Diffusion as Kinetics

1 Pick s Law Here, we look at the diffusion from a phenomenological point of view. The treatment in Sections 3.2.4 and 3.2.9 needs tracing each particle and therefore is microscopic. 

The rate of transfer is called a flux (also called a flow but it is necessary to avoid confusion from the macroscopic flow of the fluid). The transfer occurs in the absence of the solvent flow as well as in the presence of the solvent flow. The flux is defined as the mass of the solnte that moves across a unit area in a unit time. The direction of the flux is the same as that of the velocity v(r) of the solute molecules. By definition, the flux j(r) is related to v(r) by 

The local concentration variation is represented by the concentration gradient Vc(r). In one dimension, it is dddx (Fig. 3.23). When Vc is sufficiently small, the flux j(r) is proportional to Vc(r) (Fick s law). In the absence of the concentration 

The minus sign is necessary to account for the transfer from the high-c region to the low-c region. In one dimension, the flux is negative when dc/dx 0 as indicated in the figure. We will soon find that the diffusion coefficient defined in this way is equivalent to the one we defined microscopically in Section 3.2.4. The diffusion that follows this equation is called a Fickian diffusion. 

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