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What do these processes have in common? 1) Hydrogen embrittlement of pressure vessels in nuclear

What do these processes have in common? 1) Hydrogen embrittlement of pressure vessels in nuclear power plants 2) Flow of electrons through conductors 3) Dispersion of pollutants from smoke stacks 4) Transdermal drug delivery 5) Influenza epidemics 6) Chemical reactions

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What do these processes have in common? 1) Hydrogen embrittlement of pressure vessels in nuclear

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  1. What do these processes have in common? 1) Hydrogen embrittlement of pressure vessels in nuclear power plants 2) Flow of electrons through conductors 3) Dispersion of pollutants from smoke stacks 4) Transdermal drug delivery 5) Influenza epidemics 6) Chemical reactions 7) Absorption of oxygen into the bloodstream

  2. They all depend on Diffusion (conduction) What is diffusion? The transport of material--atoms or molecules--by random motion What is conduction? The transport of heat or electrons by random motion.

  3. Place a drop of ink into a glass of water. What happens? Brownian motion causes the ink particles to move erratically in all directions. A concentration of ink particles will disperse. This is NOT diffusion. How can You tell?

  4. Why does random motion cause spreading of a concentration of particles? Because there are more ways for the particles to drift apart than there are for the particles to drift closer together. DIFUS.HTM

  5. In one dimension. . . Pa Pb Nj-1 Nj Nj+1 j j-1 j+1 Net change of particles in box j per time step is ΔNj = Nj-1 Pa - Nj Pa +Nj+1Pb - Nj Pb Δ is a change in time δ is a change in space ΔNj = (Nj+1- Nj) Pb - (Nj - Nj-1)Pa Let δNa = Nj - Nj-1 δNb = Nj+1 - Nj Then ΔNj = Pb δNb - Pa δNa = δ(PδN)

  6. If the P’s are constant, i.e., the probabilities are the same from box to box, then ΔNj= P δ2(N) In three dimensions and in the continuous limit, this equation becomes the diffusion equation where C is concentration and κ is the diffusivity of the medium. or, C is temperature and κ is thermal conductivity

  7. Consider diffusion in only one dimension. Then we have Consider now the condition of “steady-state”, i.e., concentration C no longer changes with time. Then, This can be integrated to

  8. κ1 What can one learn from this equation? Here’s a heat-conducting bar with a fixed temperature C at each end: C(t,0)=0; C(t,100)=100. 2k1 = k2 . κ2 X=0 X=100 C(t,0)=0 C(t,100)=100 At steady-state: Therefore, the ratios of the temperature gradients in each section must equal the inverse ratios of the k’s.

  9. Gradient transport

  10. Diffusion processes Diffusion-2D Heat conduction Conduction-1D Diffusion-limited aggregation Setup: ρgolf ball = 1.15 ρsalt water = 1.13 Conc(sat) =1.20 Dsalt = 1.4 x 10-5 cm2/sec Initial condition: Dry salt at bottom of cylinder. Drop in ball. Add water. What happens? How long does it take?

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