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6. (15 pts) A drop of a highly toxic substance (species A) is placed into a standing pool (no flow) of water. It can be
6. (15 pts) A drop of a highly toxic substance (species A) is placed into a standing pool (no flow) of water. It can be approximated that the concentration of A initially at the point of insertion is infinitely large. The toxin diffuses radially through the body of water, diluting with respect to both time and space. Assume no flow in the pool of water, nor induced flow from the addition of A into the pool. A finite amount of A is added, defined as no (in moles), and mass is conserved, hence: 0CA(r,t)dV=n0 a) Let 4DABt serve as a diffusion length scale. Create a dimensionless radius () and dimensionless concentration by combination of variables (). Hint: use dimensional analysis. b) Transform 0CA(r,t)dV=n0 using your variables from (a)
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