Permeability equation gradient

There is a further simplification which is often justifiable, but not by consideration of the flux equations above. The nature of many problems is such that, when the permeability becomes large, pressure gradients become very small ialuci uidiii iiux.es oecoming very large. in catalyst pellets, tor example, reaction rates limit Che attainable values of the fluxes, and it then follows from equation (5,19) that grad p - 0 as . But then the... 

At the opposite limit of bulk diffusion control and high permeability, all flux models are required to he consistent with the Stefan-Maxwell relations (8.3). Since only (n-1) of these are independent, they are insufficient to determine all the flux vectors, and they permit the problem to be formulated in closed form only when they can be supplemented by the stoichiometric relations (11.3). At this limit, therefore, attention must be restricted from the beginning to those simple pellet shapes for ich equations (11.3) have been justified. Furthermore, since the permeability tends to infininty, pressure gradients within the pellet tend to zero and... 

The transmembrane potential derived from a concentration gradient is calculable by means of the Nemst equation. If K+ were the only permeable ion then the membrane potential would be given by Eq. 1. With an ion activity (concentration) gradient for K+ of 10 1 from one side to the other of the membrane at 20 °C, the membrane potential that develops on addition of Valinomycin approaches a limiting value of 58 mV87). This is what is calculated from Eq. 1 and indicates that cation over anion selectivity is essentially total. As the conformation of Valinomycin in nonpolar solvents in the absence of cation is similar to that of the cation complex 105), it is quite understandable that anions have no location for interaction. One could with the Valinomycin structure construct a conformation in which a polar core were formed with six peptide N—H moieties directed inward in place of the C—O moieties but... 

The last part of Eq. (1) is derived from the pH dependence of permeability, given a pH gradient between the two sides of the intestinal barrier, based on the well known Henderson-Hasselbalch equation. Direct measurement of in situ intestinal perfusion absorption rates confirmed this pH dependence [14]. 

The equations used to calculate permeability coefficients depend on the design of the in vitro assay to measure the transport of molecules across membrane barriers. It is important to take into account factors such as pH conditions (e.g., pH gradients), buffer capacity, acceptor sink conditions (physical or chemical), any precipitate of the solute in the donor well, presence of cosolvent in the donor compartment, geometry of the compartments, stirring speeds, filter thickness, porosity, pore size, and tortuosity. 

In PAMPA measurements each well is usually a one-point-in-time (single-timepoint) sample. By contrast, in the conventional multitimepoint Caco-2 assay, the acceptor solution is frequently replaced with fresh buffer solution so that the solution in contact with the membrane contains no more than a few percent of the total sample concentration at any time. This condition can be called a physically maintained sink. Under pseudo-steady state (when a practically linear solute concentration gradient is established in the membrane phase see Chapter 2), lipophilic molecules will distribute into the cell monolayer in accordance with the effective membrane-buffer partition coefficient, even when the acceptor solution contains nearly zero sample concentration (due to the physical sink). If the physical sink is maintained indefinitely, then eventually, all of the sample will be depleted from both the donor and membrane compartments, as the flux approaches zero (Chapter 2). In conventional Caco-2 data analysis, a very simple equation [Eq. (7.10) or (7.11)] is used to calculate the permeability coefficient. But when combinatorial (i.e., lipophilic) compounds are screened, this equation is often invalid, since a considerable portion of the molecules partitions into the membrane phase during the multitimepoint measurements. 

Ordinarily it is not possible to determine the membrane retention of solute under the circumstances of a saturated solution, so no R terms appear in the special equation [Eq. (7.25)], nor is it important to do so, since the concentration gradient across the membrane is uniquely specified by S and CA (t). The permeability coefficient is effective in this case. 

Permeability of an FML is evaluated using the Water Vapor Transmission test.28 A sample of the membrane is placed on top of a small aluminum cup containing a small amount of water. The cup is then placed in a controlled humidity and temperature chamber. The humidity in the chamber is typically 20% relative humidity, while the humidity in the cup is 100%. Thus, a concentration gradient is set up across the membrane. Moisture diffuses through the membrane, and with time the liquid level in the cup is reduced. The rate at which moisture is moving through the membrane is measured. From that rate, the permeability of the membrane is calculated with the simple diffusion equation (Fick s first law). It is important to remember that even if a liner is installed correctly with no holes, penetrations, punctures, or defects, liquid will still diffuse through the membrane. 

Transmissivity is simply the coefficient of permeability, or the hydraulic conductivity (k), within the plane of the material multiplied by the thickness (T) of the material. Because the compressibility of some polymeric materials is very high, the thickness of the material needs to be taken into account. Darcy s law, expressed by the equation Q = kiA, is used to calculate the rate of flow, with transmissivity equal to kT and i equal to the hydraulic gradient (see Figure 26.22) ... 

Darcy s equation can be used to describe flow in this region however, the value of permeability varies as a function of saturation. Also, the value of moisture potential is a function of saturation. The total potential for flow (hydraulic gradient in Darcy s equation) can be defined as the difference between the moisture potential (minus) and the elevation potential (plus). When the potential for flow is positive, flow can occur. 

Figure 5 compares the experimental data with predictions based on the new pore model. The theoretical calculations were done using Equation 6 together with the experimental 3-estradiol solubility data and the experimental ethanol-water concentration gradient data (Figure 4). The partition coefficients in the pores were derived from the solubility data using Equation 4. Henry s law seems to be obeyed, as evidenced by the similar permeability coefficients for 3-estradiol obtained from tracer level as well as saturated solution experiments (Figure 1).

Maintenance of unequal concentrations of ions across membranes is a fundamental property of living cells. In most cells, the concentration of K+ inside the cells is about 30 times that in the extracellular fluids, while sodium ions are present in much higher concentration outside the cells than inside. These concentration gradients are maintained by the Na+-K+-ATPase by means of the expenditure of cellular energy. Since the plasma membrane is more permeable to K+ than to other ions, a K+ diffusion potential maintains membrane potentials which are usually in the range of -30 to -90 mV. H+ ions do not behave in a manner different from that of other ions. If passively distributed across the plasma membrane, then the equilibrium intracellular H+ concentration can be calculated from the Nernst equation via... 

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