Thin-Membrane Model without Retention

Perhaps the simplest Fick s law permeation model consists of two aqueous compartments, separated by a very thin, pore-free, oily membrane, where the unstirred water layer may be disregarded and the solute is assumed to be negligibly retained in the membrane. At the start (t = 0 s), the sample of concentration CD 0), in mol/cm3 units, is placed into the donor compartment, containing a volume (Vo, in cm3 units) of a buffer solution. The membrane (area A, in cm2 units) separates the donor compartment from the acceptor compartment. The acceptor compartment also contains a volume of buffer (VA, in cm3 units). After a permeation time, t (in seconds), the experiment is stopped. The concentrations in the acceptor and donor compartments, CA(t) and C (t), respectively, are determined. 

Two equivalent flux expressions define such a steady-state transport model [41] 

It is useful to factor out Ca (f) and solve the differential equation in terms of just C[)(t). This can be done by taking into account the mass balance, which requires that the total amount of sample be preserved, and be distributed between the donor and the acceptor compartments (disregarding the membrane for now). At t 0, all the solute is in the donor compartment, which amounts to VpCp 0) moles. At time t, the sample distributes between two compartments  

This equation may be used to replace CA(t) in Eq. (7.3) with donor-based terms, to get the simplified differential equation 

We define this permeability as apparent, to emphasize that there are important but hidden assumptions made in its derivation. This equation is popularly (if not nearly exclusively) used in culture cell in vitro models, such as Caco-2. The sink condition is maintained by periodically moving a detachable donor well to successive acceptor wells over time. At the end of the total permeation time f, the mass of solute is determined in each of the acceptor wells, and the mole sum mA (t) is used in Eq. (7.10). Another variant of this analysis is based on evaluating the slope in the early part of the appearance curve (e.g., solid curves in Fig. 7.14)  

---