Diffusion through a flat

One-dimensional diffusion through a flat membrane will be treated in the following discussion. The effects of membrane asymmetry will be neglected since the process of permselection occurs in the thin dense layer of effective thickness, Z, at the membrane surface. In such a case, the expression for the local flux of a penetrant at any point in the dense layer can be written as shown in Equation 1 C14) ... 

As reported in Rice (1993), the simulation of catalytic effects is considered as an ODE system. Under steady-state conditions, an ideal gas G diffuses through a flat gas film with a thickness T (Figure 3.2). A catalytic surface is placed at t = T, where G undergoes the reaction G -> pU + qV. With the appropriate constants A to F, the concentrations v and u of the reaction products V and U are simulated as follows ... 

CARS signatures of obtained through a flat I -air diffusion flame (28). Such spectra, when reduced using simple algorithms deduced from computer calculations, permit temperature profiling of the flame as shown in Figure 10. There CARS measurements of... 

The first microstructural models were developed independently and essentially simultaneously (Aldushin et al 1972a,b Hardt and Phung, 1973 Aldushin and Khaikin, 1974). For these models, the elementary reaction cell, which accounts for the details of the microstructure, consists of alternating lamellae of the two reactants (A and B), which diffuse through a product layer (C), to react (see Fig. 20a). Assuming that the particles are flat allows one to neglect the change in reac-... 

A comparison of this expression with eq. (V.12) indicates that diffusion towards a spherical particle is similar to diffusion towards a flat surface through a solution layer of thickness 8 = r. Substitution of eq. (IV.20) into eq. (IV. 19) yields the expression for the rate of diffusionally-controlled particle growth ... 

Simple diffusion from a flat surface through an unstirred layer 0.025 cm thick would result in a solute permeability 20-10 cm/s. Thus, the value of computed for this model, 5.5-10 cm/s, signifies that solute transport into an interspace bounded by a basement membrane retards its diffusion from the region adjacent to the cell membrane by a factor of four. The permeability can also be translated into an electrical resistance, R, by use of the formula... 

If a load is heated electrically— by actually using the load as a resistance in a circuit or by induction heating—the flux lines will concentrate just inside the surface. In fuel-fired heating processes, heat enters the load through its surface (by radiation or convection) and diffuses throughout the piece by conduction. This heat flow requires a difference in temperature within the piece. Steady heat flow through a flat plate is described by ... 

Recourse must now be made to the use of a certain hermetically sealed enclosure in order to impede an indefinite diffusion. Flat Men say that they are dealing with un gaz, and they call pression or tension the results of a certain bombardement against the enveloping wall which is carried out by millions of molecules shot out forth in all directions from Plane P. This operation is the only phenomenon captured by the senses of a Flat Man... . They give this operation a specific name, HEAT, and they only experience it through an artificial unity, DEGREE OF TEMPERATURE. . .. Voild, the transformation of the operation into heat, which is the reverse of the preceding operations. 

A flat bilayer slab is composed of layers of material A and B, each of thickness L. A component is diffusing through the bilayer in the steady state under conditions where its concentration is maintained at c = Co = constant at one surface and at c = 0 at the other. Its diffusivity is equal to the constants DA and DB in the two layers, respectively. No other components in the system diffuse significantly. 

Since this depth is significantly smaller than the dimensions of the piece of catalyst, and at the same time is much greater than the diameter of individual pores, the phenomenon can be represented schematically by introducing the effective coefficient of diffusion through the porous substance (which depends on the number of the pores and their diameters), and by examining a layer of the catalyst of indefinite depth with a flat surface. 

In early wind tunnel experiments, Chamberlain (1953) liberated elemental 131I vapour and measured deposition on various surfaces. Metal surfaces, and also cellulose-based filter paper, were found to act as perfect sinks for the vapour, deposition being controlled by diffusion through the boundary layer over the surface. In Fig. 6.1, the results for deposition to a flat plate covered with filter paper are compared with the Polhausen equation... 

---