow in the vertical direction (corresponding to an edge-dammed laminate). The laminate is 1.4 inches thick (z direction) and is a unidirectional layup. Values for the specific permeability in the z direction, (kz, in2), the viscosity, (r, poise), and the coefficient of volume change, mv, are shown in the figure. Clearly, the pressure gradient is not linear as has been assumed in the past. 

Most of the permeability coefficients for small solutes crossing the plasma membrane range from 10-10 to 10-6 m s-1. Hence, a cell wall generally has a higher permeability coefficient than does a membrane, which means that the cell wall is usually more permeable for small solutes than is the plasma membrane. For comparison, let us consider a permeability coefficient appropriate for an unstirred liquid layer adjacent to a cell wall or membrane. Specifically, Dj for a small solute may be 1 x 10-9 m2 s-1 in water, Kj is 1 in the aqueous solution, and let us assume that Ax is 30 pm for the unstirred... 

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