Diffusion wall, steady mass through

Many practical mass transfer problems involve the diffusion of a species through a plane-parallel medium that does not involve any homogeneous chemical reactions under one-dimensional steady conditions. Such mass transfer problems are analogous to the steady one-dimensioiial heat conduction problems in a plane wall with no heal generation and can be analyzed similarly. In fact, many of the relations developed in Chapter 3 can be used for mass transfer by replacing temperature by mass (or molar) fraction, thermal conductivity by pD g (or CD ), and heat flux by mass (or molar) flux (Table 14-8). 

Consider a solid plane wall (medium B) of area A, thickness L, and density p. The wall is subjected on both sides to different concentrations of a species A to which it is permeable. The boundary surfaces at.t = 0 and x - L are located within the solid adjacent to the interfaces, and the mass fractions of A at those surfaces are maintained at and 2. respectively, at all times (Fig. 14-19). The mass fraction of species A in the wall varies in the. v-direction only and can be expressed as >v (.t). Therefore, mass transfer through the wall in this case can be modeled as steady and one-dimensional. Here we determine the rate of mass diffusion of species A through the wall using a similar approach to that used in Chapter 3 for heat conduction. 

FIGURE 14-19 Schematic for steady one-dimensional mass diffusion of species A through a plane wall. 

C Consider one-dimeusional mass diffusion of species A through a plane wall. Does Ihe species A coment of the wall change during steady mass diffusion How about during transient mass diffusion ... 

C Consider steady one-dimensional mass diffusion through a wall. Mark these statements as being True or... 

Thus, the time required for the system to attain steady state with the Knudsen mechanism is in the order of 30 seconds. It is emphasised at this point that this is the time required for the pure diffusion mechanism to reach steady state. In the presence of adsorption along the capillary, the time required will be longer because the adsorption process retards the penetration of concentration front through the capillary, that is more mass is supplied for the adsorption onto the capillary wall and hence more time is needed for the attainment of steady state. We will discuss this when we deal with diffusion and adsorption in Chapter 9. 

Mechanisms of Release. In Figure 3, Line A represents release from a reservoir system with a large core relative to the wall mass. This could be a microcapsule releasing by steady-state diffiision through a uniform nonerodible wall. Transport through the polymer membrane (or matrix) occurs by a dissolution-diffusion process, where the active ingredient first dissolves in the polymer and then diffuses across the polymer to the external surface where the concentration is lower. The diflfiision is in accordance with Fick s first law ... 

At steady state conditions Ihe quantity of the diffused component in the parallel iped is constant. That means, the mass transferred by diffesion in it is equal to the mass transferred outside with the moving fluM. Theiefoie, the quantity of the componmit transferred through the walls is ... 

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