Single fuel droplets in quiescent atmospheres

Since Fick s law will be used in many different forms in the ensuing development, it is best to develop those forms so that the later developments need not be interrupted. 

Consider the diffusion of molecules A into an atmosphere of B molecules, that is, a binary system. For a concentration gradient in A molecules alone, future developments can be simplified readily if Fick s law is now written 

When one gas diffuses into another, as A into B, even without the quasi-steady-flow component imposed by the burning, the mass transport of a species, say A, is made up of two components—the normal diffusion component and the component related to the bulk movement established by the diffusion process. This mass transport flow has a velocity Aa and the mass of A transported per unit area is pAAa. The bulk velocity established by the diffusive flow is given by Eq. (6.58). The fraction of that flow is Eq. (6.58) multiplied by the mass fraction of A, pA/p. Thus, 

Defining mA as the mass fraction of A, one obtains the following proper form for the diffusion of species A in terms of mass fraction  

This form is that most commonly used in the conservation equation. 

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