Molecular Diffusion Plus Convection and Chemical Reaction

5 MOLECULAR DIFFUSION PLUS CONVECTION AND CHEMICAL REACTION 

In Section 6.2B the flux was defined as the molar flux of A in kg moM/s-m relative to the molar average velocity of the whole or bulk stream. Also, was defined as the molar flux of A relative to stationary coordinates. Fluxes and velocities can also be defined in other ways. Table 7.5-1 lists the different types of fluxes and velocities often used in binary systems. 

Different Forms of Pick s Law for Diffusion Flux Ja = dxjdz = -pD g dwjdz 

The velocity v is the mass average velocity of the stream relative to stationary coordinates and can be obtained by actually weighing the flow for a timed increment. It is related to the velocity and Vg by 

5 Molecular Diffusion Plus Convection and Chemical Reaction 

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Sec. 7.5 Molecular Diffusion Plus Convection and Chemical Reaction... 

Figure 7.5-2. Diffusion of A and heterogeneous reaction at a surface. Sec. 7.5 Molecular Diffusion Plus Convection and Chemical Reaction...

Here, p is mass density and yk th mass fraction, t is time and div the divergence operator v is local mass flow velocity (vector) and jk the it-th molecular diffusion flux vector, added to the term pykV representing the convection of particles Ck by the motion of a material element as a whole. So the instantaneous local change (increase) of the Ck-concentration (mass per unit volume) equals minus the amount that escapes from a volume element (the divergence term) plus the amount produced by chemical reactions. Physically, the balance makes sense if we know how the flux jk depends on the gradients (most simply by Pick s law), and how the rates of possible reactions depend on the local state of the element. If also the latter information is available then the balance takes the form of convective diffusion equation, possibly with chemical reactions. [If we have no information on the reaction rates, the w -terms can be eliminated from Eqs. (C.2) by an algebraic transformation in the same manner as in Chapter 4 indeed, it is sufficient to substitute for W, in (4.3.2) and to define the components of column vector n as follows from (C.2).] Observe finally that we have... 

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