Permeability equation

DERIVATION OF MEMBRANE-RETENTION PERMEABILITY EQUATIONS (ONE-POINT MEASUREMENTS, PHYSICAL SINKS, IONIZATION SINKS, BINDING SINKS, DOUBLE SINKS)... 

The popular permeability equations [(7.10) and (7.11)] derived in the preceding section presume that the solute does not distribute into the membrane to any appreciable extent. This assumption may not be valid in drug discovery research, since most of the compounds synthesized by combinatorial methods are very lipophilic and can substantially accumulate in the membrane. Neglecting this leads to underestimates of permeability coefficients. This section expands the equations to include membrane retention. 

When membrane retention of the solute needs to be considered, one can derive the appropriate permeability equations along the lines described in the preceding section Eqs. (7.1)—(7.3) apply (with P designated as the effective permeability, Pe). However, the mass balance would need to include the membrane compartment, in addition to the donor and acceptor compartments. At time t, the sample distributes (mol amounts) between three compartments ... 

In Section 7.7.5.4, we discuss the effects of additives in the acceptor wells that create a sink condition, by strongly binding lipophilic molecules that permeate across the membrane. As a result of the binding in the acceptor compartment, the transported molecule has a reduced active (unbound) concentration in the acceptor compartment, cA(t), denoted by the lowercase letter c. The permeability equations in the preceding section, which describe the nonsink process, are inappropriate for this condition. In the present case, we assume that the reverse transport is effectively nil that is, CA(t) in Eq. (7.1) may be taken as cA(t) 0. As a result, the permeability equation is greatly simplified ... 

Avdeef [23] derived the iso-pH (same pH in donor and acceptor wells) permeability equation which directly takes into account the membrane retention of a drug ... 

During the constant rate period shown in Figure 14.1, either the boundary layer mass or heat transport is rate controlling. The flow of liquid to the surface of the green body to keep it wet is governed by the permeability equation for the flow of liquid relative to the ceramic particles [8,9], written as Fick s second law, dC/dt = V(DfVC), for diffusion considering (1 — )[= e = volume fiaction of liquid] to be the... 

Permeability for a Rock Formation. For natural consolidated porous medium, however, the definitions of the equivalent spherical diameter and the specific surface area per unit volume are not widely used because of its difficulty in determination and relation to other measurable quantities. Just to serve as a comparison, we give the permeability equation based on the previous passage model with the tortuosity given by equation 61 and assuming that the areal porosity equation 54 still holds. The permeability can then be given by... 

When equation 61 is used, the permeability equation becomes... 

Pautz and Crocker (20) adapted Barkman and Davidson s internal cake permeability equation at a constant injection flow rate and derived... 

Flow Equation (2) Gasification Reagent Transport Equation (3) Product Gases Transport Equation (4) Cavity Evolution Equation and (5) Cavity-Dependent Permeability Equation. We have implemented these equations into and solved by FASTFLO, a powerful commercial PDE solver for multiphysics. These equations are defined as... 

Note that Equation (2.45) is similar to a differential form of Darcy s law with Equation (2.11) used to replace permeability. Equation (2.45) rearranges to give ... 

Permeability equations for diffusion in solids. In many cases the experimental data for diffusion of gases in solids are not given as diffusivities and solubilities but. as permeabilities, Pm, in m of solute gas A at STP (0°C and 1 atm press) diffusing per second per m cross-sectional area through a solid 1 m thick under a pressure difference of 1 atm pressure. This can be related to Pick s equation (6.5-2) as follows. 

---