I i i i i v v show that setting i diff i i i m v v

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i i i i i V V ; show that setting i diff i i i m V V , requires 2 , 1 , diff diff m m . (ii) In the case of Fickian diffusion of species 1 into species 2, 1 , diff m is described by the relationship x D m x diff 1 12 , 1 , where ) /( 2 1 1 1 and D 12 = D 21 is the diffusion coefficient for 1 in 2. Show that Fick’s diffusion law in a stationary or moving binary mixture requires also 2 , 1 , diff diff m m so that defining i diff i i i m V V , is consistent both with Fick’s law and the above definition of mass-averaged velocity. 3. A flow is described by the velocity field u = α x , v = - αy , w = 0 where α is a positive constant. The concentration of a species (a pollutant, say) in the flow is given by c(x, y, t) = βx 2 yexp(- γt) for y > 0 where γ , β are constant coefficients. Is the bulk flow
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incompressible? Does the concentration of species c for any particular fluid element change with time? Why or why not? 4. Derive the conservation equations for the combined advection (flow) and diffusion of species i within some bulk mixture in spherical coordinates. Choose a curved element with inner radius r and outer radius r + dr
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Christopher Reinemann
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