Diffusion across sharp boundaries

The ideas of Overton are reflected in the classical solubility-diffusion model for transmembrane transport. In this model [125,126], the cell membrane and other membranes within the cell are considered as homogeneous phases with sharp boundaries. Transport phenomena are described by Fick s first law of diffusion, or, in the case of ion transport and a finite membrane potential, by the Nernst-Planck equation (see Chapter 3 of this volume). The driving force of the flux is the gradient of the (electro)chemical potential across the membrane. In the absence of electric fields, the chemical potential gradient is reduced to a concentration gradient. Since the membrane is assumed to be homogeneous, the... 

Case 1. Suppose we have diffusion of a solute across a sharp boundary at a = 0 from a solution into a solvent. The solute may be a salt dissolved in water it may be radioactive lead dissolved in lead diffusing into pure lead or it may be an ion in an ionic lattice diffusing into another lattice, e.g. silver diffusing from silver sulphide into copper sulphide, while copper passes in the opposite direction. For the equation (34) to hold we know that D must not be a function of C and that the amounts of solution and solvent must be great enough, the diffusion slow enough, or the time short enough, so that no appreciable amount of solute diffuses from the far extremity of the solution, or reaches the far extremity of the solvent (Fig. 1). In these systems, at = 0, (7 = Cq for x< 0, (7 = 0... 

The existence of a microdomain interphase due to the diffuse concentration gradient across the boundary has been predicted by statistical thermodynamic theories based on the mean-field approach. The results of several experimental works (e.g., the systematic deviation of SAXS intensity profiles from the behavior of sharp-boundary systems described by Porod s law and the modeling of rheological behavior measured by DMA ) support the view of a segmentally mixed diffuse interphase. However, various other models, such as a coarse interface with a sharp boundary, may also account for some of the observed results from SAXS data. The ambiguity... 

It is not an easy task to develop computer codes which correctly treat the advancement of a folding interface as a boundary condition to a diffusion or flow field. In addition, the interface between a solid and a liquid, for example, is usually is not absolutely sharp on an atomic scale, but varies over a few lattice constants [32,33]. In these cases, it is sometimes convenient to treat the interface as having a finite non-zero thickness. An order parameter is then introduced, which for example varies from the value zero on one side of the interface to the value one on the other, representing a smooth transition from liquid to solid across the interface. This is called the phase-field... 

In the simplest and quite common situation, poison molecules are adsorbed as soon as they have traversed the shell, and poison concentration in the fluid is so low that deactivation remains slow compared with the catalyzed reaction. If so, the boundary between shell and core remains sharp, and diffusion of poison across the shell is quasi-stationary. The remaining activity as a function of time then is [70]... 

The data from these experiments can be analysed at various levels of sophisticatioa According to the fundamental theory of enogy transfer, the shape of the fluorescence decay profile is determined by the distribution of donor-acceptor pairs in the system. In polymer dififusion across an interface, the donors and acceptors are initially confined to opposite sides of a sharp interface (see Figure 14.19). Diffusion leads to mixing and generates concentration profiles (CD(r, t) and t), respectively) for the donors and for the acceptors. Here r refers to the distance of D or A from the initial boundary between the donor-and acceptor-labelled polymers. 

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